Patent Publication Number: US-9834414-B2

Title: System and method for controlling elevator door systems

Description:
FIELD OF INVENTION 
     This invention relates generally to elevator systems, and more particularly to controlling elevator door systems. 
     BACKGROUND OF INVENTION 
     Automatic sliding doors used in high performance elevators must meet various operating regulations. For example, to protect against wedging, it is required that a maximal movement energy of all parts connected together mechanically do not exceed a preset maximum value (for example 10 joules) at a mean closing speed. This requirement sets an upper limit value for the mean closing speed. On the other hand, short door closing times are a prerequisite for good transport performance in high performance elevators. The mass of the elevator doors is related to the kinetic energy of the elevator door system, and, thus, needs to be determined. 
     Similarly, a control module in the elevator door system controls the motion of the elevator door using an electric motor as an actuator. To improve ride comfort of passengers, it is desirable to operate the elevator door movement smoothly. Hence, the control module needs to reduce vibration and noise while opening and closing the elevator door. The control module controls the motion of the elevator door according to at least the mass of the elevator door, which also necessitates the knowledge of the mass of the doors. 
     Different methods have been used to determine the mass of the doors in the elevator system. For example, one method weighs the doors of the elevator system before commissioning the elevator system. However, the weight of the door can change over time in many cases. For example, customers may change the decoration of the doors that affect its weight. Thus, there is a need to determine the mass of the elevator door online during the operation of the elevator system. 
     Another method estimates the mass of the elevator door based on a linear static model, which represents the relationship between a translational acceleration of the door and a torque of the electric motor moving the door. However, the linear static model fails to capture various physical factors affecting the movement of the door. For example, the linear static models do not take into consideration friction forces affecting dynamics of the elevator door system, and thus can produce an inaccurate estimation of the door mass. In addition, the existing methods generally estimate the mass of the elevator doors offline. 
     SUMMARY OF INVENTION 
     Some embodiments of the invention are based on recognition that the mass of the doors and/or other parameters of the elevator door system can be recursively estimated by analyzing and utilizing dynamic behavior of the door system. For example, a comparison between performances of the elevator door system estimated based on a model of the door system and measured during the operation of the door system can be used to determine parameters of the model, such as a mass of the elevator door. However, the dynamics of the elevator door system are complex and the model of the door system includes high order differential equations and numerous model parameters. To that end, identification of all parameters of the model necessarily requires persistent excitation conditions of the operation of the door system, which can lead to undesirable vibration. Therefore, it is impractical to perform parameter identification of the full model parameters of the elevator door system based on routine operations of the door system. 
     Some embodiments of the invention are based on another recognition that it is possible to concurrently reduce the order of the model of the elevator door system and reduce the complexity of the measured signal by filtering out the harmonics not represented by the reduced order model. In such a manner, the complexity of the calculation is reduced without significant drop in accuracy, but the reduction of the complexity allows estimation of the parameters of the system in real time. 
     For example, the frequency response of the reduced order model can approximate a dominant frequency response of a higher order model of the door system. The approximation reduces the number of parameters to be identified to a subset of dominant parameters of the higher order model. For example, the reduced order model can be a second order model. However, the model reduction results in the mismatch between harmonics of the signal representing the actual operation of the door system and harmonics of the frequency response of the reduced order model, which can lead inaccurate estimation of the parameters of the reduced order model. Accordingly, some embodiments of the invention remove the undesirable harmonics of the signal absent from a frequency response of the reduced order model to match the harmonics of the filtered signal to the frequency response of the reduced order model. Such a joint reduction allows recursively updating parameters of the reduced order model by reducing an error between filtered measured signals and signals estimated on the basis of the reduced order model with updated parameters. 
     Accordingly, one embodiment of an invention discloses a method for controlling an operation of a door system of an elevator system arranged in a building. The method includes controlling the operation of the door system using one or combination of parameters of a reduced order model of the door system, wherein the operation includes moving at least one door of the door system; measuring a signal representing the operation of the door system; filtering the measured signal by removing at least one dynamic of the measured signal absent from a frequency response of the reduced order model of the door system; and updating parameters of the reduced order model of the door system to reduce an error between the filtered signal and an estimated signal of the operation estimated using the updated reduced order model of the door system, wherein the parameters of the reduced order model include a mass parameter and a friction parameter. The steps of the method are performed by a processor. 
     Another embodiment discloses an elevator door system, including a motor and a pulley; a cabin door guarding an entrance to an elevator car; a landing door guarding an entrance to an elevator shaft, wherein the motor drives the pulley to move the cabin door using a belt, and wherein the cabin door is mechanically connected to the landing door for a period of time during an operation of the elevator door system; sensors for measuring a signal representing the operation of the door system; a filter for filtering the signal by removing at least one dynamic of the measured signal absent from a frequency response of a reduced order model of the elevator door system, wherein the frequency response of the reduced order model approximates a dominant frequency response of a higher order model of the door system; and a controller for controlling the operation of the elevator door system using the reduced order model of the elevator door system, wherein the controller updates parameter of the reduced order model to reduce an error between the filtered signal and an estimated signal of the operation estimated using the updated reduced order model of the door system. 
