Patent Publication Number: US-9410561-B2

Title: Control device of power transmission device

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a control device of a power transmission device which drives a joint and the like of a robot. 
     2. Description of the Related Art 
     Conventionally, in an industrial robot and the like, a position control (a servo control) is generally performed, in order to drive a joint as a power transmission device between a primary element (a driving element) and a secondary element (a driven element). Further, as a control method for the position control, a technique which adopts a sliding-mode control, for example, in Japanese Patent Application Laid-Open No. H5-134758 (hereinafter referred to as Patent Document 1) is proposed. In this technique, a switching function used for the sliding-mode control is determined by a format of proportional integral control. 
     In the position control of the power transmission device such as the joint, the position of the secondary element (the driven element) may be controlled precisely to a desired position. However it lacks flexibility under various external environments in which a position or a shape of an external object contacting the secondary element, or a disturbance and the like, is difficult to specify or predict beforehand. For example, in a case where the secondary element contacts an unpredicted external object and the like, situations where it becomes difficult to appropriately move the secondary element, or situations where an excessive external force acts on the secondary element, tends to occur. 
     Therefore, in recent years, in order to realize a robot and the like capable of operating flexibly under various external environments, a power transmission device of a structure in which the primary element and the secondary element are coupled by a member capable of deforming elastically (hereinafter sometimes referred to as an elastic deformation member), such as a spring member, and a force applied to the secondary element via the elastic deformation member is controlled to a desired value, has been studied by the present inventors and the like. 
     In an operational control (a power control) of the power transmission device of a structure in which the primary element and the secondary element are coupled via the elastic deformation member, it is generally difficult to perform stable control in which oscillation and the like of a control system does not occur with respect to various condition variation such as a variation in an inertia of a load, by a versatile control method such as a PD control. 
     Therefore, the present inventors had attempted to adopt a method of a sliding-mode control, which has a characteristics of having high robustness with respect to variation of disturbance and the like, in the operational control of the above-mentioned power transmission device including the elastic deformation member. 
     The sliding-mode control is for converging a state amount of a control object to a desired value, on a switching hyperplane that is defined by a switching function (a hyperplane represented by a format of a switching function=0). Therefore, in the sliding-mode control, there is a necessity of appropriately setting the switching hyperplane. 
     The term “hyperplane” is an expression of generalizing a plane in a phase space of a plurality of dimensions. The hyperplane means a straight line in the phase space of two dimensions, and a normal plane in the phase space of three dimensions. 
     As a method of setting the switching hyperplane to be used in the sliding-mode control (specifically, a method of determining the coefficient of the switching function), a method of determining the coefficient of the switching function so as to minimize a predetermined evaluation function by applying, for example, a method of an optimum control, or a method of determining the switching function in a manner as is shown in Patent Document 1, are conceivable. 
     However, in a case of applying the method of the optimum control in order to determine the coefficient of the switching function, there is a necessity of appropriately determining a value of a weight coefficient in the evaluation function. Further, even in the technique disclosed in Patent Document 1, there is a necessity of appropriately determining a value of a gain related to each member of the switching function. 
     A current status is that, in performing the operational control of the power transmission device performing the power transmission between the primary element and the secondary element through the intermediary of the elastic deformation member by the sliding-mode control, a guideline on how to determine the value of the weight coefficient of the evaluation function or the value of each gain in Patent Document 1, or a guideline on efficiently performing such determination, has not been established yet. 
     Therefore, in the method of determining the coefficient of the switching function so as to minimize the predetermined evaluation function, or in the method of determining the switching function in the manner as is shown in Patent Document 1, numerous trial and error must be repeated in order to determine the value of the weight coefficient in the evaluation function or to determined the value of each gain in the technique of Patent Document 1. 
     Consequently, the gradient of the switching hyperplane set in advance by the above mentioned methods may become inappropriate in some operational situation of the power transmission device, and there is a possibility of losing robustness of the control in such operational situation of the power transmission device. 
     SUMMARY OF THE INVENTION 
     The present invention had been made in view of such background, and aims at providing a control device capable of performing an operational control of a power transmission device performing power transmission via an elastic deformation member, utilizing a sliding-mode control, while enabling to stably realize high robustness in a wide operational region of the power transmission device. 
     In order to achieve such object, the control device of the power transmission device of the present invention is a control device of a power transmission device equipped with a primary element which displaces by a driving power of an actuator, and a secondary element coupled to the primary element via an elastic deformation member capable of deforming elastically, and which is provided so as to relatively displace with respect to the primary element by the elastic deformation of the elastic deformation member, and to receive a power transmission from the primary element via the elastic deformation member, the control device controlling a secondary power as a power applied to the secondary element by the power transmission to a desired value, wherein the elastic deformation member is a member configured such that an elastic deformation coefficient expressing a rate of change of a generated elastic force of the elastic deformation member with respect to a change in a deformation amount thereof, becomes constant, wherein the control device comprises: a control input determining unit configured to sequentially determine a control input for controlling the driving force of the actuator, with a control processing of a sliding-mode control using a switching function configured taking a deviation between an observed value and the desired value of the secondary power as a first variable component, and a temporal change rate of the deviation as a second variable component, so as to converge the first variable component on a switching hyperplane defined by the switching function to zero; and wherein a gradient of the switching hyperplane in a phase plane taking the first variable component and the second variable component as two coordinate axis components is set, so that a time constant of convergence of a value of the first variable component on the switching hyperplane defined by the gradient of the switching hyperplane to zero, becomes equal to or larger than a specific time constant, the specific time constant being a time constant realized in a case supposing that the value of the first variable component is changed stepwise from zero to a first permissible limit value, the first permissible limit value being a preliminarily set permissible limit value of a magnitude of the value of the first variable component, and also the convergence of the value of the first variable component to zero is performed so that a displacement acceleration of the primary element by the driving force of the actuator becomes a preliminarily set permissible limit value of the displacement acceleration (a first aspect of the invention). 
     In the present invention, “the observed value” of an arbitral state amount, such as the secondary power, means a value which could be regarded as coinciding with an actual value of the state amount. For example, a detected value of an actual value of the state amount by an arbitral sensor, or an estimated value estimated from a detected value of an actual value of one or more of other state amounts having a certain correlativity with the state amount, on the basis of the correlativity, may be listed as “the observed value”. 
     Further, “the displacement” of the primary element or the secondary element may be either of a rotational displacement and a translational displacement. 
     The term the elastic deformation coefficient being “constant” does not mean that it is strictly constant, but means that the elastic deformation coefficient is maintained constant or approximately constant within a practical deformation range of the elastic deformation member in the power transmission device. Further, the elastic deformation coefficient has a meaning as the one corresponding to a so-called spring constant. 
     In the present invention, in a case it is supposed that the value of the first variable component is changed stepwise from zero to a certain value equal to or less than the first permissible limit value, in a case where the value of the first variable component is changed from zero to the first permissible limit value, the displacement amount of the primary element with respect to the secondary element, and thus the deformation amount of the elastic deformation member becomes maximum. 
     In this case, the displacement of the primary element with respect to the secondary element (and thus the deformation of the elastic deformation member) is limited to the displacement at the displacement acceleration equal to or less than the permissible limit value. Therefore, the time constant for convergence of the value of the first variable component to zero cannot become smaller than the specific time constant. 
     As such, in the first aspect of the invention, the gradient of the switching hyperplane is set such that the time constant for the convergence of the value of the first variable component to zero on the switching hyperplane defined by the gradient of the switching hyperplane becomes equal to or larger than the specific time constant. 
     Further, in the first aspect of the invention, the gradient of the switching hyperplane is determined as is explained above, so that the control input determining unit may determine the control input by the control processing of the sliding-mode control, so as to stably perform to control the secondary power to the desired value, with high robustness in a wide operational region of the power transmission device when controlling the operation of the power transmission device. 
     Therefore, according to the first aspect of the invention, the operational control of the power transmission device which performs power transmission via the elastic deformation member may be performed utilizing the sliding-mode control, while stably realizing high robustness in a wide operational region of the power transmission device. 
     In the first aspect of the invention, it is preferable that the specific time constant is a time constant calculated as a value proportional to an inverse value of a square root of a value of the elastic deformation coefficient, from the first permissible limit value, the permissible limit value of the displacement acceleration of the primary element, and the value of the elastic deformation coefficient of the elastic deformation member (a second aspect of the invention). 
     According to the second aspect of the invention, it becomes possible to appropriately specify the specific time constant matching the value of the elastic deformation coefficient of the elastic deformation member, so that the reliability of the setting of the gradient of the switching hyperplane may be improved. 
     Moreover, the control device of the power transmission device of the present invention is a control device of a power transmission device equipped with a primary element which displaces by a driving power of an actuator, and a secondary element coupled to the primary element via an elastic deformation member capable of deforming elastically, and which is provided so as to relatively displace with respect to the primary element by the elastic deformation of the elastic deformation member, and to receive a power transmission from the primary element via the elastic deformation member, the control device controlling a secondary power as a power applied to the secondary element by the power transmission to a desired value, wherein the elastic deformation member is a member configured such that an elastic deformation coefficient expressing a rate of change of a generated elastic force of the elastic deformation member with respect to a change in a deformation amount thereof, capable of being variably controlled; wherein the control device comprises: a control input determining unit configured to sequentially determine a control input for controlling the driving force of the actuator, with a control processing of a sliding-mode control using a switching function configured taking a deviation between an observed value and the desired value of the secondary power as a first variable component, and a temporal change rate of the deviation as a second variable component, so as to converge the first variable component on a switching hyperplane defined by the switching function to zero; and a switching hyperplane variable setting unit which sequentially determines a gradient of the switching hyperplane used for the control processing of the sliding-mode control for determining the control input, according to a control value of an actual elastic deformation coefficient of the elastic deformation member, using map data or a predetermined arithmetic expression preliminarily generated so as to represent a relationship between a value of the elastic deformation coefficient of the elastic deformation member and the gradient of the switching hyperplane; and wherein the map data or the predetermined arithmetic expression is generated so that a time constant of convergence of a value of the first variable component to zero on the switching hyperplane defined by the gradient of the switching hyperplane determined by the map data or the predetermined arithmetic expression according to an arbitrary control value of the elastic deformation coefficient of the elastic deformation member, becomes equal to or larger than a specific time constant, the specific time constant being a time constant realized in a case supposing that the value of the first variable component is changed stepwise from zero to a first permissible limit value, the first permissible limit value being a preliminarily set permissible limit value of a magnitude of the value of the first variable component, and also the convergence of the value of the first variable component to zero is performed so that a displacement acceleration of the primary element by the driving force of the actuator becomes a preliminarily set permissible limit value of the displacement acceleration, in a state the elastic deformation coefficient of the elastic deformation member is maintained to the control value (a third aspect of the invention). 
     According to the third aspect of the invention, the gradient of the switching hyperplane determined by the map data or the predetermined arithmetic expression according to the arbitrary control value of the elastic deformation coefficient of the elastic deformation member by the switching hyperplane variable setting unit, is determined such that the time constant of the convergence of the value of the first variable component to zero on the switching hyperplane defined by the gradient of the switching hyperplane, becomes equal to or larger than the specific time constant corresponding to the value of the elastic deformation coefficient indicated by the control value. 
     Therefore, according to the third aspect of the invention, the control input determining unit is capable of determining the control input so as to stably perform to control the secondary power to the desired value with high robustness in a wide operational region of the power transmission device by the control processing of the sliding-mode control regardless of the control state of the elastic deformation coefficient of the elastic deformation member when controlling the operation of the power transmission device. 
     As such, according to the third aspect of the invention, it is possible to stably realize high robustness in a wide operational region of the power transmission device while performing the operational control of the power transmission device which performs power transmission via the elastic deformation member capable of variably controlling the elastic deformation coefficient by sliding-mode control regardless of the control state of the elastic deformation coefficient. 
     In the third aspect of the invention, it is preferable that in a case where the switching hyperplane variable setting unit is configured to determine the gradient of the switching hyperplane by using the map data composed of a set of a plurality of representative values of the elastic deformation coefficient preliminarily defined within a variable range of the elastic deformation coefficient of the elastic deformation member, and the gradient of the switching hyperplane corresponding to each of the representative values, the gradient of the switching hyperplane corresponding to arbitrary one representative value among a plurality of the representative values of the elastic deformation coefficient of the elastic deformation member in the map data is set such that the time constant of the convergence of the value of the first variable component on the switching hyperplane defined by the gradient of the switching hyperplane to zero becomes equal to or larger than the specific time constant calculated as a value proportional to an inverse value of a square root of the one representative value from the first permissible limit value, the permissible limit value of the displacement acceleration of the primary element, and the one representative value (a fourth aspect of the invention). 
     According to the fourth aspect of the invention, it is able to appropriately specify the specific time constant matching each representative value of the elastic deformation coefficient of the elastic deformation member. Therefore, it is able to determine the gradient of the switching hyperplane for each representative value to a preferred gradient for stabling performing to control the secondary power to the desired value with high robustness. 
     Thus, it is able to increase the reliability of the gradient of the switching hyperplane determined using the map data by the switching hyperplane variable setting unit when controlling the operation of the power transmission device. 
     In the third aspect of the invention, it is preferable that in a case where the switching hyperplane variable setting unit is configured to determine the gradient of the switching hyperplane by using the predetermined arithmetic expression, the arithmetic expression is set such that the time constant defined by the gradient of the switching hyperplane calculated by the arithmetic expression, becomes a value equal to or larger than a value proportional to an inverse value of a square root of the value of the elastic deformation coefficient (a fifth aspect of the invention). 
     According to the fifth aspect of the invention, it is able to determine the gradient of the switching hyperplane corresponding to the value of the elastic deformation coefficient such that the time constant corresponding to the gradient becomes equal to or larger than the specific time constant corresponding to the value of the elastic deformation coefficient by using the predetermined arithmetic expression in an arbitrary control state of the elastic deformation coefficient of the elastic deformation member when controlling the operation of the power transmission device, with high reliability. 
     In the first or the second aspect of the invention, it is preferable that the control device further comprises an observer which sequentially calculates an estimated value of the first variable component and an estimated value of the second variable component, that are obtained by reducing an influence of disturbance from an observed value of the first variable component calculated from the observed value of the secondary power and the desired value of the secondary power, and an observed value of the second variable component calculated as a temporal change rate of the observed value of the first variable component, and the control input determining unit is configured to calculate a value of the switching function using the estimated value of the first variable component and the estimated value of the second variable component calculated by the observer, in place of the observed value of the first variable component and the observed value of the second variable component, and to sequentially generate the control input by the control processing of the sliding-mode control using the value of the switching function (a sixth aspect of the invention). This is also similar in the third through the fifth aspect of the invention (a seventh aspect of the invention). 
     According to the sixth or the seventh aspect of the invention, the influence of the disturbance is suppressed, by calculating the value of the switching function using the estimated value of the first variable component and the estimated value of the second variable component calculated by the observer, and by sequentially generating the control input by the control processing of the sliding-mode control using the value of the switching function. 
     Therefore, the stability of the control input sequentially determined by the control input determining unit is improved. Consequently, it becomes possible to further improve the robustness of the control of the secondary power. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view showing a system configuration according to a first embodiment of the present invention; 
         FIG. 2  is a view showing a switching hyperplane of a sliding-mode control; 
         FIG. 3  is a graph for explaining a determination processing of a gradient of the switching hyperplane; 
         FIG. 4A  through  FIG. 4C  are graphs for explaining the determination processing of the gradient of the switching hyperplane; 
         FIG. 5A  is an enlarged view of portion A in  FIG. 3 , and  FIG. 5B  is an enlarged view of portion B in  FIG. 3 ; 
         FIG. 6  is a block diagram showing a processing of a control input determining unit of a control device shown in  FIG. 1 ; 
         FIG. 7  is a block diagram showing a processing of the control input determining unit according to a second embodiment of the present invention; 
         FIG. 8  is a view showing a system configuration in a third embodiment of the present invention; 
         FIG. 9  is a view showing a configuration of a rigidity variable mechanism shown in  FIG. 8 ; 
         FIG. 10  is a view showing a configuration of the rigidity variable mechanism shown in  FIG. 8 ; 
         FIG. 11  is a block diagram showing a processing of the control input determining unit of the control device shown in  FIG. 8 ; 
         FIG. 12  is a block diagram showing a processing of the control input determining unit in a fourth embodiment of the present invention; and 
         FIG. 13  is a perspective view showing a configuration of a substantial part of the power transmission device in a modified form. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     First Embodiment 
     A first embodiment of the present invention will be explained below with reference to  FIG. 1  through  FIG. 6 . 
     As is shown in  FIG. 1 , a power transmission device  1  of the present embodiment is equipped with a drive pulley  2  as a primary element, a driven pulley  3  as a secondary element, a wire  4  which performs rotational transmission between the pulleys  2 ,  3 , an electric motor  5  as an actuator for imparting a rotational driving force to the drive pulley  2 , and a load member  6  fixed to the driven pulley  3  so as to rotate integrally with the driven pulley  3 . 
     In  FIG. 1 , the load member  6  is described as an integrated structure. However, it is not limited to an integrated structure. For example, the load member  6  may be the one in which a plurality of members are coupled by joints and the like (for example, a link mechanism having a plurality of joints, and the like). 
     The drive pulley  2  is connected to an output shaft  5   a  of the motor  5  via a reducer  7 . Further, the drive pulley  2  rotates by a rotational driving force (torque) applied from the output shaft  5   a  of the electric motor  5  via the reducer  7 , in conjunction with the rotation of the output shaft  5   a  of the electric motor  5 . 
     The reducer  7  may be of an arbitral structure. For example, a reducer configured from a harmonic drive (registered trademark) or from a plurality of gears may be adopted as the reducer  7 . Alternatively, the reducer  7  may be equipped with a mechanism for converting a direct action to a rotational movement. In this case, as the actuator, for example, a direct acting actuator configured from an electric motor and a ball screw, or an electrically-operated linear motor and the like, may be adopted. 
     Further, in  FIG. 1 , the electric motor  5  and the drive pulley  2  are arranged to have coaxial core. However, rotational shaft centers thereof may not necessarily be coaxial. 
     The driven pulley  3  is provided laterally to the side of the drive pulley  2 , so that a rotational shaft center thereof becomes parallel to a rotational shaft center of the drive pulley  2 . The pulleys  2 ,  3  are coupled at outer peripheral portions thereof via the wire  4 . 
     More specifically, the wire  4  is stretched so that one of both end portion is fixed to the drive pulley  2  and the other is fixed to the driven pulley  3 , and so as to extend in a tangential direction of the pulleys  2 ,  3 . As such, the rotational transmission between the drive pulley  2  and the driven pulley  3  is performed by a tensile force of the wire  4 . 
     The wire  4  may be respectively provided, when viewing in a rotational shaft center direction of the drive pulley  2  and the driven pulley  3 , to both sides in a direction orthogonal to a direction of an interval between the pulleys  2 ,  3 . 
     Further, the wire  4  may be an endless member wound around the drive pulley  2  and the driven pulley  3 . 
     The wire  4  is configured from an elastic deformation member (a member capable of deforming elastically). Therefore, the transmission of the rotational driving force (torque) from the drive pulley  2  to the driven pulley  3  is performed via an elastic force (in this case, tensile force) generated by the elastic deformation (in this case, expansion and contradiction) of the wire  4 . Further, accompanying the elastic deformation of the wire  4 , an angular difference between a rotational angle θin of the drive pulley  2  and a rotational angle Clout of the driven pulley  3  (=θin−θout, hereinafter referred to as the between-pulley rotational angular difference) is generated. The between-pulley rotational angular difference corresponds to a deformation amount of the wire  4 . 
     In this case, the torque applied to the driven pulley  3  by the transmission of the rotational driving force from the drive pulley  2  to the driven pulley  3  (hereinafter referred to as a secondary torque τ) is proportional to (or is approximately proportional to) the between-pulley rotational angular difference, as is shown in following expression (1).
 
