Patent Publication Number: US-6217131-B1

Title: Method and device for controlling a vehicle braking system in open loop

Description:
FIELD OF THE INVENTION 
     The present invention relates to a method and a device for controlling a vehicle braking system in open loop. 
     BACKGROUND INFORMATION 
     One demand on the closed-loop control system of a vehicle braking system is the correct adjustment of the clearance (air gap) between the brake pad and the brake disc. In the classic hydraulic brake, gaskets provide for the withdrawal of the piston in the pressureless state, and thus for the lifting of the brake pads. In connection with the electromechanical brake, in which the brake application is effected, e.g., by an electric motor, the clearance must be actively adjusted by sending the current through the actuator in the negative direction. Motor-vehicle wheel brakes operated by electric motors are known, for example, from PCT Publication No. WO 94/24453 or German Published Patent Application No. 19 526 645. The size of the clearance cannot be detected by a braking-torque or braking-force sensor. Therefore, the clearance is adjusted on the basis of a path signal (travel path of the brake pads), e.g., based on a motor rotational angle, which is in relation to the travel path of the brake pads as defined by a fixed characteristic curve. In this context, the exact knowledge of the zero path or of the zero angle, at which the brake pads just contact the brake disc, is important. Furthermore, if the intention is to use only one controller for the braking torque or the braking force, the correlation between the path variable and the controlled variable is crucial. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to specify measures by which this zero variable and/or this correlation can be ascertained. 
     The design approach, described in the following, sets forth a reliable, precise procedure for determining the zero path or the zero angle at which the brake pads have in fact just contacted or just released the brake disc or brake drum. 
     This zero variable is known at any time by the estimation, so that a reliable clearance adjustment is also possible after brakings at rest and/or additional test brakings for identification of the zero variable. The need for a scanning to the zero point is eliminated. so that no time is lost in adjusting the clearance. The described procedure estimates the zero point at any instant on the basis of the braking-torque signal or the brake-application force signal and the path or angle signal, it being possible to adjust the clearance quickly and correctly even after a quick-stop braking. 
     Because of the pronounced offset drift of the torque or force sensor, as well as due to appearances of wear, and temperature influences, it cannot be assumed that the contact angle of the brake pads with the disc will not change during a braking. Furthermore, a faulty and/or drift-affected angle measurement can invalidate the result. These influences are taken into account by the constant estimation of the zero point. A constant adjustment of the torque or force sensor takes place, errors in detecting the path or angle are compensated, and characteristic curves which represent the characteristic properties of the brake are adapted. 
     In this manner, a quick and accurate clearance adjustment is made possible, even using a closed-loop braking-torque control, in all operating states, i.e., at standstill, as well. 
     If an open-loop control of the wheel brakes is carried out within the framework of a closed-loop braking-moment or braking-force control using a single controller, the described procedure ensures that the correlation between the measured path signal and the torque- or force signal, used in so doing, is constantly adapted. In this manner, the open-loop control is improved above all with a view to the comfort during braking (no sudden change during the switch-over from the measured value to a calculated) and during the adjustment of the clearance. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a synoptic block diagram of a braking system having application of the brakes by an electric motor according to the present invention, using a wheel pair as an example. 
     FIG. 2 shows a flow chart of a braking-torque controller for a wheel brake. 
     FIG. 3 shows, by way of example, the variation of the torque/angle characteristic curve. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 shows a synoptic block diagram of a braking system having application of the brakes by an electric motor, using a wheel pair as an example. This wheel pair could be allocated to one axle or to a diagonal of the vehicle. The vehicle brake pedal is represented by  10 . The driver&#39;s braking input is detected using sensor system  12  by measuring the angle, path and/or force, and is fed via lines  14  to an electronic control system  16 . In one advantageous layout, this control system is composed of decentrally distributed control units. Sensor system  12 , as well as, at least partially, electronic control system  16 , are redundantly designed. The electronic control system actuates electric motors  22  and  24  via output lines  18  and  20 , for example, by a pulse-width-modulated voltage signal, using an H-bridge output stage. In one advantageous exemplary embodiment, commutator direct-current motors are used. The electric motors  22 ,  24  are part of brake actuators  26  and  28 . The rotatory movements of these motors  22 ,  24  are converted in the downstream gear stages  58  and  60  into translatory movements which lead to displacements of brake pads  30  and  32 . The brake pads are guided in calipers  34  and  36  and act on brake discs  38  and  40  of wheels  1  and  2 . Moreover, in one preferred exemplary embodiment, provision is made for an electrically operable spring-powered brake, with whose aid the brake actuator  26 ,  28  can be retained in the prevailing position, so that the associated electric motor  22 ,  24  can be switched into the currentless state. The position of the brake actuator  26 ,  28  is then retained without energy consumption. 