     Yet another embodiment discloses a method for controlling an operation of a door system of an elevator arranged in a building, wherein the door system includes a motor, a pulley, an elevator door guarding an entrance to an elevator car and a floor door guarding an entrance to a floor of the building, wherein the motor drives the pulley to move the elevator door, and wherein the elevator door is mechanically connected to the floor door when the elevator car stops at the floor of the building to move the floor door. The method includes controlling the operation of the door system for an operating cycle using one or combination of parameters of a reduced order model of the door system, wherein the operating cycle includes one or combination of opening and closing the elevator and the floor doors; measuring a signal of the operation of the door system; filtering the signal by removing at least one dynamic of the measured signal absent from a frequency response of the reduced order model of the door system, wherein the frequency response of the reduced order model approximates a dominant frequency response of a higher order model of the door system; and updating parameters of the reduced order model of the door system to reduce an error between the filtered signal and a signal of the operation estimated using the updated reduced order model of the door system, wherein the parameters of the reduced order model include a mass parameter and a friction parameter. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a block diagram of a door system of an elevator according to some embodiments of an invention; 
         FIG. 1B  is a schematic of components of an elevator door system arranged to control the movement of the elevator doors according to another embodiment of the invention; 
         FIG. 2  is a block diagram of a method for controlling an operation of a door system according to one embodiment of the invention; 
         FIG. 3A  is a block diagram of the elevator door system according to one embodiment of the invention; 
         FIG. 3B  is a block diagram of an online parameter identifier according to one embodiment of the invention; 
         FIG. 3C  is a block diagram of a method for controlling the operation of the elevator door system according to one embodiment of the invention; 
         FIG. 4A  is a block diagram of a method for reducing an order of the model of the elevator door system according to one embodiment of the invention; 
         FIG. 4B  is an example of the full model of the elevator door system determined by one embodiment of the invention. 
         FIG. 4C  is a Hankel singular value plot  420  of the frequency analysis of the model of the system used by some embodiments of the invention; 
         FIG. 4D  is a plot with frequency responses of the full elevator door system model and a second order model according to one embodiment of the invention; 
         FIG. 4E  is a schematic of the reduced order model of the elevator door system according to one embodiment of the invention 
         FIG. 5A  is a block diagram of the parameter estimation method according to one embodiment of the invention; 
         FIG. 5B  is a block diagram of a method for filtering the signal in time domain according to one embodiment of the invention; 
         FIG. 6  is a block diagram of a method of one embodiment of parameter estimation for cases where values of model parameters of the elevator door system switches at certain times; and 
         FIG. 7  is a block diagram of a method for parameter estimation according to another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS OF INVENTION 
       FIG. 1A  shows a block diagram of a door system  100  of an elevator according to some embodiments of an invention. The door system  100  includes a controller  10 , which is connected to a motor  20  and to a hand terminal  40 . Further, the door system  100  includes a two-part cabin door  50  and balancing weights  70 . Landing doors  60 , which are arranged at various floors to guard the elevator shaft, are mechanically connected to the cabin door  50  of the elevator car  80 . For example, the cabin door can have a clutch mechanism that unlocks and moves the landing door at each floor. 
       FIG. 1B  shows a schematic of components of an elevator door system arranged to control the movement of the elevator doors according to another embodiment of the invention. The components include an electric motor (M)  101 , pulleys  102 , a belt  103  and a coupling mechanism  105  between the belt  103  and the elevator door  104 . The electric motor  101 , controlled by a control module (C)  109  according to signals measured by sensors (S)  108  and operation commands (U)  110  from passengers, rotates and drives the pulleys  102 , which consequently generates a translational movement of the belt  103 . The moving belt further leads to the translational movement (open or close) of the elevator door  104  through the coupling mechanism  105 . The elevator door moves along the rails  106  and rollers  107 . Alternative embodiments use different implementations of the elevator door system. For example, the doors of the elevator door system can be implemented as a single door leaf, a double door leaf and a rolling door with closing and opening directions in any desired positions. 
     Some embodiments of the invention are based on recognition that the mass of the doors and/or other parameters of the elevator door system can be recursively estimated by analyzing and utilizing dynamic behavior of the door system. For example, a comparison between performances of the elevator door system estimated based on a model of the door system and measured during the operation of the door system can be used to determine parameters of the model, such as a mass of the elevator door. 
     However, the dynamics of the elevator door system are complex and the model of the door system includes high order differential equations and numerous model parameters. For example, the full model of the elevator door system can include eight first order differential equations (DEs), i.e., an eighth order model. To that end, identification of all parameters of the model necessarily requires persistent excitation conditions of the operation of the door system, which can lead to undesirable vibration. The persistent excitation conditions typically cannot be satisfied during routine operation of the door system. Therefore, it can be difficult to perform parameter identification of the full model of the elevator door system based on routine operations of the door system. 
     Some embodiments of the invention are based on another recognition that it is possible to concurrently reduce one order of the model of the elevator door system and reduce the complexity of the measured signal by filtering out the harmonics not represented by the reduced order model. Estimation of model parameters can be performed by comparing the reduced order model and the filtered measured signals according certain criteria. The reduced order model parameters can be estimated from routine operation of the door system. In such a manner, not only the complexity of the calculation is reduced without significant drop in accuracy, but also the reduction of the complexity allows estimation of the parameters of the system in real time. 