τ= Ksp ·(θin−θout)  (1)
 
     In the expression (1), Ksp is an elastic deformation coefficient indicating a level of rigidity of the wire  4 , and in the present embodiment, means a rate of change of the secondary torque τ (stated otherwise, a generated elastic force of the wire  4 ) with respect to a change of the between-pulley rotational angular difference (stated otherwise, the deformation amount of the wire  4 ) (a change amount of the secondary torque τ per unit change amount of the between-pulley rotational angular difference). 
     In the present embodiment, the wire  4  is configured so that the elastic deformation coefficient Ksp in the expression (1) is maintained constant (or substantially constant). The elastic deformation coefficient Ksp of the wire  4  should only be constant (or substantially constant) within a range of practical values of the secondary torque τ or the between-pulley rotational angular difference of the power transmission device  1 , and the value of the elastic deformation coefficient Ksp may not necessarily be constant outside the range. 
     The above is a mechanistic configuration of the power transmission device  1  of the present embodiment. 
     The present embodiment is equipped with, as a configuration for an operational control of the power transmission device  1 , a control device  10 , and angle detectors  11 ,  12  respectively detecting the rotational angle θin of the drive pulley  2  and the rotational angle θout of the driven pulley  3 . 
     The angle detectors  11 ,  12  are, for example, configured from a rotary encoder, and are respectively provided opposing the drive pulley  2  and the driven pulley  3 . The angle detectors  11 ,  12  may be configured from angle sensors other than the rotary encoder, such as a potentiometer. 
     The control device  10  is configured from an electronic circuit unit including a CPU, a RAM, a ROM, an interface circuit and the like. The control device  10  is input with output signals (detection signals) of the angle detectors  11 ,  12 . Further, to the control device  10 , a desired value τ_cmd of the secondary torque τ (hereinafter referred to as a desired secondary torque τ_cmd) is sequentially input from other control device or servers outside. 
     The desired secondary torque τ_cmd is a desired value for performing desired operation of the load member  6 . The desired secondary torque τ_cmd may be sequentially determined at the control device  10 . 
     By executing a predetermined program processing using the input detecting signals and the desired secondary torque τ_cmd, the control device  10  is configured to sequentially decide a control input for controlling an operation of the electric motor  5 . Further, the control device  10  is configured to control an operation of the electric motor  5  according to the control input. 
     In this case, the control device  10  is equipped with, as a function realized by a program processing (a function realized by a software) or a main function realized by a hardware configuration, a control input determining unit  13  which sequentially determines the control input so as to make the actual secondary torque τ (an observed value) follow the desired secondary torque τ_cmd, and a motor control unit  14  which controls an energization current (and consequently an output torque) of the electric motor  5  according to the control input via a motor drive circuit not shown. 
     The control input is, in the present embodiment, for example a desired torque (a desired value of the output torque) of the electric motor  5 . However, the control input may only be the one capable of defining the desired torque of the electric motor  5 . Therefore, the control input may be other than the desired torque. For example, as the control input, a desired value of the torque imparted to the drive pulley  2  itself from the electric motor  5  side, or a desired value of the energization current of the electric motor  5 , or the like may be used. 
     The control input determining unit  13  is configured to determine the control input for making the actual secondary torque τ (the observed value) follow the desired secondary torque τ_cmd, by a control processing of a sliding-mode control. 
     Basic matters with respect to a control processing of the sliding mode will be explained. 
     A behavior of the power transmission device  1  as a system of a controlled object in the present embodiment is modeled in a discrete system by a state equation of following expression (2). 
     
       
         
           
             
               
                 
                   
                     
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     Here, θin is the rotational angle of the drive pulley  2 , θout is the rotational angle of the driven pulley  3 , Min is a temporal change rate of θin (that is, a rotational angular velocity of the drive pulley  2 ), dθout is a temporal change rate of θout (that is, a rotational angular velocity of the driven pulley  3 ), DT is a control processing cycle, Ksp is the elastic deformation coefficient of the wire  4 , Iin is an inertia of the drive pulley  2  side (an input side inertia), Iout is an inertia of the driven pulley  3  side (an output side inertia), and u is the input torque of the drive pulley  2  side (for example, the output torque of the electric motor  5 ). Further, suffixes with brackets, n, n−1, are numbers representing time of the discrete system. 
     On the other hand, by the above-mentioned expression (1), following expressions (3a), (3b) stand with respect to the secondary torque τ and a temporal change rate dτ thereof (hereinafter referred to as a secondary torque change speed dτ).
 
τ( n )= Ksp ·(θin( n )−θout( n ))  (3a)
 
 d τ( n )= Ksp ·( d θin( n )− d θout( n ))  (3b)
 
     When simplifying the above-mentioned expression (2) using these expressions (3a), (3b), and a state equation of following expression (4) is obtained as a model expressing a behavior with respect to τ, dτ in the power transmission device  1  of the present embodiment. 
     
       
         
           
             
               
                 
                   
                     
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     In the sliding mode control in the present embodiment, the control processing for determining the control input is established, according to the state equation (the model) of this expression (4). 
     More specifically, in the present embodiment, as a state variable of the control object of the sliding-mode control, as is represented by following expression (5), a state variable X (a column vector of two-rows and one-column) configured taking a secondary torque deviation τ_err which is a deviation between the actual secondary torque τ (the observed value) and the desired secondary torque τ_cmd, and a secondary torque deviation velocity dτ_err which is a temporal change rate (a differential value) of the deviation τ_err, as two components thereof. In the expression (5), a superscript suffix “T” means transposition.
 
