KimDiscreteSM - Jung-ho Kim Seung-Hyun Oh Dong-il `Dan Cho...

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Jung-ho Kim Seung-Hyun Oh Dong-il ‘‘Dan’’ Cho e-mail: [email protected] School of Electrical Engineering and Computer Science, Seoul National University, San 56-1, Shinlim-dong, Kwanak-ku, Seoul 151-742, Korea J. Karl Hedrick Department of Mechanical Engineering, University of California, Berkeley, CA 94720 Robust Discrete-Time Variable Structure Control Methods The invariance and robustness properties of variable structure control are lost in digital implementation. This paper presents three discrete-time variable structure control (DVSC) methods that can recover those properties for linear uncertain systems. The first method uses a disturbance compensator formulated in the variable structure framework and a decoupling law to separate the disturbance estimation dynamics from the closed loop dynamics. In the second approach, a recursive switching function is developed, which allows recovering the lost invariance and robustness properties, without using the disturbance compensator. The first method can result in slow transient dynamics, and the second can result in a large overshoot. In the third method, a new recursive switching function is developed and combined with the decoupled disturbance compensator method to recover the lost invariance and robustness properties. The three DVSC methods are applied to control the motion of an xy-stage of a CNC milling machine. In this experi- ment, the third method provided the best result. @ S0022-0434 ~ 00 ! 02204-8 # 1 Introduction One of the most attractive features of the variable structure control ~ VSC ! method is invariance and robustness to uncertain- ties including modeling errors and external disturbances. This is achieved by assuming that infinitely fast switching between two different control structures is possible, and that the uncertainties are bounded and matched. The invariance property implies that the so-called sliding mode is invariant to matched uncertainties. The robustness property implies that the reaching condition is always satisfied for bounded and matched uncertainties, and the system states are confined on a sliding surface. However, VSC controllers implemented in discrete time may not have those desirable properties because of the finite sampling time. The limited sampling frequency makes control input con- stant between two sampling intervals. This means that when sys- tem dynamics cross the sliding surface between sampling inter- vals, the control input cannot immediately take measures to make the system remain on the sliding surface. Therefore, in discrete- time variable structure control ~ DVSC ! , system states cannot re- main on the sliding surface, but can remain in a neighborhood of the sliding surface. Because the invariance property is achieved when the system states are in sliding mode occurring on the slid- ing surface, the invariance property may break down in DVSC.
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KimDiscreteSM - Jung-ho Kim Seung-Hyun Oh Dong-il `Dan Cho...

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