     For example, the frequency response of the reduced order model can approximate a dominant frequency response of a higher order model of the door system. The approximation reduces the number of parameters to be identified to a subset of dominant parameters of the higher order model. For example, the reduced order model can be a second order model. However, the model reduction results in the mismatch between harmonics of the signal representing the actual operation of the door system and harmonics of the frequency response of the reduced order model, which can lead to inaccurate estimation of the parameters of the reduced order model. Accordingly, some embodiments of the invention remove the undesirable harmonics of the measured signal absent from a frequency response of the reduced order model so that the harmonics of the filtered signal match the frequency response of the reduced order model. Such a joint reduction allows recursively updating parameters of the reduced order model by reducing an error between filtered measured signals and signals estimated by the reduced order model with updated parameters. 
       FIG. 2  shows a block diagram of a method for controlling an operation of a door system of an elevator arranged in a building according to one embodiment of the invention. The steps of the method are performed by a processor of, e.g., a processor of the control module  109 . The embodiment controls  202  the operation of the door system, e.g., according to an operation command  201 , using one or combination of parameters of a reduced order model  200  of the door system and a measured signal  203  representing the operation of the door system. For example, the parameters of the reduced order model include a mass parameter and a friction parameter. The signal can be a torque of a motor for moving the door and/or an acceleration of the movement of the door. The operation command  201  can be received from passengers of the elevator or an external system. The operation includes movement of at least one door of the door system. 
     The embodiment filters  204  the measured signal by removing at least one dynamic of the measured signal absent from a frequency response of the reduced order model of the door system. The frequency response of the reduced order model approximates a dominant frequency response of a higher order model of the door system, and the filtering matches the harmonics of the filtered signal to the frequency response of the reduced order model. Next, the embodiment updates  205  parameters of the reduced order model of the door system to reduce an error between the filtered signal and a signal of the operation estimated using the updated reduced order model of the door system. In some implementations of the embodiment, the parameters are updated recursively. Also, the filtering  204  can produce the filtered signals for the updating  205 . 
       FIG. 3A  shows a block diagram of the elevator door system according to one embodiment of the invention. In this embodiment, a controller  302  and motor drives  303  are components for controlling  202  the operations of the elevator door system. The elevator door system also includes sensors  304  for measuring  203  the signals reflecting the operation of the elevator door system, a processor executing an online parameter identifier  301  module for determining parameters of the reduced order model of the elevator door system. 
     For example, the controller  302  determines the commands for the motor drives, represented by desired voltages or currents of the electric motor, according to the parameters of the reduced order model of the elevator door system, measured signals  312 , and the operation command  201 . The measured signals  312  can include a position signal from an encoder of the electric motor, and current signals of the electric motor from current sensors. Current signals can be used to compute a torque signal which is generated by the electric motor to drive the elevator door. 
       FIG. 3B  shows a block diagram of the online parameter identifier  301  according to one embodiment of the invention. The online parameter identifier  301  filters the measured signal  312  by an order reduction filter  321  to produce a filtered position and a filtered torque signal  331  which are further applied as inputs of a high bandwidth low pass filter  322  to produce a filtered acceleration, a filtered velocity, a second filtered position, and a second filtered torque signal  332 . 
     A parameter identifier  323  updates and outputs parameter  311  of the reduced order model based on the filter signals  332 . For example, the parameter identifier  323  solves a least squares problem to reduce the error between the filter signal and an estimated signal of the operation estimated using the updated reduced order model of the door system. For example, the parameter identifier solves a least squares problem reducing the error between an estimated position of the door and the filtered position of the door, between an estimated acceleration of the door and the filtered acceleration of the door, between an estimated velocity of the door and the filtered velocity of the door, and between an estimated torque of the motor and the filtered torque of the motor. 
       FIG. 3C  shows a block diagram of controlling operation of the elevator door system according to one embodiment of the invention. The parameters  311  determined by the online parameter identifier  301  are used by a trajectory generator  351  to plan a smooth trajectory  361  of the elevator door for each mode of the operation, e.g., close or open the door, to suppress vibration and noise. The trajectory  361  is a set of points describing the position/velocity of the elevator door over time, and uniquely defines how the elevator door moves for each cycle of close/open operation. The parameter estimates  311  can also be used by a tracking controller  352  that generates control commands to the motor drives so that the actual movement of the elevator door tracks the planned trajectory  361  in real-time. 
     In some implementations, the trajectory generator uses the updated parameters  311  for planning the entire cycle of the trajectory. In contrast, the tracking controller can use the parameters  311  updated for each time step of the control, e.g., as fast as the online parameter identifier  301  outputs the updated parameters. The trajectory generator can also use the update parameters  311  for each step of the control for updating the trajectory  361 . 
     Some embodiments of the invention concurrently reduce the order of the model of the elevator door system that allows estimation of the parameters of the system in real time. For example, a higher order model of the door system is simplified such that the frequency response of the reduced order model approximates a dominant frequency response of the higher order model of the door system. 
       FIG. 4A  shows a block diagram of a method for reducing order of the model of the elevator door system according to one embodiment of the invention. The embodiment constructs  411  the full model  401  of the elevator door system  100  based on several assumptions, as described below. Then the frequency analysis  402  is conducted  412  based on the full elevator door system model  401  to produce  413  a simplified second order system model  403 . In some embodiments, the frequency analysis includes elimination of non-dominant and isolated harmonics  405  from the frequency response of the full elevator door system model  404 . 
       FIG. 4B  shows an example of the full model  401  of the elevator door system determined by one embodiment of the invention by treating belts as springs  410 ,  411 ,  412 ,  413  and by treating pulley  415 ,  416  and elevator door panels  417 ,  418  as rigid body. 
     Assuming no slip between pulleys and the belt, a full elevator door system model can be written as follows
 