 X=[τ _err, dτ _err] T   (5)
 
     where τ_err=τ−τ_cmd, and dτ_err=temporal change rate (differential value) of τ_err 
     In this case, a desired torque τm_cmd of the electric motor  5  as the control input of the sliding-mode control (a new desired torque determined in each control process cycle) may be determined, for example by following expression (6), using A and B defined in a where clause in the above-mentioned expression (4) and a switching function σ represented by following expression (7).
 
τ m _cmd( n )=−( S·B ) −1 ·( S·A˜X ( n )+ Ksld ·(σ( n )/(|σ( n )|+δ)))   (6)
 
σ( n )= S·X ( n )= s 1·τerr( n )+ s 2 ·dτ _err( n )  (7)
 
     where S=[s1, s2] (:vector of two-rows one-column) 
     These expressions (6), (7) are basic expressions for determining the desired torque τm_cmd of the electric motor  5  as the control input in the present embodiment. 
     In this case, each component of A, B necessary for calculation of the right side of the expression (6) is a predetermined value preliminarily set (a value of constant) based on defining expression in a where clause of the expression (4). Further, each component s1, s2 of S (coefficient component constituting the switching function σ) is a predetermined value (a value of constant) preliminarily set as is explained later. 
     Explanation will be given on the technical meaning of the expressions (6) and (7). The first column on the right side of the expression (6) means a control input component which functions so as to converge τ_err and dτ_err to zero, in a state where a pair of values of τ_err and dτ_err exists on a switching hyperplane. 
     The switching hyperplane is represented by a formula σ=0. Therefore, a gradient of the switching hyperplane σ=0 (in the present case, straight line) in a phase plane taking τ_err and dτ_err as two coordinate axis components is defined by a proportion of each components s1, s2 of S. 
     For example, as is shown in  FIG. 2 , in a case of assuming a phase plane taking the coordinate axis of the secondary torque deviation velocity dτ_err as an axis of ordinate, and the coordinate axis of the secondary torque deviation τ_err as an axis of abscissas, the gradient of the switching hyperplane σ=0 (straight line) in the phase plane becomes −s1/s2. In a case where a phase plane taking the coordinate axis of the secondary torque deviation velocity dτ_err as the axis of abscissas and the coordinate axis of the secondary torque deviation τ_err as the axis of ordinate is assumed, the gradient of the switching hyperplane σ=0 in the phase plane becomes −s2/s1. 
     On the switching hyperplane σ=0, dτ_err=(−s1/s2)·τ_err, so that when (−s1/s2) is set to a negative value, then τ_err on the switching hyperplane σ=0 converges to zero. Further, in this case, a time constant Tc of convergent response of τ_err on the switching hyperplane σ=0 is given by following expression (8).
 
 Tc=s 2 /s 1  (8)
 
     As such, the gradient of the switching hyperplane σ=0, or the time constant Tc of the convergent response of τ_err on the switching hyperplane σ=0, is defined by a proportion of the coefficient components s1, s2. 
     To supplement, in a case of assuming a phase plane taking the coordinate axis of the secondary torque deviation velocity dτ_err as the axis of ordinate, and the coordinate axis of the secondary torque deviation τ_err as the axis of abscissas, the gradient of the switching hyperplane σ=0 in the phase plane becomes −s1/s2, so that the relationship between the gradient and the time constant Tc becomes gradient=−1/Tc. 
     On the other hand, in a case of assuming a phase plane taking the coordinate axis of the secondary torque deviation velocity dτ_err as the axis of abscissas, and the coordinate axis of the secondary torque deviation τ_err as the axis of ordinate, the gradient of the switching hyperplane σ=0 in the phase plane becomes −s2/s1, so that the relationship between the gradient and the time constant Tc becomes gradient=−Tc. 
     In the present embodiment, the gradient of the switching hyperplane σ=0 is determined preliminarily as is explained later. Therefore, the values of the coefficient components s1, s2 necessary for the calculation of the expression (7) are preliminarily set according to the gradient. 
     In this case, one of the values of s1, s2 may be a value of constant, and for example, s1=1 (or s2=1). In this case, by determining the gradient of the switching hyperplane σ=0, the value of the coefficient component s2 (or the coefficient component s1) is determined unambiguously. 
     The above-mentioned time constant Tc is determined unambiguously according to the gradient of the switching hyperplane σ=0. Therefore, determining the gradient of the switching hyperplane σ=0 is equivalent to determining the above-mentioned time constant Tc. 
     The second column on the right side of the expression (6) means a control input component functioning to converge the value of the switching function σ to zero (stated otherwise, to converge a set of values of τ_err and dτ_err on the switching hyperplane σ=0). Further, Ksld and δ respectively are parameters defining a convergence characteristics of the value of the switching function σ. 
     In this case, δ is a predetermined value (a value of constant) preliminarily set according to experiments and the like. 
     Further, the value of Ksld is determined according to a predetermined value (a steady value) or a value of a switching function, for example by a following guideline. 
     That is, in order to converge the value of the switching function σ to zero, a differential value (temporal change rate) of a Liapunov function σ 2  of σ must be a negative value. 
     This necessary condition is equivalent to a condition of satisfying (σ(n)) 2 −(σ(n−1)) 2 &lt;0 in the discrete system. And, from this condition and from the expressions (6), (7), a condition of following expression (9) related to Ksld is obtained.
 
| Ksld|&lt;|σ ( n )|+δ  (9)
 
     Therefore, the value of Ksld only needs to be set so as to satisfy the condition of the expression (9). 
     In the present embodiment, the value of Ksld is determined variably according to the value of σ, so that a magnitude of Ksld becomes larger, as an absolute value of the switching function σ in each control processing cycle becomes larger. 
     For example, Ksld is determined so as to become a value proportional to |σ(n)|, in each control processing cycle, as is shown in following expression (10).
 
 Ksld =(1 /K 0)·|σ( n )|  (10)
 
     K0 in expression (10) is a value of constant preliminarily set so as to satisfy the condition of expression (9), within a range of actual values that σ(n) could take (for example, an integer of 3 or more). 
     The value of Ksld may be a steady value. Further, the value of Ksld may be set so that |Ksld|&lt;δ holds. 
     Next, explanation will be given on an advance preparation process for determining the values of the coefficient components s1, s2 of the above-mentioned switching function σ. In the present embodiment, the advance preparation process is performed according to a following procedure. 
     (Procedure 1) First, by an arbitrary control method (for example, PD control and the like), an experiment (or a simulation) of controlling the secondary torque τ of the power transmission device  1  to converge from various arbitral initial states of the power transmission device  1  to various arbitral desired values (desired values changed stepwise) is performed. 
     In the experiment, the output torque of the electric motor  5  is operated so as to converge a deviation between the desired value of the secondary torque τ and the observed value of the actual value to zero, by a versatile control law such as a PD control law, according to the deviation. In this case, the observed value of the actual value of the secondary torque τ may be calculated on the basis of the above-mentioned expression (1), for example from a detected value of the between-pulley rotational angular difference of the power transmission device  1 . Alternatively, the actual value of the secondary torque τ may be detected using an arbitral torque sensor. Further, the operational control of the electric motor  5  may be performed using an arbitral computer and the like. 
     Further, a transition (temporal change) of a set of the values of the secondary torque deviation τ_err and the value of the secondary torque deviation velocity dτ_err in each experiment of the above-mentioned convergence control is measured. Further, by plotting the measured data on the phase plane taking τ_err and dτ_err as the two coordinate axis components, a response characteristics data indicating a trajectory of the transition of the set of values of τ_err and dτ_err is created. 
     As is explained above, a plurality of the response characteristics data in which conditions such as the initial state and the desired value of the secondary torque τ are varied, are created. 
       FIG. 3  shows a few representative examples of the response characteristics data created as explained above. Each of the trajectories allotted with references a1 through a6 in  FIG. 3  shows an example of the response characteristics data. 
     (Procedure 2) Subsequently, from a plurality of the response characteristics data created as explained above, a response characteristics data satisfying a predetermined requirement is selected as a specific response characteristics data for determining the gradient of the switching hyperplane σ=0 in the phase plane (hereinafter referred to as a response characteristics data for determining gradient). 
     The response characteristics data for determining gradient selected herein is a response characteristics data satisfying a selection requirement 1 and a selection requirement 2 described below. The selection requirement 1 is a requirement that a magnitude (an absolute value) of the value of the secondary torque deviation τ_err on a trajectory indicated by the response characteristics data for determining gradient becomes a magnitude equal to or smaller than a predetermined first permissible limit value τ_err_lim, and also a magnitude (an absolute value) of the value of the secondary torque deviation velocity dτ_err on the trajectory becomes a magnitude equal to or smaller than a predetermined secondary permissible limit value dτ_err_lim. 
     The selection requirement 2 is a requirement that, in a phase plane taking τ_err and dτ_err as the two coordinate axis components, the trajectory intersects either of a line in which a magnitude (an absolute value) of the value of τ_err coincides with a preliminarily set first set value τ_err_a (a line indicated by a formula τ_err=+τ_err_a or τ_err=−τ_err_a in the phase plane), or a line in which a magnitude (an absolute value) of the value of dτ_err coincides with a preliminarily set second set value dτ_err_a (a line represented by a formula dτ_err=+dτ_err_a or dτ_err=−dτ_err_a in the phase plane). 
     The selection requirement 1 is, stated otherwise, a requirement that the value of τ_err and dτ_err in an arbitral point on the trajectory indicated by the response characteristics data satisfy the condition that −τ_err_lim≦τ_err≦+τ_err_lim and also −τ_err_lim≦dτ_err≦dτ_err_lim. 
     Further, the above-mentioned selection requirement 2 is, stated otherwise, a requirement that at least one point that satisfies |τ_err|=|τ_err_a| or |dτ_err|=|dτ_err_a| exists on the trajectory indicated by the response characteristics data. 
     In the procedure 2, specifically, first, the first permissible limit value τ_err_lim (&gt;0) and the secondary permissible limit value dτ_err_lim (&gt;0) related to the selection requirement 1 are determined (procedure 2-1). 
     The first permissible limit value τ_err_lim means the permissible limit value of the magnitude of the value of the secondary torque deviation τ_err, and the secondary permissible limit value dτ_err_lim means the permissible limit value of the magnitude of the value of the secondary torque deviation velocity dτ_err. 
     If the magnitude of τ_err is too large, when it is attempted to control the output torque of the electric motor  5  to converge τ_err to zero, there are cases where the rotational angular velocity or the rotational angular acceleration of the drive pulley  2  (the primary element) exceeds respective permissible limit values. The first permissible limit value τ_err_lim is a limit value of the magnitude of τ_err so as to avoid the rotational angular velocity and the rotational angular acceleration of the drive pulley  2  (the primary element) from exceeding respective permissible limit values. 
     The respective permissible limit values of the rotational angular velocity and the rotational angular acceleration of the drive pulley  2  are values preliminary set by design, from capacity of the electric motor  5 , or under conditions of machine restrictions of the power transmission device  1  and the like. The value may include an allowance of a certain margin with respect to the actual permissible limit value. 
     In the present embodiment, the first permissible limit value τ_err_lim is determined as follows, according to a permissible limit value ω1_lim of the rotational angular velocity of the drive pulley  2  (hereinafter referred to as a primary velocity limit value ω1_lim), a permissible limit value dω1_lim of the rotational angular acceleration of the drive pulley  2  (hereinafter referred to as a primary acceleration limit value dω1_lim), and the elastic deformation coefficient Ksp of the wire  4 . 
     A change amount of the between-pulley rotational angular difference necessary for converging the secondary torque deviation τ_err from an initial state in which the value thereof is τ_err_0 (≠0) to zero is τ_err_0/Ksp. 
     As is shown in  FIG. 4C , a time necessary for changing the between-pulley rotational angular difference by τ_err_0/Ksp is represented by ta. And, for example as is shown in  FIG. 4A , a case is assumed in which the drive pulley  2  is made to relatively rotate with respect to the driven pulley  3  so as to accelerate the drive pulley  2  at the rotational angular acceleration in the positive direction having the magnitude of the primary acceleration limit value dω1_lim, in the first half of the time ta (a period from 0 to ta/2), and in which the drive pulley  2  is made to relatively rotate with respect to the driven pulley  3  so as to decelerate the drive pulley  2  at the rotational angular acceleration in a negative direction having the magnitude of the primary acceleration limit value dω1_lim, in the latter half of the time ta (a period from ta/2 to ta). 
     Stated otherwise, a case is assumed in which the acceleration and deceleration of the rotational angular velocity of the drive pulley  2  is sequentially performed at the rotational angular acceleration of the magnitude of the primary acceleration limit value dω1_lim, so as to relatively rotate the drive pulley  2  by the rotational angle of τ_err_0/Ksp with respect to the driven pulley  3 , and the relative rotation of the drive pulley  2  with respect to the driven pulley  3  is stopped when the relative rotational angle of the drive pulley  2  with respect to the driven pulley  3  reached τ_err_0/Ksp. 
     In this case, the relationship between τ_err_0/Ksp and dω1_lim and ta is represented by following expression (11).
 
