Internal Model Control for Assisting Unit of Wheeled Walking Frames

1. Internal Model Control for Assisting Unit of Wheeled Walking Frames 報 告 者: 蔡 耀 德 授課老師: 曾 慶 耀 出 處: 2004 IEEE

2. 大綱 • 1.INTRODUCTION • 2.IMPLEMENTATION FOR SPEED CONTROL ASSISTING UNIT OF WHEELED WALKING FRAME • 3.CONTROL SYSTEM DESIGN FOR ASSISTING UNIT • 4.MODELING AND CONTROL DESIGN • 5.CONCLUSION

3. 1.INTRODUCTION • Inthe aging society of recent years, the expectation for the wheeled walking frames increases. Wheeled walking frames are supporting equipments, to he used by elderly people or handicapped in rehabilitation. • The control application to speed control of wheeled walking frames technology would he challenging by using the GIMC design structure with LQ control

4. 2.IMPLEMENTATION FOR SPEED CONTROL ASSISTING UNIT OF WHEELED WALKING FRAME

6. 3.CONTROL SYSTEM DESIGN FOR ASSISTING UNIT 3.1 Problem Formulation Consider the linear time invariant system with disturbance as follows The closed-loop system is obtained as follows • The internal model of the closed-loop system is described as follows

7. 3.2 Limiting Properties of LQ Control and Observer

8. The closed-loop system with the limiting feedback gain has disturbance decoupling property like Lemma 1 [Lemma 1] The closed-loop system (1) with Fe, can arrive at a disturbance decoupled system, that is, the following statement holds

9. Now shown by using the limiting property of the LQR [Lemma 2] Suppose that the minimum phase system (A, B,C) has a block diagonal interactor matrix as follows: By choosing the optimal feedback law with the limiting feedback The closed-loop system can arrive at a decoupled system such that

10. Finally we show the limiting property of observers [Lemma 3] For the system (A,D,C) , the state observer is described as follows:

11. 3.3 Property of Two-Degree-of-Freedom Servo System using Stabilizing Controller • Propose the generalized IMC with servo compensation shown in Fig . The proposed method is based on a two-degree-of-freedom servo system using an observer-based Stabilizing Controller.

12. The error equation is obtained by • The augmented system is given

13. We clarify the limiting properties of the augmented system [Property 1] Suppose the system (A, B. C) is minimum phase. If the system has a block diagonal interactor matrix, then the transfer function from reference input r to output y is arrived at as .Thus the closed loop system isarrived at the approximate decoupled system [proof] By choosing and from Lemma 2 [Remark] Not able to obtain for the following augmented system However, if the input signal is limited to step input, then the closed loop system with LQ control achieves astatic decoupled system.

14. Next, we obtain the disturbance decoupling property for the augmented system . In this case, the disturbance is not limited to the step disturbance [Property 2] Suppose the system ( A , B,C) is minimum phase. The closed loop system can immediately arrive at disturbance decoupled system by multiplicative of the disturbance decoupling property of the IMC design structure and the disturbance decoupling property of LQ control [proof] from Lemma 1 from Lemma 3

15. [Property 3] [proof]

16. Finally, we show numerical examples to confirm the proposed properties. confirm validity of the disturbance decoupling control in Property 2 and the disturbance estimation in Property 3, respectively.

17. 4.MODELING AND CONTROL DESIGN

19. 5.CONCLUSION • It proposed the generalized internal model control with servo compensation based on LQ control, and the experimental results showed that the generalized IMC with servo compensation is effective on speed control of the assisting unit for the wheeled walking frame.

20. THE END Thanks for your patient !!!