 M   r   {umlaut over (x)}=k   1 ( Rθ   r   −x   r )+ c   1 ( R{dot over (θ)}   r   −{dot over (x)}   r )+ k   2 ( Rθ   l   −x   r )+ c   2 ( R{dot over (θ)}   l   −{dot over (x)}   r )+ k   r   x   r   +C   r   {dot over (x)}   r ,
 
( M   l   +M   n ) {umlaut over (x)}   l   =k   4 ( Rθ   l   −x   l )+ c   4 ( R{dot over (θ)}   l   −{dot over (x)}   l )+ k   3 ( Rθ   r   −x   l )+ c   3 ( R{dot over (θ)}   r   −{dot over (x)}   r )+ k   l   x   l   +c   l   {dot over (x)}   l ,
 
 J   r {umlaut over (θ)} r   =Rk   3 ( x   1   −Rθ   r )+ Rc   3 ( {dot over (x)}   r   −R{dot over (θ)}   r )+ Rk   1 ( x   r   −Rθ   r )+ Rc   1 ( {dot over (x)}   r   −R{dot over (θ)}   r )+ T,  
 
 J   l {umlaut over (θ)} l   =Rk   2 ( x   r   −Rθ   l )+ Rc   2 ( {dot over (x)}   r   −Rθ   l )+ Rk   4 ( x   l   −Rθ   l )+ Rc   4 ( {dot over (x)}   l   −R{dot over (θ)}   l ),
 
where T is the motor torque, M is the mass of the elevator door panels, J is the inertia of the pulleys, x is the position of the elevator door panels, θ is the rotation angle of pulleys, and subscripts r and l represent the right and left, respectively, and dots represent derivatives.
 
     With k i =k j ,c i =c j , 1≦i,j≦4, the stiffness and damping coefficients, the 8th-order dynamics are further written in state space form 
                         x   .     1     =     x   5       ,     
     ⁢         x   .     2     =     x   6       ,     
     ⁢         x   .     3     =     x   7       ,     
     ⁢         x   .     4     =     x   8       ,     
     ⁢                 x   .     5     =       ⁢       1     M   r       ⁢     (               -     (       2   ⁢     k   1       +     k   r       )       ⁢     x   1       -       (       2   ⁢     c   1       +     c   r       )     ⁢     x   5       +                   k   1     ⁢     R   ⁡     (       x   3     +     x   4       )         +       c   1     ⁢     R   ⁡     (       x   7     +     x   8       )                 )         ,                 =       ⁢       1     M   r       ⁢     (               -     (       2   ⁢     k   1       +     k   r       )       ⁢     x   1       +       k   1     ⁢     Rx   3       +       k   1     ⁢     Rx   4       -                   (       2   ⁢     c   1       +     c   r       )     ⁢     x   5       +       c   1     ⁢     Rx   7       +       c   1     ⁢     Rx   8               )         ,                   (   1   )                             x   .     6     =       ⁢       1       M   l     +     M   n         ⁢     (               -     (       2   ⁢     k   1       +     k   l       )       ⁢     x   2       -       (       2   ⁢     c   1       +     c   l       )     ⁢     x   6       +                   k   1     ⁢     R   ⁡     (       x   3     +     x   4       )         +       c   1     ⁢     R   ⁡     (       x   7     +     x   8       )                 )         ,                 =       ⁢       1       M   l     +     M   n         ⁢     (               -     (       2   ⁢     k   1       +     k   l       )       ⁢     x   2       +       k   1     ⁢     Rx   3       +                   k   1     ⁢     Rx   4       -       (       2   ⁢     c   1       +     c   l       )     ⁢     x   6       +       c   1     ⁢     Rx   7       +       c   1     ⁢     Rx   8               )         ,                                                   x   .     7     =       ⁢       1     J   r       ⁢     (               -   2     ⁢     k   1     ⁢     R   2     ⁢     x   3       -     2   ⁢     c   1     ⁢     Rx   7       +                   Rk   1     ⁡     (       x   1     +     x   2       )       +       Rc   1     ⁡     (       x   5     +     x   6       )       +   T           )         ,                 =       ⁢       1     J   r       ⁢     (               Rk   1     ⁢     x   1       +       Rk   1     ⁢     x   2       -     2   ⁢     k   1     ⁢     R   2     ⁢     x   3       +                   Rc   1     ⁢     x   5       +       Rc   1     ⁢     x   6       -     2   ⁢     c   1     ⁢     Rx   7       +   T           )         ,                                             x   .     8     =       ⁢       1     J   l       ⁢     (               -   2     ⁢     k   1     ⁢     R   2     ⁢     x   4       -     2   ⁢     c   1     ⁢     Rx   8       +                   Rk   1     ⁡     (       x   1     +     x   2       )       +       Rc   1     ⁡     (       x   5     +     x   6       )               )                       =       ⁢       1     J   l       ⁢     (               Rk   1     ⁢     x   1       +       Rk   1     ⁢     x   2       -     2   ⁢     k   1     ⁢     R   2     ⁢     x   4       +                   Rc   1     ⁢     x   5       +       Rc   1     ⁢     x   6       -     2   ⁢     c   1     ⁢     Rx   8               )         )     ,           ⁢     
     ⁢       y   =       (       x   1     ,     x   2       )     T       ,                             
where x 1 =x r ,x 2 =x l ,x 3 =θ r ,x 4 =θ l .
 
