離散型全程擬滑動模式控制器設計及其應用

Toward the Discrete-time Global Quasi-Sliding Mode Controller Design and Its Application

吳明(Wu, Ming)

指導教授 ： 陳建祥

國立清華大學/工學院/動力機械工程學系/博士(2015年)

摘要

本文主要目的在於推廣全程滑動模式至離散時間，因為在有限取樣時間下，必須放寬滑動模式為擬滑動模式，因此提出全程擬滑動模式之想法，提出廣義強制函數設計之三條件，使能夠全程沿著滑動平面作zigzag運動以擬滑動之行為朝相空間原點收斂，其次，為了改善zigzag運動所造成輸出控制力產生顫震現象，改用連續近似法取代傳統理想切換函數，並且針對傳統連續近似法所具有之缺點加以改善，用廣義平滑飽和函數取代，並提出一套利用等效D2小波濾波器以迫近濾波器的觀點根據系統取樣時間決定平滑區間。另外，為了探究全程滑動模式控制實際之可行性，本文將全程擬滑動模式控制器應用於不同硬體平台中，實驗驗證顯示，全程擬滑動行為與理論相符，系統狀態軌跡確實能夠全程沿著滑動平面以zigzag型式運動，最後採用廣義平滑飽和函數為基礎之連續近似法來替換傳統的線性飽和函數。從本文推廣的邊界層滑動模式理論顯示，廣義平滑飽和函數總是能夠覆蓋線性飽和函數，能夠使切換控制項輸出更多控制力，使得系統狀態軌跡收斂速率比採用線性飽和函數更快，並降低因全程擬滑動所產生的跳切現象，因此，廣義平滑飽和函數是平衡輸出控制力與系統響應速度之較佳選擇，使得全程擬滑動模式控制器能夠應用於實際硬體平台上。

關鍵字

全程擬滑動模式 ； 滑動平面 ； 平滑飽和函數 ； 強制函數 ； D2小波函數

並列摘要

A novel concept of global quasi-sliding mode control scheme which is extended from a global sliding mode control to establish a quasi-sliding motion that ensures a zigzag motion, which will directly move forward to the original phase portrait throughout the entire sliding dynamic response in discrete-time. The new design of an augmented forcing function is followed by three conditions extended from global sliding mode control. In order to reduce chattering phenomenon from zigzag motion, we also propose a redesign of continuous approximation with smooth saturation and utilize an equivalent D2 wavelet filter to decide smooth interval according to sampling time in system. Finally, in discrete time, we propose a global quasi-sliding mode approach for the different hardware platforms. The experimental results show that it matches global quasi-sliding mode theory and maintain zigzag motion throughout the entire response. And then generalized smooth saturation is adopted to ensure that switching control term will output more force and state response will be converge faster. Therefore, the switching function adopted generalized smooth function gsat(.) would be a balance between control force response and state response.

並列關鍵字

global quasi-sliding mode control scheme ； sliding surface ； smooth saturation function ； augmented forcing function ； D2 wavelet function

參考文獻

[2] V.I. Utkin, “Sliding Mode Control Design Principles and Applications to Electric Drives,” IEEE Transactions on Industrial Electronics, vol. 40, 1993, pp.23-36.

[3] V.I. Utkin, “Variable structure systems with sliding mode: a survey,” IEEE Transactions Automatic Control, vol. AC-22, no. 2, pp. 212-222, 1977

[4] E. Baily and A. Arapostathis, “Simple sliding mode control scheme applied to robot manipulator,” International Journal of Control, vol. 45, pp. 234-237, 1998.

[5] J. Wang, H.V. Brussel and J. Swevers, “Robust Perfect Tracking Control With Discrete Sliding Mode Controller,” Journal of Dynamic Systems, Measurement, and Control, vol. 125, no. 1, pp. 27, 2003.

[6] W.C. Yu, G.J. Wang and C.C. Chang,“Discrete sliding mode control with forgetting dynamic sliding surface” Mechatronics, vol. 14, no. 7, pp. 737-755, 2004.