     Employed at each wheel  1 ,  2  are force or torque sensors  42  and  44 , whose signals are fed to electronic control system  16  via measuring lines  46  and  48 . In one design variant, the axial supporting forces of the actuators  26 ,  28  during a braking process are measured by these sensors  42 ,  44 , and thus form a measure for the normal forces acting on the brake discs  38 ,  40 . This variant is named in the following force measurement. Therefore, understood by braking force is the force with which the brake shoes press against the brake disc or drum. In another design variant, the radial supporting forces of the brake pads are measured, and thus form a measure for the friction forces or their friction moments occurring in the brake discs  38 ,  40 . This measurement—as well as the use of a direct torque sensor—is designated in the following as torque measurement. In addition, the wheel speeds are detected using sensors  50  and  52 , and are transmitted to control system  16  via input lines  54  and  56 . Provision is further made for angular-position sensors  62  and  64 , whose signals are fed to control system  16  via lines  66  and  68 . In one preferred exemplary embodiment, these angular-position sensors are Hall-effect sensors which, for example, detect the revolution of the electric motor  22 ,  24  of the associated brake actuator  26 ,  28  and deliver several pulses per revolution, the number of pulses being a measure for the angle covered, and thus for the path covered. In other exemplary embodiments, other sensors (e.g. variable-inductance sensing elements, potentiometers, etc.) are used for measuring the path or angle. 
     Setpoint values for the individual wheel brakes or groups of wheel brakes are determined in electronic control system  16  from the detected braking input provided by the driver, in accordance with pre-programmed families of characteristics. For example, these setpoint variables correspond to the braking torques or braking forces to be adjusted at a wheel or a wheel pair  1 , 2 , whose quantities are a function, inter alia, of the axle load distribution of the vehicle. From the ascertained, possibly wheel-individual setpoint values, system deviations are determined by comparison with the actual values of the braking forces or braking torques measured in sensors  42  and  44 , the system deviations being fed to controller algorithms, for example, in the form of time-discrete PID (proportional-plus-integral-plus-derivative controllers) controllers. The controlled variable of this controller is used to drive the electric motors  22 ,  24 , with corresponding drive signals being output via lines  18  and  20 . The point of time for the clearance adjustment is at the end of a braking process. 
     FIG. 2 shows a flow diagram of an example of a controller structure for a wheel brake having a torque controller. The following described procedure is used in the preferred exemplary embodiment in conjunction with such a controller structure. In other embodiments, different structures are used, as well. For example, the following described procedure can also be used when the clearance is adjusted within the framework of a closed-loop angle or position control (zero-point determination as described in the following); the control of the braking process is carried out as a closed-loop torque or braking-force control. 
     Actuating angle β of the brake pedal  10  is detected using sensors  12  shown in FIG.  1 . On the basis of characteristic curve  100 , which represents a desired pedal-path/braking-torque characteristic, a braking-torque setpoint value MVOR is determined from the actuating angle of the brake pedal. In one preferred exemplary embodiment, characteristic curve  100 , i.e., the desired pedal-path/braking-torque characteristic, is predefined in such a way that a negative braking-torque setpoint selection results in the range of the released brake pedal. The meaning of the negative braking-torque setpoint value at an actuating angle 0 of the brake pedal, i.e., given a released brake pedal, is the setpoint selection of a predetermined clearance adjustment. 
     During the travel of the vehicle, the application force of the brakes is adjusted within the framework of a closed-loop braking-torque control. The braking-torque setpoint value MVOR, ascertained from characteristic curve  100 , is fed as braking-torque setpoint value MSOLL to controller  102 . The controller includes a control algorithm, in one preferred exemplary embodiment, a control algorithm having a proportional component, an integral component, and a differential component having proven to be suitable. Controller  102 , as a function of setpoint variable MSOLL and of actual torque MIST, calculates a controlled variable U in accordance with the implemented control algorithm, controlled variable U being supplied to controlled system  104 , i.e., to the electrically operable brake actuator  26 ,  28 . Controlled system  104  is provided with measuring devices for ascertaining rotational angle (p of the rotor of the electric motor  22 ,  24 , as well as for ascertaining braking torque MIST′. The measured actual braking torque is fed back, via switching element  106 , as actual braking torque MIST to controller  102 . Switching element  106  transmits the measured braking-torque value as actual braking-torque value to controller  102  when the vehicle velocity exceeds a predefined limiting value. In this context, controller  102  brings the actual braking torque more into line with the braking-torque setpoint value, and thus with the driver input. 