     Simplify the notation M l :M l +M n . The model (1) is abbreviated as follows
 
 {dot over (x)}=Ax+Bu,  
 
 y=Cx,   (2)
 
where x=(x 1 , . . . , x 8 ) T , and
 
     
       
         
           
             
               
                 
                   
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     The frequency analysis  402  performed by some embodiments demonstrates that the full elevator door system model can be reduced to a simplified second or forth order model. Moreover, such a reduced order model is sufficiently accurate for determining mass of the elevator door and other parameters of the elevator door system. As an example, one embodiment uses the following parameter values of the elevator door system during frequency analysis. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Notations 
               
            
           
           
               
               
               
            
               
                   
                 Notation 
                 Description 
               
               
                   
                   
               
               
                   
                 M r   
                 mass of right door 
               
               
                   
                 M l   
                 mass of left door and hall panel 
               
               
                   
                 J r   
                 inertia of right pulley 
               
               
                   
                 J l   
                 inertia of left pulley 
               
               
                   
                 R 
                 radius of pulleys 
               
               
                   
                 k 1   
                 belt stiffness 
               
               
                   
                 c 1   
                 belt damping 
               
               
                   
                 k r   
                 stiffness 
               
               
                   
                 c r   
                 damping between guide rail and door panels 
               
               
                   
                   
               
            
           
         
       
     
     In this case, M r , M l  are symmetric, thus y 1 =x r  and y 2 =x l  have the same transfer functions 
               G   ⁡     (   s   )       =       k   ⁡     (       s   2     +     ω   4   2       )             (       s   2     +     2   ⁢     ζ     1   ⁢     ω   1     ⁢   s         +     ω   1   2       )     )     ⁢     (       s   2     +     2   ⁢     ζ   2     ⁢     ω   2     ⁢   s     +     ω   2   2       )     ⁢     (       s   2     +     2   ⁢     ζω   3     ⁢   s     +     ω   3   2       )               
where k is a constant gain.  FIG. 4C  shows a Hankel singular value plot  420  of G(s) of the frequency analysis of the model of the system. Some embodiments are based on the following observation from the plot  420 . The part s 2 +ω 4   2  corresponds to a frequency which is far from the frequency of interest, the frequency characterizing important physical parameters of the door, and thus can be ignored. The first four states  421 ,  422 ,  423 , and  424  of the plot  420  have significantly larger energy than the other states. Therefore, the full elevator door system model can be reduced to 2nd or 4th order.
 
     The states  421  and  422  correspond to s 2 +2ζ 2 ω 2 s+ω 2   2 , and the states  423  and  424  correspond to s 2 +2ζ 1 ω 1 s+ω 1   2 . A transfer function including the four states, corresponding to a reduced forth order model, is 
     
       
         
           
             
               
                 G 
                 4 
               
               ⁡ 
               
                 ( 
                 s 
                 ) 
               
             
             = 
             
               
                 k 
                 
                   
                     ( 
                     
                       
                         s 
                         2 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                           ζ 
                           1 
                         
                         ⁢ 
                         
                           ω 
                           1 
                         
                         ⁢ 
                         s 
                       
                       + 
                       
                         ω 
                         1 
                         2 
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         s 
                         2 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                           ζ 
                           2 
                         
                         ⁢ 
                         
                           ω 
                           2 
                         
                         ⁢ 
                         s 
                       
                       + 
                       
                         ω 
                         2 
                         2 
                       
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
     The first two states  421  and  422  are far from the frequency range of, and thus ignored by some embodiments. The transfer function G(s) can be further reduced to a reduced second order model: 
     
       
         
           
             
               
                 G 
                 2 
               
               ⁡ 
               
                 ( 
                 s 
                 ) 
               
             
             = 
             
               
                 k 
                 
                   
                     ω 
                     2 
                     2 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         s 
                         2 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                           ζ 
                           1 
                         
                         ⁢ 
                         
                           ω 
                           1 
                         
                         ⁢ 
                         s 
                       
                       + 
                       
                         ω 
                         1 
                         2 
                       
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
       FIG. 4D  shows a plot with frequency responses of transfer functions G(s)  430 , G 2 (s)  432 , and G 4 (s)  434  showing that the full elevator door system model, without the coulomb friction effect, can be captured fairly well by a simplified second order model. The second order transfer function G 2  (s) represents a mass-spring-damper system:
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   1   x   2   −kx   1   +bu,  
 
 y=x   1 ,  (3)
 
with appropriate values of d 1 , k, b, wherein d 1 , k, b typically represent viscous damping coefficient, stiffness, and control gain constant, respectively.
 
