A H(subscript∞) Tracking-Based Adaptive Sliding-Mode Controller for Nonlinear Pneumatic Path Tracking Systems via a Functional Approximation Approach

以具H(下標 ∞)追蹤及函式近似法之適應性滑動模式控制器實現氣壓伺服系統之軌跡追蹤控制

江茂雄(Mao-Hsiung Chiang) ； 李聯旺(Lian-Wang Lee) ； 郭中豐(Chung-Feng Jeffrey Kuo) ； 陳義男(Yih-Nan Chen)

《中國機械工程學刊》 30卷2期 (2009/04) Pp. 83-94

https://doi.org/10.29979/JCSME.200904.0002

摘要

氣壓伺服系統具時變及高度非線性，不易得到準確之數學模式進行滑動模式控制器設計，本文旨在發展具H(下標∞)追蹤及函式近似法之適應性滑動模式控制器，實現氣壓伺服系統之軌跡追蹤控制，本控制器以Fourier級數之函式近似法估測未知函數，故可省略精確之數學模式，以H(下標∞)追蹤結合適應性滑動模式控制器，可使控制器避免估測誤差、未考慮到之動態及干擾所造成之影響，因此，無需數學模式及試誤法進行控制器設計及估測函式選擇。以Lyapunov函數進行穩定性分析。此外，本文所發展之控制器可藉由H(下標∞)追蹤控制器改善滑動模式控制器之嚴重不連續振顫問題。最後，本文以實驗驗證所發展之具H(下標∞)追蹤及函式近似法之適應性滑動模式控制器，實現於無桿氣壓缸組成之氣壓伺服系統的軌跡追蹤控制。

並列摘要

It's difficult for pneumatic actuator systems to fit into an accurate dynamic model for model-based sliding-mode control design because of the nonlinear and time-varying characteristics. The objective of this research is to develop a new H(subscript ∞) tracking-based adaptive sliding-mode controller for nonlinear pneumatic actuator systems. The controller initially uses a Fourier series-based functional approximation to reach an unknown function so as to circumvent the prerequisites of the models. The H(subscript ∞) tracking technique can then be incorporated into an adaptive sliding-mode control method to protect the derived controller from approximated errors, un-modeled dynamics and disturbances. Thus, system dynamic models are not necessary for achieving the proposed controller design with H(subscript ∞) tracking performance and trial-and-error is not required to select an approximation function. System stability is ensured through the new laws for the coefficients of the Fourier-series functions which are derived from a Lyapunov function. In addition, the serious chattering problem can be reduced through the projected H(subscript∞)tracking-based adaptive sliding-mode controller control method by means of the H(subscript∞) tracking controller in comparison with the Fourier series-based adaptive sliding-mode controller. Consequently, the practical experiments on a rodless pneumatic servo system are successfully implemented with different path tracking profiles, which validates the proposed method.

並列關鍵字

Adaptive control ； H(subscript∞) tracking ； sliding-mode control ； nonlinear ； approximation technique ； rodless pneumatic servo control ； path tracking control and Fourier series