     Traveling speed V is determined on the basis of at least one wheel speed according to known procedures. It is fed to a threshold switching element  108  which monitors for the undershooting of a predefined limiting value of, e.g., several kilometers per hour. If the traveling speed is above this limiting value, i.e., in the case of greater traveling speeds, switching element  106  remains in the position indicated, while if the traveling speed falls below the limiting value, a corresponding signal switches switching element  106  over into the position not shown. In this position, switching element  106  couples the calculated actual torque MIST″ to the actual torque MIST fed to the controller. 
     At low speeds in the range of standstill, braking-torque signal MIST′ is no longer correlated with the application force of the wheel brakes. Therefore, a torque signal, which was determined from at least the rotational angle of the electric motor  22 ,  24 , is coupled back to controller  102 . For this purpose, provision is made for a characteristic curve  110 , in which the rotational angle of the electric motor is converted into a braking torque MIST″. Used in so doing as the rotational angle is rotational angle Δφ, which is determined in node (estimator)  112  from rotational angle φ, measured at controlled system  104 , and zero angle φ0 which exists when the brake pads  30 ,  32  are lifted off from the disc or drum. The difference between these two variables forms the absolute rotational angle Δφ which is fed to characteristic curve  110 . Zero angle φ0 and/or characteristic-curve parameters h are estimated by estimator  112  in accordance with measured rotational angle φ and measured braking torque MIST′ within the framework of the following described procedure. 
     If the conditions (block  115 ) exist for a clearance adjustment, switching element  116  is closed. The conditions are, e.g., released brake pedal  10  (e.g. negative torque input), and motor rotational angle φ being in the range of zero angle φ0. A component M1 which, on the basis of a characteristic curve  124 , is linked to rotational angle Δφ, is connected to setpoint torque MVOR. Thus, if the conditions for the clearance adjustments are present, then the setpoint torque is varied on the basis of the motor rotational angle, and becomes 0 precisely when the adjusted motor rotational angle corresponds to the desired clearance. If the rotational angle is too great (positive Δφ), then, as a result of the superimposition of M1, the setpoint torque is reduced, so that a negative system deviation at the input of controller  102  leads to a negative output voltage, and thus to a removal of the brake pads  30 ,  32  of the brake disc or drum. In the case of rotational angles which are too small, i.e., given negative Δφ, the process is reversed. 
     The accuracy of characteristic curve  110  and the determination of zero angle φ0 are crucial for the functioning method and the comfort of such a closed-loop control. 
     FIG. 3 shows various motor-angle braking-torque characteristic curves of the actuator. The measured braking torque M (corresponds to MIST′) is plotted over measured angle φ. Characteristic curve  1  shows a situation with low pad wear, average temperature, and non-existing sensor offset; characteristic curve  2   a  shows a situation with great pad wear, average temperature, and non-existing sensor offset; characteristic curve  2   b  shows a situation with great pad wear, low temperature, and non-existing sensor offset; characteristic curve  2   c  shows a situation with great pad wear, high temperature, and non-existing sensor offset; characteristic curve  3  shows a situation with average pad wear, average temperature, and negative sensor offset; characteristic curve  4   a  shows a situation with very great pad wear, average temperature and positive sensor offset; characteristic curve  4   b  shows a situation with very great pad wear, low temperature, and positive sensor offset; characteristic curve  4   c  shows a situation with very great pad wear, high temperature, and positive sensor offset. 
     One is able to see the great variation of the characteristic curves as a function of the variables indicated, which makes it necessary to adapt the characteristic curve to the changing marginal conditions for optimal control. 
     In one approximation, the characteristic curve can be represented as a quadratic equation, a compression or elongation of the characteristic curve being obtained on the basis of the temperature influence, a horizontal shift being obtained on the basis of the pad wear or a temperature-caused thickening of the brake disc  38 ,  40 , and a vertical shift of the characteristic curve being obtained on the basis of the sensor offset. Yielded thus is: 
     