     Some embodiments of the invention determine the parameters d 1 , k, b in the second order model. In addition, some embodiments establish a relationship between parameters d 1 , k, b and the parameters of the actual, i.e., physical, elevator door system, such as door mass. 
       FIG. 4E  shows a schematic of the reduced order model  440  of the elevator door system according to one embodiment of the invention. This embodiment used the following interpretation of frequency analysis results to approximate the relationship between the parameters of the model and actual parameters. First, the dynamics of the pulley are non-dominant, and can be omitted due to low energy in the 5-8 states in  FIG. 4B . Second, the belt can be treated as rigid body because the associated dynamics have a resonant frequency, which is much higher than (or isolated from) the dominant frequency. 
     Based on the aforementioned model reduction results, the order reduction filter is designed to remove harmonics with frequencies higher than the dominant frequency, but to keep the dominant frequency as much as possible. In one embodiment, the order reduction filter is a low pass filter. Given the knowledge of the dominant frequency (or the bandwidth of the low-pass filter), different signal processing methods are used by various embodiments to design the order reduction filter to preserve the dominant frequency according to the frequency analysis results. 
     According the frequency analysis, the mechanical sub-system of the elevator door system, if ignoring the coulomb friction effect, can be simplified as a second order mass-spring-damper system (3). With the coulomb friction effect, between door panels and its rails, modeled as −d 0  sgn(x 2 ) where sgn(.) is a sign function and sgn(x 2 )&gt;0 for x 2 &gt;0, one embodiment of the simplified second order model of the elevator door system is given as follows
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   0   −d   1   x   2   −kx   1   +bu,  
 
 y=x   1 ,  (4)
 
where x 1  and x 2  are the position and velocity of the elevator door, respectively, u is the control input (electric motor torque), d 0  denotes the static coulomb friction force, d 1  the viscous damping coefficient, k the stiffness, and b is the control gain constant. Note that assuming sgn(x 2 )&gt;0 is without loss of generality. All parameters d 0 ,d 1 &gt;0,k,b&gt;0 are unknown and to be identified. The model (4) is valid under the assumption that the linkage between the motor drive and the elevator door is rigid, i.e., no deformation or relative movement.
 
     Some embodiments assume parameters d 1 ,d 2  and b are the same during the opening and closing operations of the elevator door. Thus the sampled data whiling opening the door are useful to identify parameters d 1 ,d 0 ,k,b. 
     Another embodiment of the reduced order model is based on recognition that modelling the spring force as a linear function of the door position, i.e., kx 1  is inaccurate due to factors such as elastic belts. Accordingly, the embodiment address this issue in another simplified second model of the elevator door system as follows
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   0   −d   1   x   2   −k sat( x   1 )+ bu,  
 
 y=x   1 ,  (5)
 
where sat is a saturation function.
 
     Another embodiment further neglects the spring force from the model (4), which yields the following simplified second order model
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   0   −d   1   x   2   +bu,  
 
 y=x   1 ,  (6)
 
     In some implementations, the elevator door system has a switching feature due to different dynamics of movement of the cabin and the landing doors. That is, the model parameter values are different over different periods of time. If model (6) is appropriate for no-switching case, the switching dynamics and the corresponding reduced order model of the elevator door system for the switching case can be written as follows
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   01   −d   11   x   2   +b   1   u,  
 
 y=x   1 ,  (7)
 
for 0≦t≦t 1 , and
 
 {dot over (x)}   1   =x   2 ,
 
 {dot over (x)}   2   =−d   02   −d   12   x   2   +b   2   u,  
 
 y=x   1 ,  (8)
 
for t 1 ≦t≦t f , where t f  is the time duration of one open or close cycle of the elevator door, t 1  is the time instant when the switch happens.
 
     Some embodiments formulate model parameter estimation as a least squares problem. For example, the reduced second order model of the elevator door system of  FIG. 4E  can be further simplified under assumption of the symmetry of the elevator door system, i.e., k r =k l =0, M r =M l  and c l =c r . The symmetry of the elevator door system allows deriving the simplified second order model as follows
 
( MR   2   +J ){umlaut over ( x )}( t )= Ru+d   1   R   2   {dot over (x)}+R   2   d   0 ,  (9)
 
where x is the filtered position signal output from the order reduction filter, u the filtered motor torque signal output from the order reduction filter, M=M r +M l ,J=J r +J l ,d 1 =c l +c r  and d 0  captures the coulomb friction effect. Note that the simplified second order model in the form of (9) is equivalent to the form of (6), and the form (9) is suitable to formulate the parameter estimation as a least squares problem.
 
