Disturbance Gain Estimation for Electric Wheel Chair 
                                          Drive
       Background
       
         Electric Drive propulsion for wheel chair, medical application 
         by Delphi Corporation (Kokomo IN, Flint MI)
       
         Chair consists of :
            
             Wheel chair chassis
            
             24V battery, electric drive motor on each rear wheel (2)
            
             Hand controller (joystick)
            
             Puff and Sip controller
            
             Central controller (motor controller, accessory controls)
       
         Electric propulsion
            
             DC motors and drives
            
             Control of dc motors
      09/11/22                       CJS AAE 666 Final Project                     2
           Disturbance Gain Estimation for Electric Wheel Chair 
                                          Drive
       Motivation
       
         2 main electric drive modes for motors
            
             Speed and current control with speed sensors
            
             IR drop compensation for operation without speed sensors
       
         Drivability in both modes is both a “quality of feel” and 
         safety issue
       
         IR drop compensation is target of stability and drivability (no 
         speed sensor)
            
             Stability and steady state gain due to driver command
            
             Disturbance rejection capability (obstacles , incline/decline 
            surfaces)
      09/11/22                       CJS AAE 666 Final Project                     3
             Disturbance Gain Estimation for Electric Wheel Chair 
                                                 Drive
         Objective
         
           Analyze disturbance rejection capability of wheel chair under 
           IR Drop Compensation control
         
           Application and demonstration of both linear and non-linear 
           analysis tools presented in class
         
           Analysis techniques:
                                             H
                 Disturbance gain from          estimation from Lyapunov equation
                                                1
               Disturbance gain from          tH     hrough simulation of state space    
                                                 1
                  representation                
              LMI characterization of        gain 
                                              L
              Comparison of these techniques to detailed model simulation         
                 
       09/11/22                             CJS AAE 666 Final Project                              4
                Disturbance Gain Estimation for Electric Wheel Chair 
                                                            Drive
          System Representation
          
             DC machine system relationships (open loop)
                 Using                             , after simplification:
                            T K i
                               e          T     a
                  dw                B                   K                 T
                        r            m w                T i            L
                    dt                J           r       J        a        J
                  di              r              K                   V
                      a  a i                     v w  a
                   dt             L a             L           r       L
        09/11/22                                      CJS AAE 666 Final Project                                          5
             Disturbance Gain Estimation for Electric Wheel Chair 
                                                Drive
        System Representation
        
          With IR drop compensation
                       V K w*i r
             Using                                            into previous equations:       
                          a        v      r     a    a
                                        
                 dwr       Bm          Kv                   1     
                                                 w                     T 
                   dt           J          J        r             0     L
                 di          K       r (k  1)  i          J        V 
                    a          v     a            a     0      0       
                  dt          L          L     
                V Kvw*                    K K
                        L       r             v       T
                                    wr
                ywr 1 0 
                                      i  
                                       a 
       09/11/22                            CJS AAE 666 Final Project                            6