       
           M=m   temp   *s   0 *(φ absolut −φ0) 2   +M   offset   (1)  
       
     
     where M=braking torque 
     s0=brake-specific constant 
     φ0=zero angle 
     φ absolute =rotational angle 
     m temp =factor by which the characteristic curve is compressed or elongated based on the brake-specific constant 
     M offset =sensor offset error 
     If there is no brake-pad wear, no temperature stress and no offset drift, the braking-torque characteristic is a function of the motor rotational angle, based on the following equation: M=S 0 *φ absolut ) 2 . Since both the rotational angle and the braking torque (or the application force) are measured, the missing parameters can be estimated from these variables. In principle, there are two possibilities in doing this, an offline or an online estimation. In the offline estimation, the parameters sought are estimated from a number of measuring results. In the online estimation, at each step, a new correction vector, which is composed both of the newest measuring results and the previous estimating result, is added to the estimating result as well. 
     The offline estimation shall be described first. 
     Yielded from equation 1 is: 
     
       
           M=m   temp   ·s   0 ·φ absolut 2−2· m   temp   ·s   0 ·φ 0 · absolut +( m   temp   ·s   0 ·φ 0   2   +M   offset )   (2)  
       
     
     If several series of measurements are included, then the following matrix equation results:                              [           M   1             ⋮             M   n           ]                    M   _           =                          [             s   0     ·     ϕ     absolut   1     2               -   2     ·     s   0     ·     ϕ     absolut   1             1           ⋮       ⋮       ⋮               s   0     ·     ϕ     absolut   n     2               -   2     ·     s   0     ·     ϕ     absolut   n             1         ]          ·               Φ   _                                            [           m   temp                 m   temp     ·     ϕ   0                     m   temp     ·     s   0     ·     ϕ   0   2       +     M   offset             ]                    p   _                         (   3   )                         
     If matrix Φ is not quadratic, then equation 3 cannot be resolved in this form, since it is under-defined for n&lt;3, and over-defined for n&gt;3. However, for the case of n&gt;3, a regression parabola can be created, so that a weighting criterion is minimized. If an error vector e is introduced, then equation (3) can be resolved as follows: 
     
       
           e=M−Φ·p   (4)  
       
     
     Thus, it is now only necessary to find a suitable criterion for the minimization of the error. For example, this criterion can be the sum of the error squares. 
     
       
           I=Σe   i   2   =e   T   ·e   (5)  
       
     
     
       
           I= ( M−Φ·p ) T ·( M−Φ·p )=( M   T   −p   T Φ T )( M−Φ·p )= M   T   M− 2 M   T   Φp+p   T Φ T   Φp    (6)  
       
     
     For minimization, the first partial derivative is formed and set at zero.                  ∂   I       ∂     p   _         =           -   2            Φ   _     T          M   _       +     2          Φ   _     T          Φ   _            p   _     ^         =     0   _               (   7   )                         
     Thus, following for the estimation {circumflex over (p)} is: 
     
       
           {circumflex over (p)} =(Φ T Φ) −1 Φ T   M=Φ   +   M   (8)  
       
     
     Therefore, the multiplication of the pseudo-inverse matrix Φ +  by the measuring vector M is yielded as the solution for the estimation vector {circumflex over (p)}. The unknown variables φ0, m temp , and Moffset can then be calculated from the estimation vector. 
     In the following, the online estimation is described more precisely. 
     A recursive calculation of the parameters presents itself for operation in the vehicle, in order to constantly adjust the parameters during operation as well. The recursive solution can be derived from the offline method, by writing equation (8) for the kth instant and expanding it to the k+1-th instant. 
     
       
           {circumflex over (p)} ( k )=(Φ T ( k )Φ( k )) −1 Φ T ( k ) M ( k )  (9)  
       
     
     In this case, the matrices Φ and M are composed as follows:                  Φ   _          (   k   )       =     [             s   o     ·         ϕ   absolut          (   1   )       2               -   2     ·     s   o     ·       ϕ   absolut          (   1   )             1           ⋮       ⋮       ⋮               s   o     ·         ϕ   absolut          (   k   )       2               -   2     ·     s   o     ·       ϕ   absolut          (   k   )             1         ]             (   10   )                   M   _          (   k   )       =     [           M        (   1   )               ⋮             M        (   k   )             ]             (   11   )                         
     or for the next sampling step:                        Φ   _          (     k   +   1     )       =     [             Φ   _          (   k   )                     s   0     ·         ϕ   absolut          (     k   +   1     )       2       -       2   ·     s   0     ·       ϕ   absolut          (     k   +   1     )                       1             ]                 =     [             Φ   _          (   k   )                   φ   _          (     k   +   1     )             ]                   (   12   )                   M   _          (     k   +   1     )       =     [           M        (   k   )                 m        (     k   +   1     )             ]             (   13   )                         
     Thus, valid for the parameter vector in the next step is: 
     