(¼)· dω 1_lim· ta   2 =τ_err_0 /Ksp   (11)
 
     A maximum rotational angular velocity of the drive pulley  2  in this case is, as is shown in  FIG. 4B , (½)·dω1_lim·ta, so that it is necessary for a condition of following expression (12) to be satisfied.
 
(½)· dω 1_lim· ta≦ω 1_lim  (12)
 
     From the above-mentioned expression (11) and expression (12), a condition of following expression (13) with respect to a magnitude (an absolute value) of τ_err_0 is obtained.
 
|τ_err_0|≦(ω1_lim 2   /dω 1_lim)· Ksp   (13)
 
     As such, in the present embodiment, the first permissible limit value τ_err_lim, which is the permissible limit value of the magnitude of the value of the secondary torque deviation τ_err, is determined by following expression (14).
 
τ_err_lim=(ω1_lim 2   /dω 1_lim)· Ksp   (14)
 
     τ_err_lim thus determined becomes a large value as the elastic deformation coefficient Ksp becomes larger. τ_err_lim may be a value slightly smaller than the value determined by expression (14). 
     Further, if the magnitude of the secondary torque deviation velocity dτ_err is too large, when it is attempted to control the output torque of the electric motor  5  so as to converge the secondary torque deviation τ_err to zero, oscillation of a power transmission system from the electric motor  5  to the driven pulley  3  tends to generate, by a resonance phenomenon induced by the natural oscillation of the power transmission system. The secondary permissible limit value dτ_err_lim is a limit value of the magnitude of dτ_err in order to avoid generation of such oscillation. 
     In this case, when a natural frequency (a natural frequency in a dimension of an angular frequency) of the power transmission system from the electric motor  5  to the driven pulley  3  is set as ωvb, the secondary torque change speed dτ_vb when the rotational angle of the drive pulley  2  in the natural frequency ωvb oscillates relatively with respect to the driven pulley  3  is obtained by following expression (15).
 
 dτ _ vb=Ksp·ωvb   (15)
 
     Therefore, in the present embodiment, the secondary permissible limit value dτ_err_lim, which is the permissible limit value of the magnitude of the value of the secondary torque deviation velocity dτ_err, is determined by following expression (16).
 
 dτ _err_lim=Ksp·ωvb  (16)
 
     dτ_err_lim determined as such becomes a larger value as the elastic deformation coefficient Ksp becomes larger. 
     In this case, the value of the natural frequency ωvb may be specified, for example, based on experiments and measurements. Alternatively, the value of ωvb may be determined approximately by following expression (17).
 
ω vb =sqrt(( Ksp /( I in+ I out))  (17)
 
     In the expression (17), sqrt( ) is a square root function. Further, Iin is an inertia of a system on the drive pulley  2  side (in this case, a system configured by the drive pulley  2 , the reducer  7 , and the electric motor  5 ), and Iout is an inertia of a system on the driven pulley  3  side (in this case, a system configured by the driven pulley  3  and the load member  6 ), of the power transmission device  1 . 
     The secondary permissible limit value dτ_err_lim may be determined to a value slightly smaller than the value determined by the expression (16). 
     In the phase plane of  FIG. 3 , examples of lines on a positive side and a negative side (lines respectively represented by formula τ_err=+τ_err_lim and formula τ_err=−τ_err_lim) that are defined by the first permissible limit value τ_err_lim are lines L1p, L1n, and examples of lines on a positive side and a negative side (lines respectively represented by formula dτ_err=+dτ_err_lim and formula dτ_err=−dτ_err_lim) that are defined by the secondary permissible limit value dτ_err_lim are lines L2p, L2n. 
     In the procedure 2, subsequently, the first set value τ_err_a (&gt;0) and the second set value dτ_err_a (&gt;0) related to the selection requirement 2 are determined (procedure 2-2) 
     The first set value τ_err_a is a value between zero and the first permissible limit value τ_err_lim (a value that becomes 0&lt;τ_err_a&lt;τ_err_lim), and is determined according to the first permissible limit value τ_err_lim so as not to approach too close to zero. For example, τ_err_a is determined to a value which is Ma1 times τ_err_lim (=Ma1·τ_err_lim). However, Ma1 is a positive constant smaller than 1, and is a value for example in a range such as 0.25 to 0.75. 
     Similarly, the second set value dτ_err_a is a value between zero and the secondary permissible limit value dτ_err_lim (a value that becomes 0&lt;dτ_err_a&lt;dτ_err_lim), and is determined according to the secondary permissible limit value dτ_err_lim so as not to approach too close to zero. For example, dτ_err_a is determined to a value which is Ma2 times dτ_err_lim (=Ma2·dτ_err_lim). However, Ma2 is a positive constant smaller than 1, and is a value for example in a range such as ¼ through ⅙. 
     In the phase plane of  FIG. 3 , examples of lines on a positive side and a negative side (lines respectively represented by formula τ_err=−τ_err_a and formula τ_err=−τ_err_a) that are defined by the first set value τ_err_a are lines LL1p, LL1n, and lines on a positive side and a negative side (lines respectively represented by formula dτ_err=+dτ_err_a and formula dτ_err=−dτ_err_a) that are defined by the second set value dτ_err_a are lines LL2p, LL2n. 
     In procedure 2, subsequently, the response characteristics data for determining gradient that satisfies the above-mentioned selection requirements 1, 2 is selected, using the first permissible limit value τ_err_lim and the secondary permissible limit value dτ_err_lim, and the first set value τ_err_a and the second set value dτ_err_a, that are determined as is explained above (procedure 2-3). 
     For example, in the example shown in  FIG. 3 , the response characteristics data allotted with references a1 through a6, each satisfy the selection requirement 1. On the other hand, the response characteristics data allotted with references a1 through a5, each satisfy the selection requirement 2, but the response characteristics data allotted with reference a6 does not satisfy the selection requirement 2. 
     Therefore, the response characteristics data excluding the response characteristics data of a6 (the response characteristics data of a1 through a5) is selected as the response characteristics data for determining gradient. 
     As is explained above, the response characteristics data for determining gradient is selected in procedure 2. 
     (Procedure 3) Subsequently, among the intersections between a trajectory of the response characteristics data for determining gradient selected as explained above, and lines LL1p, LL1n, LL2p, and LL2n that are represented respectively by the first set value τ_err_a and the second set value dτ_err_a, the intersection satisfying a predetermined requirement condition related to the intersection (hereinafter referred to as an intersection requirement condition) is used to determine the gradient of the switching hyperplane σ=0. 
     The intersection requirement condition is a condition that a gradient of a line connecting the intersection and an origin of the phase plane (a point that becomes τ_err=0, dτ_err=0) is within a preliminarily determined gradient requirement range. 
     As is explained above, the gradient of the switching hyperplane σ=0 is for defining the time constant Tc of the convergent response of τ_err on the switching hyperplane σ=0. And the above-mentioned gradient requirement range is a requirement range of the gradient of the switching hyperplane σ=0 corresponding to a requirement range of the time constant Tc. 
     In a case of structuring a system which controls the secondary torque τ to a desired value (the desired secondary torque τ_cmd) in the power transmission device  1 , usually, there is a requirement (desire) from design to set the time constant Tc of the convergent response of the secondary torque τ to a value within a certain range. Therefore, the gradient requirement range is set, for example, corresponding to the requirement range from design of the value of the time constant Tc. 
     In this case, in a case where the requirement range from design of the value of the time constant Tc is set to a range of Tc_L≦Tc≦Tc_H, and a relationship between the gradient of the switching hyperplane σ=0 and the time constant Tc is set to gradient=−1/Tc, then the gradient requirement range should be set to a range of −(1/Tc_L)≦gradient≦−(1/Tc_H). 
     Further, in a case where the relationship between the gradient of the switching hyperplane σ=0 and the time constant Tc is set to gradient=−Tc, then the gradient requirement range should be set to a range of −Tc_H≦gradient≦−Tc_L. 
     However, the rotational angular acceleration of the drive pulley  2  must be limited to a magnitude equal to or smaller than the above-mentioned primary acceleration limit value dω1_lim. Therefore, the value of the time constant Tc cannot be made small with no limitation. 
     More specifically, a value of the time constant Tc of the convergent response in a case where the magnitude of the secondary torque deviation τ_err is converged to zero, from the initial state in which τ_err coincides with the first permissible limit value τ_err_lim by relatively rotating the drive pulley  2  with respect to the driven pulley  3  at the rotational angular acceleration of a magnitude of the primary acceleration limit value dω1_lim, as is shown in  FIGS. 4A through 4C , is set to Tcx. 
     At this time, the time constant Tc of the convergent response of τ_err when the magnitude of the secondary torque deviation τ_err in the initial state is the first permissible limit value τ_err_lim cannot be made smaller than Tcx (hereinafter referred to as a specific time constant Tcx). 
     Therefore, the gradient of the switching hyperplane σ=0 needs to be determined so as to satisfy a constraint condition (hereinafter referred to as a time constant constraint condition) that the time constant Tc corresponding thereto becomes a value equal to or more than the specific time constant Tcx. 
     In a case where the magnitude of the secondary torque deviation τ_err is converged to zero, from the initial state in which τ_err coincides with the first permissible limit value τ_err_lim by relatively rotating the drive pulley  2  with respect to the driven pulley  3  at the rotational angular acceleration of a magnitude of the primary acceleration limit value dω1_lim, as is shown in  FIGS. 4A through 4C , the time ta required for the convergence is set to tax, then the relationship between tax and the specific time constant Tcx is approximately represented by following expression (18).
 
 Tcx=tax/ 3  (18)
 
     Further, tax is a value of ta when τ_err_0 in above-mentioned expression (11) is substituted by τ_err_lim, so that following expression (19) stands.
 
(¼)· dω 1_lim· tax   2 =τ_err_lim/ Ksp   (19)
 
     From above-mentioned expressions (18), (19), following expression (20) is obtained.
 
 Tcx =(⅔)·sqrt((τ_err_lim/ dω 1_lim)/ Ksp )  (20)
 
