AAE 666 Final Project

1. AAE 666 Final Project Disturbance Gain Analysis of Electric Drive System on Wheelchair Chuck Sullivan 4/30/2005 CJS AAE 666 Final Project

2. 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 CJS AAE 666 Final Project

3. 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) CJS AAE 666 Final Project

4. 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: Disturbance gain from estimation from Lyapunov equation Disturbance gain from through simulation of state space representation LMI characterization of gain Comparison of these techniques to detailed model simulation CJS AAE 666 Final Project

5. Disturbance Gain Estimation for Electric Wheel Chair Drive System Representation DC machine system relationships (open loop) Using , after simplification: CJS AAE 666 Final Project

6. Disturbance Gain Estimation for Electric Wheel Chair Drive System Representation With IR drop compensation Using into previous equations: CJS AAE 666 Final Project

7. Disturbance Gain Estimation for Electric Wheel Chair Drive System Parameters radius=.178 m GR=15.46 Jmot=.00106 kg*m^2 J=GR^2*Jmot kg*m^2 Bmot=.46/1000 Nm/rpm Btot=GR^2*Bmot = 1.05 Nm/(rad/sec) Mrider=100 Mchair=40 Mass=Mrider+Mchair = 140 kg Jgear=0 Jm=Mass*radius^2 = 4.426 kgm^2 Jtotal=J+Jgear+Jm/2 = 2.466 kgm^2 Kv=.059 Nm/A (V/(rad/sec)) R=.24 ohm factor=.8 Rest=factor*R L=.0002 CJS AAE 666 Final Project

8. Disturbance Gain Estimation for Electric Wheel Chair Drive Upper Bound Estimation For convolution system where impulse response “H” is L1, system is Lp stable with (AAE 666 Notes, Corless, p225) y = w (angular speed of wheel) u = TL (load torque) = disturbance H = transfer function y/u (output-to-noise) For standard state space representation (A,B,C,D), an upper bound for (Corless, notes): Where is any scalar for which is A.S., and (Lyapunov Equation) CJS AAE 666 Final Project

9. Disturbance Gain Estimation for Electric Wheel Chair Drive Upper Bound Estimation R_est is estimated armature resistance in control algorithm With R_actual fixed and known, assess disturbance gain due to inaccuracy of R_est during IR Drop Compensation control operation Strategy for analysis: Choose various % error values for R_est For each value of R_est, apply , check ( ) Solve Lyapunov equation for  = disturbance gain Minimization problem: choose such that Lyapunov equation is feasible and is minimized. CJS AAE 666 Final Project

10. Disturbance Gain Estimation for Electric Wheel Chair Drive Upper Bound Estimation Example, norm vs. for R_est = .95 R_actual CJS AAE 666 Final Project

11. Disturbance Gain Estimation for Electric Wheel Chair Drive Upper Bound Estimation Minimization results: CJS AAE 666 Final Project

12. Disturbance Gain Estimation for Electric Wheel Chair Drive “True” y = w (angular speed of wheel) u = TL (load torque) = disturbance as input H = transfer function y/u (output-to-noise) An alternate approach to find an upper bound for (From time simulation): CJS AAE 666 Final Project

13. Disturbance Gain Estimation for Electric Wheel Chair Drive “True” Comparison to Lyapunov equation technique for Strategy for analysis: Choose various % error values for R_est For each value of R_est, simulate alternate state space in Simulink Steady state output value = CJS AAE 666 Final Project

14. Disturbance Gain Estimation for Electric Wheel Chair Drive “True” Time simulation vs. Lyapunov minimization: CJS AAE 666 Final Project

15. Disturbance Gain Estimation for Electric Wheel Chair Drive LMI Characterization of L gain(chapter 18, AAE 666 Notes, Corless) y = w (angular speed of wheel) u = TL (load torque) = disturbance as input Non-linear model (motor armature resistance Vs temperature) Background: suppose symmetric P  0, scalars 0, 1,2 0 such that (18.7, 18.8 AAE 666 Notes, Corless) Then, (18.9, 18.10 AAE 666 Notes, Corless) CJS AAE 666 Final Project

16. Disturbance Gain Estimation for Electric Wheel Chair Drive LMI Characterization of L gain (chapter 18 Notes) Approach u = TL (load torque) = disturbance as input Take x0 = 0, disturbance gain normalized around steady state equilibrium point For this application, D=0 LMI applied to non-linear system (temperature effects modeled) Now, effect of temperature on motor armature resistance: For 25T 125: CJS AAE 666 Final Project

17. Disturbance Gain Estimation for Electric Wheel Chair Drive LMI Characterization of L gain(chapter 18 Notes) (continued….) Finally Then, CJS AAE 666 Final Project

18. Disturbance Gain Estimation for Electric Wheel Chair Drive LMI Characterization of L gain (chapter 18 Notes) Using LMI Toolbox Fix R_est, determine A1,A2 (i.e. Actual R varies with temp.) Adjust  to minimize  Results: CJS AAE 666 Final Project

19. Disturbance Gain Estimation for Electric Wheel Chair Drive Time Simulation of IR Drop Compensation y = w (angular speed of wheel) u = TL (load torque) = disturbance as input Establish steady state operation, then apply load, quantify change in speed CJS AAE 666 Final Project

20. Disturbance Gain Estimation for Electric Wheel Chair Drive Time Simulation of IR Drop Compensation CJS AAE 666 Final Project

21. Disturbance Gain Estimation for Electric Wheel Chair Drive Time Simulation of IR Drop Compensation Results: CJS AAE 666 Final Project

22. Disturbance Gain Estimation for Electric Wheel Chair Drive Time Simulation of IR Drop Compensation L gain Results (Vs LMI) R_estimate fixed at .95 R_actual @ 25C R_actual simulated at 25C, 125C R_estimate = .66 R_actual @ 125C CJS AAE 666 Final Project

23. Disturbance Gain Estimation for Electric Wheel Chair Drive Summary Demonstrating a few different analysis techniques from class, the disturbance gain was characterized for IR Drop Compensation control on an electrically driven wheel chair. Disturbance was treated as input, and disturbance gain Vs R_estimation inaccuracy was analyzed using: estimation using Lyapunov equation and minimization: estimation from state space simulation LMI characterization of gain of non-linear system System time simulation CJS AAE 666 Final Project

24. Disturbance Gain Estimation for Electric Wheel Chair Drive Summary (cont.) System exhibits good disturbance rejection, even for very inaccurate estimation of R_armature Methods showed similar trends and values, as disturbance gain was minimized for more accurate R_estimate values (near 95% of actual armature resistance) Assuming system model is complete and accurate  estimation methods (Vs simulation) proved viable but with some measurable deviation (future investigation?) Various techniquestoestimate disturbance gain demonstrated decent correlation CJS AAE 666 Final Project