       
           {circumflex over (p)} ( k+ 1)=(Φ T ( k+ 1)Φ( k+ 1)) −1 Φ T ( k+ 1) M ( k+ 1)   (14)  
       
     
     By multiplying out the part outside of the round brackets, yielded finally with equations (12) and (13) is: 
     
       
           {circumflex over (p)} ( k+ 1)=(Φ T ( k+ 1)Φ( k + 1)) −1 ·(Φ T ( k ) M ( k )+φ T ( k+ 1) m ( k+ 1))   (15)  
       
     
     From equation (8), one obtains: 
     
       
         Φ T ( k ) M ( k )=(Φ T ( k )Φ( k )) {circumflex over (p)} ( k )  (16)  
       
     
     If equation (16) is inserted into equation (15), one obtains: 
     
       
           {circumflex over (p)} ( k+ 1)=(Φ T ( k+ 1)Φ( k+ 1)) −1 ·(Φ T ( k )Φ( k ) {circumflex over (p)} ( k )φ T ( k+ 1) m ( k+ 1))   (17)  
       
     
     In this case, the following transformation can be carried out:                            Φ   _     T          (     k   +   1     )              Φ   _          (     k   +   1     )         =         [             Φ   _          (   k   )                   φ   _          (     k   +   1     )             ]     T          [             Φ   _          (   k   )                   φ   _          (     k   +   1     )             ]                   =       [           Φ   _     T          (   k   )                           φ   _     T          (     k   +   1     )         ]          [             Φ   _          (   k   )                   φ   _          (     k   +   1     )             ]                   =             Φ   _     T          (   k   )              Φ   _          (   k   )         +           φ   _     T          (     k   +   1     )              φ   _          (     k   +   1     )                         (   18   )                         
     or 
     
       
         Φ T ( k )Φ( k )=Φ T ( k+ 1)Φ( k+ 1)−φ T ( k+ 1)φ( k+ 1)   (19)  
       
     
     Yielded thus with equations (19) and (17) is: 
     
       
           {circumflex over (p)} ( k+ 1)=(Φ T ( k+ 1)Φ( k+ 1)) −1 ·(Φ T ( k+ 1)Φ( k+ 1) {circumflex over (p)} ( k )−φ T ( k+ 1)φ( k+ 1) {circumflex over (p)} ) k )+φ T ( k+ 1) m ( k+ 1))   (20)  
       
     
     
       
           {circumflex over (p)} ( k+ 1)= {circumflex over (p)} ( k )+(Φ T ( k+ 1)Φ( k+ 1)) −1 φ T ( k+ 1)·( m ( k+ 1)−φ( k+ 1) {circumflex over (p)} ( k ))   (21)  
       
     
     For simplification, the column vector q is introduced. 
     
       
           q ( k° 1)=(Φ T ( k + 1)Φ( k+ 1)) − φ T ( k+ 1)  (22)  
       
     
     Following thus is: 
     
       
           {circumflex over (p)} ( k+ 1)= {circumflex over (p)} ( k )+ q ( k+ 1)·( m ( k+ 1)−φ( k+ 1) {circumflex over (p)} ( k ))  (23)  
       
     
     However, according to equation (4), the term in the brackets represents precisely the estimate of the model error, which is calculated with the assistance of the parameter vector estimated one step before. 
     
       
           ê ( k+ 1)= m ( k+ 1)−φ( k+ 1) {circumflex over (p)} ( k )  (24)  
       
     
     Resulting therefore for the parameter estimate vector is 
     
       
           {circumflex over (p)} ( k+ 1)= {circumflex over (p)} ( k )+ q ( k+ 1)· ê ( k+ 1)  (25)  
       