     Therefore, in the present embodiment, the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 being equal to or more than the specific time constant Tcx calculated by above-mentioned expression (20) (Tc≧Tcx) is set as the time constant constraint condition. Further, the gradient requirement range of the switching hyperplane σ=0 is set within the range satisfying the time constant constraint condition. 
     In this case, in the case where a lower limit value Tc_L of the design requirement range of the value of the time constant Tc satisfies the above time constant constraint condition (in the case where Tc_L≧Tcx), the gradient requirement range of the switching hyperplane σ=0 is set to a range of Tc_L≦Tc≦Tc_H, corresponding to the requirement range of the time constant Tc. For example, in the case where the relationship between the gradient of the switching hyperplane σ=0 and the time constant Tc is a relationship that gradient=−1/Tc, then the gradient requirement range is set to a range of −(1/Tc_L)≦gradient≦−(1/Tc_H). 
     Further, in the case where the lower limit value Tc_L of the design requirement range of the value of the time constant Tc does not satisfy the time constant constraint condition (in the case where Tc_L&lt;Tcx), the gradient requirement range of the switching hyperplane σ=0 is set to a range of Tcx≦Tc≦Tc_H, corresponding to the requirement range of the time constant Tc. For example, in the case where the relationship between the gradient of the switching hyperplane σ=0 and the time constant Tc is gradient=−1/Tc, then the gradient requirement range is set to a range of −(1/Tcx)≦gradient≦−(1/Tc_H). 
     The intersection requirement condition in procedure 3 is a condition that the gradient of the line connecting the intersection and the origin of the phase plane is within the gradient requirement range preliminarily determined as is explained above. 
     In the phase plane of  FIG. 3 , lines Lb_max, Lb_min that are represented by a two-dot-and-dash line represent examples of a line with a gradient of maximum magnitude and a line with a gradient with a minimum magnitude, in the gradient requirement range determined as explained above. In this case, in the phase plane of  FIG. 3 , a relationship that gradient=−1/Tc holds, so that the magnitude of the gradient of the line Lb_max is 1/max(Tc_L,Tcx), and the magnitude of the gradient of the line Lb_min is 1/Tc_H. Here, max(Tc_L, Tcx) is a function meaning a larger value of Tc_L and Tcx. 
     In the procedure 3, an intersection satisfying the intersection requirement condition defined by the gradient requirement range is extracted. For example, in the example shown in  FIG. 3 , intersections of white circles indicated in  FIG. 5A , which is an enlarged view of dashed frame portion A in  FIG. 3 , and intersections of white circles indicated in  FIG. 5B , which is an enlarged view of dashed frame portion B in  FIG. 3 , are extracted as the intersections satisfying the intersection requirement condition. 
     Thereafter, using a set of the values of τ_err and dτ_err in a plurality of the extracted intersections, a gradient coinciding or approximating as much as possible with a gradient of the line connecting each intersection and the origin, is calculated by a least squares method. The calculated gradient is determined as the gradient of the switching hyperplane σ=0. 
     For example, in the example shown in  FIG. 3 , a gradient of a line Lc indicated by a dot-and-dash line in the Figure is determined as the gradient of the switching hyperplane σ=0. 
     The gradient of the switching hyperplane σ=0 may be determined by a statistical identification approach other than the least squares method. For example, a mean value of the gradients of the lines connecting each intersection satisfying the intersection requirement condition and the origin may be determined as the gradient of the switching hyperplane σ=0. 
     (Procedure 4) Subsequently, based on the gradient of the switching hyperplane σ=0 determined in (Procedure 3) as is explained above, the values of the coefficient components s1, s2 of the switching function σ are determined. Specifically, gradient=−s1/s2 (or −s2/s1), so that the values of s1, s2 are determines such that −s1/s2 (or −s2/s1) coincides with the gradient of the switching hyperplane σ=0 determined in (Procedure 3). In this case, the value of either of s1, s2 may be an arbitral value of constant (for example, 1). 
     In the case where the value of one of s1, s2 is a value of constant, the value of the other is set unambiguously according to the gradient of the switching hyperplane σ=0. For example, in the case where gradient=−s1/s2, and in the case where the value of the coefficient component s2 is “1”, then the value of s1 becomes a value (−1) times the gradient. Therefore, in the case where the value of either s1, s2 is a value of constant, then procedure 4 may practically be omitted. 
     The above is the determination method of the values of the coefficient components s1, s2 of the switching function σ of the present embodiment. 
     In the present embodiment, the gradient requirement range defining the intersection requirement condition in procedure 3 is set reflecting the time constant constraint condition. However, the gradient requirement range may be determined simply according to requirement range from design of the time constant Tc, without taking the time constant constraint condition into consideration. 
     In this case, the gradient of the switching hyperplane σ=0 is provisionally determined by methods such as the least squares method, similarly to the above, based on the intersections satisfying the intersection requirement condition defined by the gradient requirement range. Thereafter, in the case where the value of the time constant Tc defined by the provisional gradient satisfies the time constant constraint condition, then the provisional gradient itself may be determined as the gradient of the switching hyperplane σ=0. 
     Further, in the case where the value of the time constant Tc defined by the provisional gradient does not satisfy the time constant constraint condition, the gradient of the switching hyperplane σ=0 may be determined using the intersections satisfying the intersection requirement condition defined by the gradient requirement range in which the time constant constraint condition is reflected as is explained above. 
     Subsequently, explanation will be given on the operation of the control device  10  when controlling the output torque of the electric motor  5  so as to make the secondary torque τ of the power transmission device  1  follow the desired secondary torque τ_cmd. 
     In the following explanation, a suffix “_act” will be attached to references indicating an actual value of an arbitral state amount (angle, torque and the like), or an observed value (a detected value or an estimated value) thereof. 
     In the present embodiment, the control device  10  sequentially determines the desired torque τm_cmd of the electric motor  5  as the control input, with the control input determining unit  13  executing the process indicated by a block diagram of  FIG. 6 . 
     In each control processing cycle of the control device  10 , the control input determining unit  13  is sequentially input with the actual rotational angle θin_act (detected value) of the drive pulley  2  respectively indicated by the output signals (detection signals) of the angle detectors  11 ,  12 , and the actual rotational angle θout_act (detected value) of the driven pulley  3 , and is also sequentially input with the desired secondary torque τ_cmd. 
     Thereafter, the control input determining unit  13  calculates an estimated value of the actual secondary torque τ_act, by a secondary torque detecting unit  13   f , by performing the calculation of the right side of the expression (1), using the values (current values) of θin_act, θout_act in the current control processing cycle, and a value of the elastic deformation coefficient Ksp of the wire  4  (preset value memorized and held in a memory not shown). 
     Further, the control input determining unit  13  corrects τ_cmd, by adding an output value of a low-pass filter  13   b  to the input desired secondary torque τ_cmd (current value) in a calculating unit  13   a . Hereinafter, τ_cmd after correction will be referred to as a corrected desired secondary torque τ_cmd_c. 
     This correction is a correction for compensating an influence of an offset component (a steady error component) included in the secondary torque τ_act. In this case, the low-pass filter  13   b  is sequentially input with output values of the calculation result of the calculating unit  13   c.    
     The calculating unit  13   c  calculates a difference between the value (a previous value) of the corrected desired secondary torque τ_cmd_c calculated by the calculating unit  13   a  in a previous control processing cycle, and an estimated value (a current value) of the secondary torque τ_act calculated by the secondary torque detecting unit  13   f  in the current control processing cycle. 
     Thereafter, the low-pass filter  13   b  performs a filtering process of a low-pass characteristics to the output value of the calculation result of the calculating unit  13   c , so as to extract the offset component. The offset component is output from the low-pass filter  13   b  to the calculating unit  13   a.    
     Subsequently, the control input determining unit  13  calculates a deviation between the value (current value) of the corrected desired secondary torque τ_cmd_c calculated by the calculating unit  13   a  and the estimated value (current value) of the secondary torque τ_act calculated by the secondary torque detecting unit  13   f , that is, the secondary torque deviation τ_err, by a calculating unit  13   d.    
     Thereafter, the control input determining unit  13  sequentially inputs the secondary torque deviation τ_err to a sliding-mode control processing unit  13   e.    
     The sliding-mode control processing unit  13   e  calculates the value of the switching function σ according to expression (7). Further, the sliding-mode control processing unit  13   e  sequentially calculates the desired torque τm_cmd of the electric motor  5  as the control input, by performing the calculation of the right side of expression (6) using the calculated value of the switching function σ. 
     In this case, the secondary torque deviation velocity dτ_err necessary for the calculation of expression (7) is calculated as a temporal change rate of the secondary torque deviation τ_err input to the sliding-mode control processing unit  13   e . Further, the values of the coefficient components s1, s2 are preset values preliminarily determined as is explained above, and are memorized and held in a memory not shown. 
     Further, each component of A, B necessary for the calculation of expression (6) are preset values determined based on the definitional expression of the where clause of expression (4). The preset values are memorized and stored in a memory not shown. 
     The control input determining unit  13  sequentially determines the desired torque τm_cmd of the electric motor  5  (the control input) by the above-mentioned processing. 
     In the case where the offset component (the steady error component) included in the secondary torque τ_act is sufficiently small, then the calculation units  13   a ,  13   c  and the low-pass filter  13   b  may be omitted and τ_cmd may be input to the calculation unit  13   d  as it is. 
     The control device  10  inputs the desired torque τm_cmd sequentially determined by the control input determining unit  13  as is explained above into the motor control unit  14 , and executes the processing of the motor control unit  14 . The motor control unit  14  determines a command value (desired value) of the energization current of an armature winding not shown of the electric motor  5 , according to the input desired torque τ_cmd. Thereafter, the motor control unit  14  feedback controls the energization current of the armature winding so as to coincide the actual energization current to the determined command value. 
     By doing so, the actual output torque of the electric motor  5  is controlled to the desired torque τm_cmd. Consequently, the actual secondary torque τ_act is controlled so as to follow the desired secondary torque τ_cmd. 
     In the embodiment explained above, the gradient of the switching hyperplane σ=0 for the sliding-mode control for the control of the secondary torque τ by the control device  10  is determined using the response characteristics data for determining gradient satisfying the selection requirements 1, 2, among a plurality of the response characteristics data created using a versatile control method such as the PD control law. 
     In this case, the response characteristics data for determining gradient is an appropriate data capable of satisfying a condition that the magnitude of the rotational angular acceleration and the rotational angular velocity of the drive pulley  2  do not exceed the respective allowable limit values, that is, the primary acceleration limit value dω1_lim and the primary velocity limit value ω1_lim, by satisfying the selection requirement 1. 
     Further, the trajectory of the response characteristics data may be the one generating oscillation at a region near the origin of the phase plane. However, the response characteristics data for determining gradient is a data including a set of the values of the secondary torque deviation τ_err and the secondary torque deviation velocity dτ_err the magnitude thereof not being minute in the vicinity of zero, by satisfying the selection requirement 2. 
     Thereafter, the gradient of the switching hyperplane σ=0 is determined by a method such as the least squares method, based on the intersection satisfying the intersection requirement condition corresponding to the requirement range of the time constant Tc, among the intersections between any one of the lines LL1p, LL1n in which the magnitude of the value of τ_err becomes the first set value τ_err_a and the lines LL2p, LL2n in which the magnitude of τ_err becomes the second set value τ_err_a, and the trajectories of the response characteristics data for determining gradient satisfying the selection requirements 1, 2. 
     In this case, the magnitude of the value of the secondary torque deviation τ_err at the intersection (=the first set value τ_err_a) has a magnitude of a certain extent that is smaller than the first permissible limit value τ_err_lim and not too close to zero. Similarly, the magnitude of the value of the secondary torque deviation velocity dτ_err in the intersection (=the second set value τ_err_a) has a magnitude of a certain extent that is smaller than the secondary permissible limit value dτ_err_lim and is not too close to zero. 
     Since the intersection satisfies the intersection requirement condition, it satisfies the requirement from design and the time constant constraint condition related to the time constant Tc. 
     Accordingly, the intersection used for determining the gradient of the switching hyperplane σ=0 has high reliability and stability, as a point on the trajectory of the response characteristics data that could favorably converge the secondary torque deviation τ_err to zero. Therefore, by determining the gradient of the switching hyperplane σ=0 using the intersection, the gradient is determined so as to favorably converge the secondary torque deviation τ_err to zero. 
     Further, the response characteristics data may be obtained using a versatile control method, so that numerous response characteristics data may be effectively and easily collected. Consequently, the determination of the favorable gradient of the switching hyperplane σ=0 may be performed efficiently. 
     Further, in the processing of the control input determining unit  13  of the control device  10 , the control input (the desired torque τm_cmd of the electric motor  5 ) is determined by the processing of the sliding-mode control using the switching hyperplane σ=0 having the gradient (and consequently the values of the coefficient components s1, s2) determined as explained above. As such, the control of the secondary torque τ may be performed appropriately so as to realize required convergence characteristics and high robustness. 
     Specifically, in the present embodiment, the gradient of the switching hyperplane σ=0 (and consequently the time constant Tc corresponding to the gradient) is set so as to satisfy the time constant constraint condition. Therefore, the control of the secondary torque τ may be performed with high robustness in a wide operating range of the power transmission device  1 . 
     A corresponding relationship between the present embodiment explained above and the present invention will be supplemented. The drive pulley  2 , the driven pulley  3 , the wire  4 , and the electric motor  5  respectively correspond to a primary element, a secondary element, an elastic deformation member, and an actuator of the present invention. Further, the rotation of the drive pulley  2  corresponds to a displacement of the primary element of the present invention, the secondary torque τ corresponds to a secondary power of the present invention, and the elastic deformation coefficient Ksp corresponds to an elastic deformation coefficient of the present invention. 
     Further, the control input determining unit  13  of the control device  10  corresponds to a control input determining unit of the present invention. 
     Further, the secondary torque deviation τ_err, and the secondary torque deviation velocity dτ_err correspond respectively to a first variable component and a second variable component of the present invention. Also, the first permissible limit value τ_err_lim of the present embodiment correspond to a first permissible limit value of the present invention. 
     Further, the specific time constant Tcx correspond to a specific time constant of the present invention. 
     Second Embodiment 
     Next, a second embodiment of the present invention will be explained with reference to  FIG. 7 . In the present embodiment, a part of the processing of the control input determining unit  13  of the control device  10  differs from the first embodiment. Therefore, explanation of the present embodiment will be made mainly for matters differing from the first embodiment, and explanation of matters identical with the first embodiment will be omitted. 
     In the present embodiment, in order to reduce the influence of disturbance in the processing of the control input determining unit  13 , the values of the secondary torque deviation τ_err and the secondary torque deviation velocity dτ_err are sequentially estimated using an observer. Thereafter, in place of the actual secondary torque deviation τ_err_act calculated using the actual secondary torque τ_act (the estimated value by the secondary torque detecting unit  13   f ) as it is, and the actual secondary torque deviation velocity dτ_err_act obtained as the temporal change rate thereof, the control input (the desired torque τm_cmd) is determined by executing the processing of the sliding-mode control using estimated values τ_err_hat, dτ_err_hat by the observer. 
     Specifically, in the present embodiment, as is shown in  FIG. 7 , a sliding-mode control processing unit  13   g  of the control input determining unit  13  includes a function as an observer  13   h.    
     Thereafter, the sliding-mode control processing unit  13   g  is input with the deviation (an output of a calculating unit  33   d ) between the estimated value of the actual secondary torque τ_act calculated by the secondary torque detecting unit  13   f  and the corrected desired secondary torque τ_cmd_c, as the actual secondary torque deviation τ_err_act. The calculation processing of the corrected desired secondary torque τ_cmd_c is the same as in the first embodiment. 
     The observer  13   h  sequentially updates and calculates an estimated value τ_err_hat of the secondary torque deviation τ_err with the disturbance component reduced (hereinafter referred to as a secondary torque deviation estimated value τ_err_hat), and an estimated value dτ_err_hat of the secondary torque deviation velocity dτ_err with the disturbance component reduced (hereinafter referred to as a secondary torque deviation velocity estimated value dτ_err_hat), in the control processing cycle of the control device  10 , by a calculation of following expression (21). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             τ_err 
                             ⁢ 
                             _hat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             τ_err 
                             ⁢ 
                             _hat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
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                       A 
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                         [ 
                         
