A Study of Transformed Lur''e Problem for Sliding Mode Control and Chattering Reduction

• Main Authors: Lin, Ming-Jye, 林明傑
• Other Authors: Ching-Yei Chung
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/91142531508296591396

碩士 === 逢甲大學 === 自動控制工程研究所 === 84 === The primary objective of this thesis is to present that the sliding control can be transformed as a frequency-domain Lur''e problem and to eliminate the chattering phenomenon. The traditional sliding mode is often performed by the state space approach. In the formulation, it is shown that with the classical nonlinear sign function,the sliding mode control can only quarantee the overall system stable but not asymptotically stable. We prove that if thenonlinear sign function contains a hysteresis loop,even it is very small,there will exist ahigh frequency and small amplitude limit cycle. This coincides theso- called "chattering phenomenon" in the sliding mode control. In the conventional sliding mode control, the relative degree of the chosensliding surface is usually one. This paper addresses a general class of slidingsurface whose relative degree is no- longer restricted to one. We show that whenthe relative degree is more than two,it is inevitable that there exists a limitcycle for the nonlinear sign function.Even in the case of relative degree two,the system reveals zero degree phase margin. However, these disadvantages can be remedied by introducing a suitable boundary layer width for the nonlinear saturation function that ensures global,exponential stability of the overall system.