     
     Thus, the parameter estimate vector for the k+1-th step is calculated from the estimate vector of the last sampling step, the weighting vector q and the estimate of the model error. q can be calculated as known, in simplified manner, according to the following schema:                  q   _          (     k   +   1     )       =           P   _          (   k   )                φ   _     T          (     k   +   1     )           1   +         φ   _          (     k   +   1     )              P   _          (   k   )                φ   _     T          (     k   +   1     )                     (   26   )                         P ( k+ 1)= P ( k )− q ( k+ 1)φ( k+ 1) P ( k )  (27) 
     Thus, a recursive online estimation of the parameter vector can be carried out with the assistance of equations (26), (27), (24) and (25). 
     The estimation can be improved by a weighting of the working point. Usually, the characteristic curve will not be as noisy in the high torque range as in the lower range; therefore, the measured values at high torques should be weighted more strongly. In addition, the introduction of a forget factor presents itself, so that errors which are brought in have less and less effect during progressive estimation. In this case, an estimation according to the IV method known from the literature would provide a solution. 
     The weighting vector q in equation (26) is calculated from the covariance matrix P, as well as from the new measured value of the motor rotational angle φ. In the following, the new measured value should not go directly into the weighting vector, but rather a calculated value φ b  (equation 30 and 31), which is derived from the previously determined estimate values, should be used as weighting. In this manner, the error due to a disturbed signal is reduced. This holds true primarily when one of the two measured signals exhibits a better signal-to-noise ratio than the other. Assuming the torque signal is the signal having the greater reliability, the result is:                  q   _          (     k   +   1     )       =           P   _          (   k   )              w   _          (     k   +   1     )           1   +         φ   _          (     k   +   1     )              P   _          (   k   )              w   _          (     k   +   1     )                     (   28   )                         
     w being composed as follows:                  w   _          (     k   +   1     )       =     [             s   0     ·     ϕ   b   2                   -   2     ·     s   0     ·     ϕ   b               1         ]             (   29   )                         
     where 
     
       
           m ( k+ 1)= w ( k+ 1) T   ·{circumflex over (p)}   h ( k )  
       
     
     and                      p   _     ^     h          (   k   )       =     [               p   ^     1          (   k   )                     p   ^     2          (   k   )                     p   ^     3          (   k   )             ]             (   30   )                         
     the result for angle φ b  is:                ϕ   b     =           s   0     ·         p   ^     2          (   k   )         +           (       s   0     ·         p   ^     2          (   k   )         )     2     -       s   0     ·         p   ^     1          (   k   )       ·     (           p   ^     3          (   k   )       -     m        (     k   +   1     )         )                 s   0     ·         p   ^     1          (   k   )                   (   31   )                         
     In this case, auxiliary estimate vector {circumflex over (p)} h (k) is composed recursively from the finally calculated value, as well as from the last estimate of the parameter vector. The weighting is effected with variable γ, which should lie in the range between 0 and 1: 
     
       
           {circumflex over (p)}   h ( k )=(1−γ)· {circumflex over (p)}   h ( k− 1)+γ· {circumflex over (p)} ( k− 1)  (32)  
       
     
     Also valid is 
     
       
           ê ( k+ 1)= m ( k+ 1)−φ( k+ 1) {circumflex over (p)} ( k )  (33)  
       
     
     
       
           {circumflex over (p)} ( k+ 1)= {circumflex over (p)} ( k )+ q ( k+ 1)· ê ( k+ 1)  (34)  
       
     
     
       
         
           
             
               
                 
                   
                     
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                   ) 
                 
               
             
           
         
         
         
             
         
       
     
     In this case, σ represents the forget factor, which can be changed depending on the working point. It is suggested to increase the forget factor at high torques, since it must be expected that this range will be less disturbed than the range of low braking torques. The factor should lie in the range between 0.95 and 0.99. 
     It is also necessary in the case of recursive estimate methods that the system be appropriately excited. Given low excitation, no reliable statement can be made about the estimate parameters. If the system is not excited, then, in the extreme case, one would have k value pairs for the identification of the parameters which all would have been recorded in response to the same braking torque. Since in this case, the rank of matrix Φ coincides on 1, (all lines of the equation are contingent linearly upon one another), an estimate of the parameters sought is not possible. Therefore, either the forget factor is increased in response to a strong excitation, while it is reduced in response to low excitations, or the estimate is discontinued during static braking phases, and is only started again in response to dynamic operations. 
     With the assistance of these methods, it is possible during a braking to calculate the parameters for determining the clearance, and to detect and compensate for the offset drift of the torque sensor  42 ,  44 , as well. 
     Besides ascertaining a rotational-angle signal, in other embodiments, the method is also used for a path measurement (e.g., measuring the path of the brake pads  30 ,  32 ). 
     In addition to utilization for an electromechanical brake, this procedure can also be used for adjusting the clearance in the case of other braking systems, e.g., for electrohydraulic or electropneumatic brakes which are provided with the appropriate sensors.