                           
                             
                               
                                 τ_err 
                                 ⁢ 
                                 _hat 
                                 ⁢ 
                                 
                                     
                                 
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                                     n 
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                                     1 
                                   
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                                 d 
                                 ⁢ 
                                 
                                     
                                 
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                                     n 
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                       ⁢ 
                       
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                       K 
                       ⁢ 
                       
                           
                       
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                         obs 
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                           ( 
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       τ_err 
                                       ⁢ 
                                       _act 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       d 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       τ_err 
                                       ⁢ 
                                       _act 
                                       ⁢ 
                                       _filt 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                             - 
                             
                               [ 
                               
                                 
                                   
                                     
                                       τ_err 
                                       ⁢ 
                                       _hat 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           n 
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                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       d 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       τ_err 
                                       ⁢ 
                                       _hat 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           n 
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                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     This expression (21) is formed on the premise of the state equation of above-mentioned expression (4), and A, B in expression (21) are respectively a matrix (two-rows, two-columns), and a vector (two-rows, one-column) that are defined by the where clause of expression (4). The values of each component of A, B are predetermined preset values. The present values are memorized and stored in a memory not shown of the control device  10 . 
     In this case, as a value of u(n−1) of the right side of expression (21), the value (previous value) of the desired torque Tm_cmd determined in the previous control processing cycle is used. Further, Kobs is a predetermined preset value. The preset value is memorized and stored in a memory not shown of the control device  10 . 
     Further, dτ_err_act_filt is a value performed with a filtering processing of a low-pass characteristics, to the value of the temporal change rate of the secondary torque deviation τ_err_act input to the sliding-mode control processing unit  13   g.    
     Alternatively, a value obtained by removing a noise component from the value of the temporal change rate of the estimated value of the secondary torque deviation τ_err_act by arbitral processing other than the filtering processing of the low-pass characteristics (for example, processing proposed by the Applicant in Japanese Patent Application No. 2011-159322 (Japanese Patent Application Laid-Open No. 2013-22677), and the like), may be used in place of dτ_err_act_filt. 
     The sliding-mode control processing unit  13   g  of the present embodiment calculates the value of the switching function σ using the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat that are calculated by the observer  13   h  as is explained above, according to the expression (7). Further, the sliding-mode control processing unit  13   g  sequentially calculates the desired torque τm_cmd of the electric motor  5  as the control input using the calculated value of the switching function σ and performing the calculation of the right side of the expression (6). 
     The present embodiment is the same as the first embodiment, other than the matters explained above. 
     A similar effect as the first embodiment may be obtained by the present embodiment. 
     In addition, in the present embodiment, the control processing of the sliding mode control is performed using the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat calculated by the observer  13   h , in place of the actual secondary torque deviation τ_err_act and the secondary torque deviation velocity dτ_err_act as the temporal change rate thereof, that are calculated using the estimated value of the actual the secondary torque τ_act sequentially calculated by the secondary torque detecting unit  13   f  as it is. Therefore, the control input (the desired torque τm_cmd) may be determined while reducing the influence of the disturbance component included in the estimated value of the secondary torque τ_act and the temporal change rate thereof. 
     Therefore, it becomes possible to further improve the robustness of the control of the secondary torque τ by the control device  10 . 
     A corresponding relationship between the present embodiment explained above and the present invention will be supplemented. In the present embodiment, the observer  13   h  corresponds to an observer of the present invention. Other than this, the corresponding relationship between the present embodiment and the present invention is the same as in the first embodiment. 
     Third Embodiment 
     Subsequently, a third embodiment of the present invention will be explained with reference to  FIG. 8  through  FIG. 11 . The present embodiment differs from the first embodiment in the configuration of a part of the power transmission device, and a part of the control processing. Therefore, explanation of the present embodiment will be mainly on the matters differing from the first embodiment, and the matters identical with the first embodiment will be omitted. 
     With reference to  FIG. 8 , a power transmission device  21  of the present embodiment is equipped with, similarly to the power transmission device  1  of the first embodiment, the drive pulley  2 , the driven pulley  3 , the wire  4 , the electric motor  5 , and the load member  6 . Further, the power transmission device  21  is configured to rotate and drive the driven pulley  3  together with the load member  6 , by transmitting the rotational driving force (torque) imparted to the drive pulley  2  from the output shaft  5   a  of the electric motor  5  via the reducer  7 , to the driven pulley  3  via the wire  4  configured from the elastic deformation member. 
     However, the power transmission device  21  of the present embodiment is further equipped with a rigidity variable mechanism  22  for varying a rigidity of the wire  4  (and consequently the elastic deformation coefficient). 
     The rigidity variable mechanism  22  is configured, for example as is shown in  FIG. 9  and  FIG. 10 . That is, the rigidity variable mechanism  22  is equipped with a rotational bar  24 , in which rollers  23 ,  23  are pivotally fixed so as to rotate freely at both end portions thereof. The rotational bar  24  is capable of rotating integrally with a rotational axis  24   a  fixed to a central portion of the rotational bar  24 . In this case, the rotational axis  24   a  is arranged at a position between the drive pulley  2  and the driven pulley  3 , and facing a direction parallel to the rotational shaft center of the pulleys  2 ,  3 . 
     Rotational shaft centers of respective rollers  23 ,  23 , on both end portions of the rotational bar  24  are facing a direction parallel to the rotational shaft centers of the drive pulley  2  and the driven pulley  3 . 
     Further, the drive pulley  2  and the driven pulley  3  are coupled by two wires  4 ,  4 . These wires  4 ,  4 , are provided so as to have an interval in the direction approximately orthogonal to the interval direction of the pulleys  2 ,  3 , and both ends thereof are fixed to an outer peripheral portion of the drive pulley  2  and an outer peripheral portion of the driven pulley  3 , respectively. 
     Further, among the rollers  23 ,  23 , an outer peripheral portion of an inner end side of one of the roller  23  (a side towards the other roller  23 ) is press-contacted against one of the wires  4 ,  4 , and an outer peripheral portion of an inner end side of the other roller  23  (a side towards the one of the roller  23 ) is press-contacted against the other of the wires  4 ,  4 . 
     Further, the rigidity variable mechanism  22  is equipped with a gear (a spur gear)  25  which is coupled to the rotational bar  24  via the rotational axis  24   a  and is provided so as to be able to rotate integrally with the rotational bar  24 , a worm gear  26  meshing with the gear  25 , and an electric motor  27  which rotary drives the worm gear  26 . 
     Therefore, by rotationally driving the worm gear  26  with the electric motor  27 , the gear  25  rotates integrally with the rotational bar  24 . 
     In this case, accompanying the rotation of the rotational bar  24 , each of the rollers  23 ,  23  rotates (revolves) about the shaft center of the rotational axis  24   a  while maintaining press-contact with the contacting wire  4 . Further, for example when the rotational bar  24  rotates from the state shown in  FIG. 9  to the state shown in  FIG. 10 , the wires  4 ,  4  are biased in a expanding direction. 
     The wires  4 ,  4  of the present embodiment are configured from an elastic deformation member having a nature of increasing the rigidity as the same expands. Therefore, in the power transmission device  21  of the present embodiment, the elastic deformation coefficient Ksp (a rate of change of the secondary torque τ with respect to a change of a between-pulley rotational angle) which defines a relationship between the between-pulley rotational angle and a torque (the secondary torque τ) transmitted from the drive pulley  2  side to the driven pulley  3  side by the elastic deformation (expansion and contradiction) of the wires  4 ,  4  accompanying the same, changes depending on the rotational angle of the rotational bar  24 . 
     More specifically, in the present embodiment, the rigidity of the wires  4 ,  4  becomes the minimum (the elastic deformation coefficient Ksp is minimum) in a state where the rotational bar  24  is extending in a direction orthogonal to the interval direction of the drive pulley  2  and the driven pulley  3 , as is shown in  FIG. 9 . Hereinafter, this state will be referred to as a minimum rigidity state. 
     Thereafter, when the rotational bar  24  is rotated from the minimum rigidity state, the rigidity of the wires  4 ,  4  increases (the elastic deformation coefficient Ksp increases) accompanying the increase of the rotational angle thereof (a rotational angle taking the minimum rigidity state as a reference). 
     The rotational driving of the rotational bar  24  may be performed by a mechanism of a similar configuration to the mechanism performing rotational driving of the drive pulley  2  by the electric motor  5 . 
     Further, the wire  4  may be an endless member wound around the drive pulley  2  and the driven pulley  3 . 
     Returning to  FIG. 8 , the present embodiment is further provided with, as a configuration for operational control of the power transmission device  21 , similarly to the first embodiment, a control device  30  configured from an electronic circuit unit, and the angle detectors  11 ,  12  respectively detecting the rotational angle θin of the drive pulley  2  and the rotational angle θout of the driven pulley  3 . Further, the output signals (the detected signals) of the angle detectors  11 ,  12  are input to the control device  30 . 
     Further, the control device  30  is sequentially input with the desired secondary torque τ_cmd from the outside other control device or the server and the like similarly to the first embodiment, and in addition, a desired value Ksp_cmd of the elastic deformation coefficient Ksp of the wires  4 ,  4  (hereinafter referred to as a desired deformation coefficient Ksp_cmd) is sequentially input from the outside other control device or the server and the like. 
     In the present embodiment, the elastic deformation coefficient Ksp is defined according to the rotational angle of the rotational bar  24  of the rigidity variable mechanism  22 . As such, a desired value of the rotational angle of the rotational bar  24 , or a desired value of the rotational angle of the output shaft of the electric motor  27  of the rigidity variable mechanism  22  may be input to the control device  30 , in place of the desired elastic deformation coefficient Ksp_cmd. 
     Further, as a function realized by a program processing (a function realized by a software) or a main function realized by a hardware configuration, the control device  30  is equipped with a control input determining unit  33  and a motor control unit  34  respectively having a function similar to the first embodiment, and further is equipped with a rigidity control unit  35  which controls the rigidity of the wires  4 ,  4  according to the desired elastic deformation coefficient Ksp_cmd, by controlling the electric motor  27  of the rigidity variable mechanism  22 . 
     In the present embodiment, the control input determining unit  33  sequentially determines the desired torque τm_cmd of the electric motor  5  as the control input, by the control processing of the sliding-mode control, similarly to the first embodiment. That is, the control input determining unit  33  calculates the value of the switching function σ based on the expression (7), and determines τm_cmd by the calculation of the expression (6) using the value of σ. 
     However, the elastic deformation coefficient Ksp of the wires  4 , 4  is variable in the present embodiment. Therefore, in order to appropriately converge the secondary torque deviation τ_err to zero, it is necessary to change the gradient of the switching hyperplane σ=0 (and consequently the time constant Tc of the convergent response of the secondary torque deviation τ_err on the switching hyperplane σ=0) according to the value of Ksp. 
     Therefore, in the present embodiment, a correlation data for determining the gradient of the switching hyperplane σ=0 (or the time constant Tc) according to the value of the elastic deformation coefficient Ksp of the wires  4 ,  4  is created preliminarily as is explained below. 
     Specifically, a plurality of representative values Ksp_i (i=1, 2, . . . , M) of the value of Ksp are selected within the variable range of the elastic deformation coefficient Ksp. Thereafter, the same advance preparation process as the procedures 1 through 3 explained in the first embodiment is executed, in the state where the rigidity variable mechanism  22  is controlled so as to stably maintain the actual elastic deformation coefficient Ksp_act of the wires  4 ,  4  to respective representative value Ksp_i (in a state where the rotational angle of the rotational bar  24  is held to the rotational angle corresponding to the representative value Ksp_i). With this processing, the suitable gradient of the switching hyperplane σ=0 (or the time constant Tc of the convergent response of τ_err on the switching hyperplane σ=0) for each representative value Ksp_i of the elastic deformation coefficient Ksp is determined. 
     In this case, by the processing of the above-mentioned procedure 3, the gradient of the switching hyperplane σ=0 for each representative value Ksp_i of the elastic deformation coefficient Ksp is determined so that the corresponding time constant Tc becomes a time constant equal to or more than the specific time constant Tcx determined by the expression (20) according to the respective value Ksp_i (so as to satisfy the time constant constraint condition). 
     Further, in the advance preparation process of the present embodiment, an arithmetic expression which approximates a relationship between the value of Ksp and the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding to the gradient) is determined, using a plurality of the respective values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp, and the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding to the gradient) determined corresponding to each of the respective values Ksp_i. 
     Specifically, according to experiments and considerations by the inventors of the present application, the relationship between the value of the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 determined as explained above, and a value of the elastic deformation coefficient Ksp, may be roughly approximated by a format of following expression (22).
 