     The simplified second order model (9) can be rewritten as the following linear regression formula: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ¨ 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                 - 
                                 
                                   
                                     x 
                                     . 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 u 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         ︸ 
                         
                           Ψ 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           1 
                           
                             
                               MR 
                               2 
                             
                             + 
                             J 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     R 
                                     2 
                                   
                                   ⁢ 
                                   
                                     d 
                                     
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                                       ⁢ 
                                       
                                           
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
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                         ︸ 
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                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     A concise representation of the linear regression formula is
 
{umlaut over ( x )}( t )=Ψ( t )θ.
 
     With {umlaut over (x)}(t) and Ψ(t) measured or estimated, estimation of θ is reduced to a least squares problem 
     
       
         
           
             
               min 
               θ 
             
             ⁢ 
             
               
                 
                    
                   
                     
                       
                         x 
                         ¨ 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     - 
                     
                       
                         Ψ 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       θ 
                     
                   
                    
                 
                 2 
               
               . 
             
           
         
       
     
     Alternative linear regression form is 
     
       
         
           
             
               
                 
                   
                     u 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                 - 
                                 
                                   
                                     x 
                                     . 
                                   
                                   ⁡ 
                                   
                                     ( 
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                                     ) 
                                   
                                 
                               
                             
                             
                               
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                         ] 
                       
                       
                         ︸ 
                         
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                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             1 
                             R 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       R 
                                       2 
                                     
                                     ⁢ 
                                     
                                       d 
                                       
                                         0 
                                         ⁢ 
                                         
                                             
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       R 
                                       2 
                                     
                                     ⁢ 
                                     
                                       d 
                                       1 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
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                                       2 
                                     
                                     + 
                                     J 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         
                           ︸ 
                           θ 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Assuming u(t) and Ψ(t) are known, the parameter estimation is formulated as a least squares problem according to the linear regression formula (11). That is to find θ* by solving the following optimization problem: 
     
       
         
           
             
               min 
               θ 
             
             ⁢ 
             
               
                 
                    
                   
                     
                       u 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     - 
                     
                       
                         Ψ 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       θ 
                     
                   
                    
                 
                 2 
               
               . 
             
           
         
       
     
     Given linear regression formulas, numerous least squares (LS) or reclusive least squares (RLS) solvers can be used to produce estimates of θ, on the basis of which the physical parameter M,d 0 ,d 1  can be uniquely determined. However, inappropriate uses of existing estimation algorithms can result in inaccurate or biased estimation. 
     Accordingly, some embodiments modify least squares algorithms to accurately estimate parameters d 0 ,d 1 ,M from positions and/or torque measurements x and u. Because only the filtered door position x and the filtered motor torque u are measured, some embodiments reconstruct the filtered door acceleration {umlaut over (x)} and the filtered door velocity x from the measurements to form Ψ(t). A number of different filters are used by the embodiments to estimate {dot over (x)} and {umlaut over (x)} from x, such as sliding-mode-based filter and a high-gain-based filter. 
     One embodiment uses the high-gain-based high-bandwidth low pass filter G f  defined by following differential equations 
                     d   ⁢               d   ⁢           ⁢   t       ⁡     [           ξ   1               ξ   2               ξ   3           ]       =         [         0       1       0           0       0       1             -     λ   3               -   3     ⁢     λ   2               -   3     ⁢   λ           ]     ⁡     [           ξ   1               ξ   2               ξ   3           ]       +       [         0           0             λ   3           ]     ⁢       x   1     ⁡     (   t   )             ,     
     ⁢       x   ^     =     ξ   1       ,     
     ⁢         x   .     ^     =     ξ   2       ,     
     ⁢         x   ¨     ^     =     ξ   3             
where λ is the value of poles of the filter, and is taken much larger than the dominant frequency of the simplified second order model, e.g., λ&gt;100, {circumflex over (x)}=ξ 1  is the second filtered position, {dot over ({circumflex over (x)})}=ξ 2  is the filtered velocity, and {umlaut over ({circumflex over (x)})}=ξ 3  is the filtered acceleration.
 
     Alternative embodiment also applies the filter G f  to the electric motor torque to ensure that the equality of linear regression formula holds. The embodiment reconstructs the second filtered torque signal from u by the following filter (which has the exactly same expression as G f ) 
                     d   ⁢               d   ⁢           ⁢   t       ⁡     [           ζ   1               ζ   2               ζ   3           ]       =         [         0       1       0           0       0       1             -     λ   3               -   3     ⁢     λ   2               -   3     ⁢   λ           ]     ⁡     [           ζ   1               ζ   2               ζ   3           ]       +       [         0           0             λ   3           ]     ⁢     u   ⁡     (   t   )             ,     
     ⁢       u   ^     =     ζ   1             
where û=ζ 1  is the second filtered torque signal.
 
     Thus the aforementioned linear regression formulae (10) and (11) are rewritten as follows 
                 ξ   3     ⁡     (   t   )       =         [         1         -       ξ   2     ⁡     (   t   )                 ζ   1     ⁡     (   t   )             ]       ︸     Ψ   ⁡     (   t   )           ⁢           ⁢   θ               and                   ζ   1     ⁡     (   t   )       =         [         1         -       ξ   2     ⁡     (   t   )               ξ   3           ]       ︸     Ψ   ⁡     (   t   )           ⁢           ⁢   θ       ,         
respectively.
 