 Tc=c 2/sqrt( Ksp )+ c 1 ·Ksp+c 0  (22)
 
     Therefore, in the present embodiment, values of coefficients c2, c1, and c0 in each column of a right side of expression (22) is determined by a statistical identification approach such as the least squares method, using a plurality of the representative values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp, and the values of the time constant Tc corresponding to the gradients of the switching hyperplane σ=0 determined corresponding respectively to the Ksp_i. By doing so, the arithmetic expression approximating the relationship between Ksp and the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 is determined. 
     In this case, the values of the coefficients c2, c1, and c0 are determined, such that the value of the time constant Tc calculated by the expression (22) corresponding to each representative value Ksp_i of the elastic deformation coefficient Ksp becomes a value equal to or larger than the specific time constant Tcx determined by the expression (20) corresponding to the representative value Ksp_i. 
     In the present embodiment, the arithmetic expression and the values of the coefficients c2, c1, and c0 determined by the advance preparation process as is explained above, are memorized and stored in a memory not shown of the control device  30 . 
     Here, the expression (22) may be converted to an arithmetic expression approximating the relationship between the gradient of the switching hyperplane σ=0 and the value of the elastic deformation coefficient Ksp using the relational expression between the gradient of the switching hyperplane σ=0 and the time constant Tc (a relational expression that gradient=−1/Tc, or gradient=−Tc), and the arithmetic expression and the value of the coefficient concerning the arithmetic expression may be memorized and stored in a memory not shown of the control device  30 . 
     Subsequently an operation of the control device  30  when controlling the output torque of the electric motor  5  so as to make the secondary torque τ of the power transmission device  21  follow the desired secondary torque τ_cmd, will be explained. 
     In the present embodiment, the control device  30  executes the processing of the rigidity control unit  35  according to the input desired elastic deformation coefficient Ksp_cmd in each control processing cycle. 
     The rigidity control unit  35  determines a desired value of the rotational angle of the rotational bar  24  corresponding to the desired elastic deformation coefficient Ksp_cmd (current value), for example, by a predetermined map (or a predetermined arithmetic expression) preliminarily memorized and stored in a memory not shown. Thereafter, by controlling the energization current of the armature winding not shown of the electric motor  27  of the rigidity variable mechanism  22  by a method of known servo control, the rigidity control unit  35  controls the actual rotational angle of the rotational bar  24  to the desired value. By this control, the actual elastic deformation coefficient Ksp_act of the wires  4 , 4  is controlled to the desired elastic deformation coefficient Ksp_cmd. 
     Concurrently with the control processing of the rigidity control unit  35 , the control device  30  sequentially determines the desired torque τm_cmd of the electric motor  5  as the control input, by executing the processing shown in block diagram in  FIG. 11  by the control input determining unit  33 . 
     In each control processing cycle of the control device  30 , the control input determining unit  33  is sequentially input with the actual rotational angle θin_act (detected value) of the drive pulley  2  and the actual rotational angle θout_act (detected value) of the driven pulley  3 , that are indicated by the output signals (detected signals) of the angle detectors  11 ,  12 , respectively, and also is sequentially input with the desired secondary torque τ_cmd and the desired elastic deformation coefficient Ksp_cmd. 
     Further, the control input determining unit  33  calculates the secondary torque deviation τ_err, by executing the processing of a secondary torque detecting unit  33   f , an arithmetic unit  33   c , a low-pass filter  33   b , an arithmetic unit  33   a , and an arithmetic unit  33   d . These processing are the same as the processing of the secondary torque detecting unit  13   f , the arithmetic unit  13   c , the low-pass filter  13   b , the arithmetic unit  13   a , and the arithmetic unit  13   d  of the first embodiment. 
     However, in this case, the secondary torque detecting unit  33   f  is input with the value (current value) of the desired elastic deformation coefficient Ksp_cmd. Further, the secondary torque detecting unit  33   f  calculates an estimated value of the actual secondary torque τ_act, by performing the calculation of the right side of the expression (1), using the value of Ksp_cmd and the values (current values) of θin_act, θout_act. 
     Subsequently, the control input determining unit  33  inputs the secondary torque deviation τ_err and the desired elastic deformation coefficient Ksp_cmd calculated as explained above to a sliding-mode control processing unit  33   e.    
     The sliding-mode control processing unit  33   e  includes a switching hyperplane variable setting unit  33   g  which variably determines the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto). The sliding-mode control processing unit  33   e  first executes the processing of the switching hyperplane variable setting unit  33   g  in every control processing cycle. 
     The switching hyperplane variable setting unit  33   g  calculates the value of the time constant Tc, by performing the calculation of the right side of the expression (22), using the value (current value) of the desired elastic deformation coefficient Ksp_cmd in the present control processing cycle, as the value of Ksp in the right side of the expression (22). By doing so, the gradient of the switching hyperplane σ=0 is also determined substantively. Further, the value of the time constant Tc calculated by the expression (22) may be converted to the value of the gradient of the switching hyperplane σ=0. 
     Thereafter, the sliding-mode control processing unit  33   e  calculates the value of the switching function σ by the expression (7), using the values of the coefficient components s1, s2 (in this case, one of the values of s1, s2 is a value of constant (for example, 1)) of the switching function σ defined by the value of the time constant Tc calculated as is explained above. Further, the sliding-mode control processing unit  33   e  sequentially calculates the desired torque τm_cmd of the electric motor  5  as the control input, by performing the calculation of the right side of the expression (6) using the calculated value of the switching function σ. 
     In this case, the secondary torque deviation velocity dτ_err necessary for the calculation of the expression (7) is calculated as a temporal change rate of the secondary torque deviation τ_err input to the sliding-mode control processing unit  33   e.    
     Further, of each components of A, B necessary for the calculation of the expression (6), components other than the component of second row, first column of the matrix A are memorized and stored in a memory not shown, as preset values based on the definition in the where clause of expression (4). On the other hand, the component of the second row, first column of the matrix A (=−rin·DT−rout·DT) is calculated according to the value (current value) of the desired elastic deformation coefficient Ksp_cmd in the present embodiment. 
     That is, the values of rin, rout are respectively calculated according to the value (current value) of Ksp_cmd according to the definition of the where clause of the expression (2), and the component of the second row first column of the matrix A is calculated from the calculated value of rin, rout, and the value (preset value) of the control processing cycle DT. The values of the input side inertia In and the output side inertia Iout used for calculating rin, rout are preset values. 
     The control input determining unit  33  sequentially determines the desired torque τm_cmd of the electric motor  5  (the control input) by the processing explained above. 
     Similar to the case of the first embodiment, in the case where the offset component (steady error component) included in the secondary torque τ_act is sufficiently minute, the arithmetic units  33   a ,  33   c , and the low-pass filter  33   b  may be omitted, and τ_cmd may be input to the arithmetic unit  33   d  as it is. 
     The control device  30  inputs the desired torque τm_cmd sequentially determined by the control input determining unit  33  as is explained above to the motor control unit  34 , and executes the processing of the motor control unit  34 . Similarly to the motor control unit  14  of the first embodiment, the motor control unit  34  determines the command value (desired value) of the energizing current of the armature winding not shown of the electric motor  5  according to the input desired torque τ_cmd. Therefore, the motor control unit  34  feedback controls the energization current of the armature winding so as to coincide the actual energization current to the determined command value. 
     By doing so, the actual output torque of the electric motor  5  is controlled to the desired torque τm_cmd. Consequently, the actual secondary torque τ_act is controlled so as to follow the desired secondary torque τ_cmd, while the elastic deformation coefficient Ksp of the wires  4 ,  4  (the rigidity of the wires  4 ,  4 ) are arbitrarily changed. 
     In the embodiment explained above, the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) corresponding to each of a plurality of the representative values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp of the wires  4 ,  4  is determined using a plurality of the response characteristics data, in the advance preparation process, in the same manner as in the first embodiment. 
     As such, the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) corresponding to each representative value Ksp_i of Ksp is determined so as to preferably converge the secondary torque deviation τ_err to zero, while maintaining Ksp to the representative value Ksp_i. 
     Further, the arithmetic expression approximating the relationship between the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) and the value of the elastic deformation coefficient Ksp is determined by a method of least squares method and the like, based on the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) corresponding to a plurality of the representative values Ksp_i (i=1, 2, . . . , M). 
     Thereafter, in the control processing of the secondary torque τ of the power transmission device  21  by the control device  30 , the gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) corresponding to the desired elastic deformation coefficient Ksp_cmd of an arbitral value is determined on the basis of the above-mentioned arithmetic expression. As such, a preferable gradient of the switching hyperplane σ=0 (or the time constant Tc corresponding thereto) with respect to Ksp of the arbitral value of the wires  4 ,  4  is determined Consequently, the preferable values of the coefficient components s1, s2 (preferable with respect to the elastic deformation coefficient Ksp of the wires  4 ,  4 , in each control processing cycle) of the switching function σ used for determining the control input in the processing of the sliding-mode control may be determined. 
     As a result, the control input (the desired torque τm_cmd of the electric motor  5 ) may be determined by the processing of the sliding-mode control, so as to appropriately perform the control of the secondary torque τ with high robustness, while variably controlling the elastic deformation coefficient Ksp of the wires  4 ,  4  to an arbitral value. That is, it becomes possible to appropriately perform the control of the secondary torque τ with high robustness, in any rigidity, while controlling the rigidity of the wires  4 , 4  to a desired rigidity. 
     Specifically, the gradient of the switching hyperplane σ=0 determined by the switching hyperplane variable setting unit  33   g  according to the desired elastic deformation coefficient Ksp_cmd by the arithmetic expression (22) is basically determined so that the time constant Tc corresponding to the gradient becomes equal to or larger than the specific time constant Tcx calculated by the expression (20) corresponding to Ksp_cmd. As such, the control of the secondary torque τ may be stably performed with high robustness in a wide operating region of the power transmission device  1 , without depending on the control state of the elastic deformation coefficient Ksp_cmd. 
     The corresponding relationship between the present embodiment explained above and the present invention will be supplemented. Similarly to the case of the first embodiment, the drive pulley  2 , the driven pulley  3 , the wire  4 , and the electric motor  5  respectively corresponds to the primary element, the secondary element, the elastic deformation member, and the actuator of the present invention. Further, the rotation of the drive pulley  2  corresponds to the displacement of the primary element, the secondary torque τ corresponds to the secondary power of the present invention, and the elastic deformation coefficient Ksp (the elastic deformation coefficient Ksp made variable by the rigidity variable mechanism  22 ) corresponds to the elastic deformation coefficient of the present invention. 
     Further, the control input determining unit  33  of the control device  30  corresponds to the control input determining element of the present invention, and the switching hyperplane variable setting unit  33   g  of the sliding-mode control processing unit  33   e  corresponds to a switching hyperplane variable setting element of the present invention. 
     Further, similar to the case of the first embodiment, the secondary torque deviation τ_err and the secondary torque deviation velocity dτ_err respectively corresponds to the first variable component and the second variable component of the present invention. Further, the first permissible limit value τ_err_lim corresponds to the first permissible limit value of the present invention. 
     Further the specific time constant Tcx corresponds to the specific time constant of the present invention. Further, the desired elastic deformation coefficient Ksp_cmd corresponds to a control value of the elastic deformation coefficient of the present invention. 
     Fourth Embodiment 
     Subsequently, a fourth embodiment of the present invention will be explained with reference to  FIG. 12 . The present embodiment differs from the third embodiment in a part of the processing of the sliding-mode control processing unit. Therefore, explanation of the present embodiment will be mainly on the matters differing from the third embodiment, and the explanation on the identical matters with the third embodiment will be omitted. 
     In the present embodiment, in the processing of the control input determining unit  33 , similarly to the second embodiment, the values of the secondary torque deviation τ_err and the secondary torque deviation velocity dτ_err are sequentially estimated using an observer, so as to reduce the influence of disturbance. Thereafter, the control input (the desired torque τm_cmd) is determined by executing the processing of the sliding-mode control using the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat, that are estimated values by the observer, in place of the actual secondary torque deviation τ_err_act calculated using the actual secondary torque τ_act as it is (the estimated value by the secondary torque detecting unit  13   f ) and the actual secondary torque deviation velocity dτ_err_act obtained as the temporal change rate thereof. 
     Specifically, in the present embodiment, as is shown in  FIG. 12 , a sliding-mode control processing unit  33   h  of the control input determining unit  33  includes a function as an observer  33   i.    
     Thereafter, the control input determining unit  33  determines the corrected desired secondary torque τ_cmd_c by performing the same processing as the third embodiment by the secondary torque detecting unit  33   f , the arithmetic unit  33   c , the low-pass filter  33   b , and the arithmetic unit  33   a.    
     The sliding-mode control processing unit  33   h  is input with the deviation (the output of the arithmetic unit  33   d ) between the estimated value of the actual secondary torque τ_act calculated by the secondary torque detecting unit  33   f , and the corrected desired secondary torque τ_cmd_c, as the actual secondary torque deviation τ_err_act. Further, the sliding-mode control processing unit  33   h  is input with the desired elastic deformation coefficient Ksp_cmd. 
     In each control processing cycle of the control device  30 , the observer  33   i  calculates the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat with the disturbance component reduced, similarly to the second embodiment, by the calculation of the expression (21). 
     However, in the present embodiment, Kobs in the right side of above-mentioned expression (21) is determined variably by a predetermined map or an arithmetic expression, according to the value (current value) of the desired elastic deformation coefficient Ksp_cmd. Further, the component of the second row, first column of the matrix A of the expression (21) is calculated according to the value (current value) of the desired elastic deformation coefficient Ksp_cmd, by the same calculating method as the calculating method explained in the third embodiment. 
     The calculation processing (processing of the observer  33   i ) of the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat in the present embodiment is the same as the second embodiment, except for those related to the value of Kobs in the expression (21), and the value of the components of the second row, first column of the matrix A. 
     The sliding-mode control processing unit  33   h  of the present embodiment calculates the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 corresponding to the current value of the desired elastic deformation coefficient Ksp_cmd, by performing the same processing as the third embodiment in the switching hyperplane variable setting unit  33   g.    
     Thereafter, the sliding-mode control processing unit  33   h  calculates the value of the switching function σ according to the expression (7), using the values of the coefficient components s1, s2 (in this case, one of the values of s1, s2 is a value of constant (for example, 1)) of the switching function σ defined by the value of the time constant Tc calculated by the switching hyperplane variable setting unit  33   g , and the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat calculated by the observer  33   i . Further, the sliding-mode control processing unit  33   h  sequentially calculates the desired torque τm_cmd of the electric motor  5  as the control input by performing the calculation of the right side of above-mentioned expression (6) using the calculated value of the switching function σ. 
     The present embodiment is the same as the third embodiment, other than matters explained above. 
     Similar effect as the third embodiment may be obtained in such embodiment. 
     In addition, in the present embodiment, the control processing of the sliding-mode control is performed using the secondary torque deviation estimated value τ_err_hat and the secondary torque deviation velocity estimated value dτ_err_hat calculated by the observer  33   i , in place of the actual secondary torque deviation τ_err_act and the secondary torque deviation velocity dτ_err_act as the temporal change rate thereof calculated using the estimated value of the actual secondary torque τ_act sequentially calculated by the secondary torque detecting unit  13   f . Therefore, the control input (the desired torque τm_cmd) may be determined while reducing the influence of the disturbance component included in the estimated value of the secondary torque τ_act or the temporal change rate thereof. 
     Therefore, the robustness of the control of the secondary torque τ by the control device  30  may be improved further. 
     The corresponding relationship between the present embodiment explained above and the present invention will be supplemented. In the present embodiment, the observer  33   i  corresponds to the observer of the present invention. The corresponding relationship of the present embodiment and the present invention is the same as the third embodiment other than the above. 
     Modification 
     Subsequently, several modifications related to each embodiment will be explained. 
     In each embodiment, the actual secondary torque τ_act is calculated by multiplying the between-rotor angular difference calculated from the detected value of the rotational angle θin_act of the drive pulley  2  and the detected value of the rotational angle θout_act of the driven pulley  3  with the value (preset value or desired value) of the elastic deformation coefficient Ksp. 
     However, the secondary torque τ_act may be detected directly, by using an appropriate torque sensor configured from a strain gauge and the like. 
     Further, in each embodiment, the electric motor  5  is used as the actuator generating the driving force. However, an eclectic actuator other than the electric motor  5 , or an actuator of another type, such as a hydraulic actuator, may be used. 
     Further, in the third embodiment and the fourth embodiment, during the operational control of the power transmission device  21 , the switching hyperplane variable setting unit  33   g  determines the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 according to the desired elastic deformation coefficient Ksp_cmd, using above-mentioned expression (22) which is the predetermined arithmetic expression. 
     However, the time constant Tc (or the gradient of the switching hyperplane σ) corresponding the desired elastic deformation coefficient Ksp_cmd may be determined by preparing a map data on a plurality of the representative values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp and the time constant Tc (or the gradient of the switching hyperplane σ) respectively corresponding thereto, and using the map data. 
     In this case, in the case where the desired elastic deformation coefficient Ksp_cmd coincides with any of the representative values Ksp_i, then the time constant Tc (or the gradient of the switching hyperplane σ) corresponding to the representative value Ksp_i in the map data may be determined as it is as the time constant Tc (or the gradient of the switching hyperplane σ) corresponding to the desired elastic deformation coefficient Ksp_cmd. 
     Further, in the case where the desired elastic deformation coefficient Ksp_cmd does not coincide with any of the representative values Ksp_i, then the time constant Tc (or the gradient of the switching hyperplane σ) corresponding to the desired elastic deformation coefficient Ksp_cmd may be determined by an interpolation calculation based on the map data. 
     Further, in the first embodiment and the second embodiment, the gradient of the switching hyperplane σ=0 is preliminarily determined by using the intersection on the trajectory of a plurality of the response characteristic data obtained by experiment (or simulation). 
     Similarly, in the second embodiment and the third embodiment, the gradient of the switching hyperplane σ=0 corresponding to each of a plurality of the representative values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp are determined by using the intersection on the trajectory of a plurality of the response characteristic data obtained by experiment (or simulation), in order to obtain the arithmetic expression (22) used to determined the time constant Tc (or the gradient) corresponding to the gradient of the switching hyperplane σ during operational control of the power transmission device  21 . 
     However, in the first embodiment and the second embodiment, the gradient of the switching hyperplane σ=0 may be determined by a method other that the method explained in the first embodiment, as long as the gradient of the switching hyperplane σ=0 is set so that the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 becomes equal to or larger than the specific time constant Tcx calculated by the expression (22). 
     For example, the gradient of the switching hyperplane σ=0 may be determined so that the time constant Tc corresponding to the gradient of the switching hyperplane σ=0 becomes equal to or larger than the specific time constant Tcx calculated by the expression (22), by appropriately adjusting the weight coefficient of the evaluation function in the method of optimum control. 
     Furthermore, in the third embodiment and the fourth embodiment, the gradient of the switching hyperplane σ=0 may be determined by a method other that the method explained in the first embodiment, when determining the gradient of the switching hyperplane σ=0 corresponding to each of a plurality of the representative values Ksp_i (i=1, 2, . . . , M) of the elastic deformation coefficient Ksp. 
     Further, in each embodiment, the power transmission between the drive pulley  2  and the driven pulley  3  is performed via the wire  4  as the elastic deformation member. However, the elastic deformation member connecting the two elements such as the pulleys  2 ,  3  (between the primary element and the secondary element) so as to perform power transmission between the two elements may adopt various modes. 
     For example, the power transmission (rotation transmission) between two rotating elements as the primary element and the secondary element may be performed via a torsion bar as the elastic deformation member. 
     Further, in the case of performing the power transmission between the two rotational elements by the elastic deformation member with the rigidity thereof variable, for example a conductive polymer actuator may be adopted as the elastic deformation member. 
     For example, as is exemplified in  FIG. 13 , a driven rotational member  42  (the secondary element) is inserted into a hollow tubular portion  41   a , which is formed to a leading end portion of a driving rotational element  41 (the primary element). Thereafter, a power transmission between the driving rotational member  41  and the driven rotational member  42  may be performed via a conductive polymer actuator  43  (the elastic deformation member) provided between an outer circumferential surface of the driven rotational member  42  and an inner circumferential surface of the tubular portion  41   a.    
     In this case, the rigidity of the conductive polymer actuator  43  (and consequently the elastic deformation coefficient) may be changed to a desired rigidity, by changing a voltage applied to the conductive polymer actuator  43 . 
     Further, the power transmission device as the target of the present invention is not limited to those transmitting the rotational driving force, and may be of a configuration of transmitting a translational force accompanying a translational displacement of the primary element to the secondary element via the elastic deformation member. 
     Further, the elastic deformation member performing the power transmission between the primary element and the secondary element may have viscosity, in addition to being capable of deforming elastically. 
     In this case, it is preferable to determine the control input by the sliding-mode control, based on a state equation (a model of a power transmission system) taking the viscosity of the elastic deformation member into consideration. 
     For example, similar to the power transmission device  1  (or  21 ) shown in  FIG. 1  (or  FIG. 8 ), in the power transmission device performing the power transmission (the rotation transmission) between the drive pulley  2  and the driven pulley  3  via an appropriate elastic deformation member, in the case where the elastic deformation member has viscosity, then a behavior of the power transmission device may be modeled in the discrete system by a state equation of following expression (23). 
     
       
         
           
             
               
                 
                   
                     
                       
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                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     in 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     out 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     out 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                         ⁢ 
                         
                             
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     
                                       DT 
                                       / 
                                       Iin 
                                     
                                   
                                 
                                 
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     0 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             · 
                             
                               u 
                               ⁡ 
                               
                                 ( 
                                 
                                   n 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                             
 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           where 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         r 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                       
                       ≡ 
                       
                         K 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sp 
                           / 
                           I 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         r 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         out 
                       
                       ≡ 
                       
                         K 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sp 
                           / 
                           I 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         out 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       Cin 
                       ≡ 
                       
                         K 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           dmp 
                           / 
                           I 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       Cout 
                       ≡ 
                       
                         K 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           dmp 
                           / 
                           I 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         out 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     The meaning of θin, θout, Ksp, DT, Iin, and Iout in the expression (23) is the same as the expression (1). 
     Further, Kdmp corresponds to a viscosity coefficient of the elastic deformation member between both pulleys  2 ,  3 . More specifically, Kdmp is a change amount of a viscous force (in this case, a viscous force in a dimension of a torque) per unit change amount of relative angular velocity of the drive pulley  2  with respect to the driven pulley  3 . 
     Thereafter, after simplifying the expression (23) using above-mentioned expressions (3a), (3b), a state equation of following expression (24) is obtained, as a model expressing a behavior related to the secondary torque τ and the temporal change rate thereof (the secondary torque change speed) dτ of the power transmission device equipped with the elastic deformation member having viscosity between both pulleys  2 ,  3 . 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               τ 
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               d 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 τ 
                                 ⁡ 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           A 
                           ′ 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   d 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         
                           
                             B 
                             ′ 
                           
                           · 
                           u 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             n 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     where 
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       A 
                       ≡ 
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               DT 
                             
                           
                           
                             
                               
                                 
                                   
                                     - 
                                     rin 
                                   
                                   · 
                                   DT 
                                 
                                 - 
                                 
                                   rout 
                                   · 
                                   DT 
                                 
                               
                             
                             
                               
                                 1 
                                 - 
                                 
                                   Cin 
                                   · 
                                   DT 
                                 
                                 - 
                                 
                                   Cout 
                                   · 
                                   DT 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     B 
                     ≡ 
                     
                       [ 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               Ksp 
                               · 
                               
                                 DT 
                                 / 
                                 Iin 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     Therefore, the control input (the desired torque τm_cmd of the electric motor  5 ) by the sliding-mode control may be calculated by an expression in which A, B of above-mentioned expression (6) is substituted by A′, B′ defined by the where clause of expression (24).