     The aforementioned least squares problem formulations assume measurement errors on the left hand side of (10) or (11), which can be suboptimal if the used sensors generating Ψ(t) are not of high quality. To that end, one embodiment formulates the model parameter estimation as a total least squares problem. That is, taking (11) as an example, instead of instead of solving (11), the embodiment solves the following problem 
                 min     θ   ,     δ   ⁢           ⁢     u   ⁡     (   t   )         ,     δΨ   ⁡     (   t   )           ⁢            [       δ   ⁢           ⁢     u   ⁡     (   t   )         ,     δΨ   ⁡     (   t   )         ]          p       ,     
     ⁢     subject   ⁢           ⁢   to                   u   +     δ   ⁢           ⁢   u       =       (     Ψ   +   δΨ     )     ⁢   θ           
where |[δu(t),δΨ(t)]| p  represents p—norm of the vector [δu(t), δΨ(t)]. Usually, p=2.
 
       FIG. 5A  shows a block diagram of the parameter estimation method according to one embodiment of the invention. This embodiment filters the measured signal not only in frequency domain  510  but also in a time domain  520  to further suppress the influence of the model mismatch and noisy measurements. This embodiment is based on recognition that a model mismatch between the filtered signals and the simplified second order model is mainly due to nonlinearity of friction effect at low velocity regions, i.e., and the noisy measurements happen during the region when sensed signals  312  have small amplitude, such that the values of the measured position/torque signals are below a corresponding threshold. 
     Thus, the embodiment can improve accurate estimation of model parameters by removing the samples of measurements corrupted by the model mismatch and sensor noises. Accordingly, the embodiment filters  510  the signal in a frequency domain to produce an intermediate signal  515  and filters  520  the intermediate signal in a time domain to produce the filtered signal  525 . 
       FIG. 5B  shows a block diagram of a step  520  for filtering the signal in time domain according to one embodiment of the invention. At each time step, a block  501  reads and sends intermediate signal  515  to block  502  testing if the sampled data is noisy based on the following criteria. If the amplitude of the filtered velocity is larger than a certain positive threshold THR V , the sampled data is acceptable for model reconstruction. Otherwise, the sampled data is noisy. In one implementation, the signal  515  is further processed in time domain by a block  503  which tests if the amplitude of the filtered acceleration is larger than a certain positive threshold THR A , otherwise, the sampled data is noisy. The resulted filtered signal  525  is used for iterative model-based signal estimation  530  and dynamic update  540  of the parameters of the model. The values of the threshold THR I , and threshold THR A  can be determined, e.g., based on sensor resolution, signal to noise ratio of output of the sensor, and operation condition of the door system. 
       FIG. 6  shows a block diagram of a method of one embodiment of parameter estimation for cases where values of model parameters of the elevator door system switches at certain times. To that end, in some embodiments, the parameters of the reduced order model of the door system include at least two sets of parameters switching at an instant of time during the operation. For example, the sets of parameters include a first set of parameters  601  and a second set of parameters  611 . The embodiment update  604  the first set of parameters  601  if the error  621  between the filtered signal  341  and the estimated signal of the operation estimated  602  using the reduced order model of the door system with the first set of parameters is below  603  a threshold. Otherwise, the embodiment updates  614  the second set of parameters. 
     Similarly, the embodiment update  614  the second set of parameters  611  if the error  631  between the filtered signal  341  and the estimated signal of the operation estimated  612  using the reduced order model of the door system with the second set of parameters is below  613  a threshold. Otherwise, the embodiment updates  604  the first set of parameters. 
       FIG. 7  shows a block diagram of a method for parameter estimation for cases where values of model parameters of the elevator door system switches at certain times according another embodiment of the invention. This embodiment determines the errors between the filtered signal and the estimated signal estimated with the first and with the second set of parameters and selects the parameters of the first or the second set of parameters as a set of parameters corresponding to a smaller error. 
     For example, the parameter updater #0, labeled  703 , estimates parameters based on a short memory of filtered signals  341  (one way to implement this is to use a small forgetting factor in standard recursive least squares algorithms). On the other hands, the parameter updaters #1/#2, labeled  701  and  702  respectively, estimate parameters based on a long memory of filtered signals  341  (one way to implement this is to use a large forgetting factor in standard recursive least squares algorithms). Using an output of parameter updater  703  as benchmark, outputs of blocks  701  and  702 , labeled as  711  and  712 , are compared to  713 , which yields absolute values  714  and  715  of error signals. A referee block  704 , based on absolute values of  714  and  715 , determines which parameter updater should run at the current step, and outputs decision signal as  716  to enable the parameter updater #1 or #2. One embodiment of output signal  711  is Ψ(k){circumflex over (θ)} 1  (k) with k the current time step and {circumflex over (θ)} 1  (k) the parameter estimates of parameter updater #1, when the estimation algorithm is based on the regression formula (11). Another embodiment of output signal  711  could be the estimated value of parameter, such as elevator door mass. 
     The embodiments of the present invention can be implemented in any of numerous ways. For example, the embodiments may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. Such processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component. Though, a processor may be implemented using circuitry in any suitable format. 
     Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments. 
     Also, the embodiments of the invention may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. 
     Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.