On Robust, Multi-Input Sliding-Mode Based Control with a State-Dependent Boundary Layer

G. Herrmann, S. K. Spurgeon and C. Edwards
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G. Herrmann: University of Leicester
S. K. Spurgeon: University of Leicester
C. Edwards: University of Leicester

Journal of Optimization Theory and Applications, 2006, vol. 129, issue 1, No 6, 89-107

Abstract: Abstract This paper proposes a nonlinear multi-input control law using sliding mode concepts for continuous-time, uncertain, linear systems. The control law introduces a state-dependent layer around the sliding mode plane to remove chattering. This layer combines two types of boundary layers: a constant layer and a sector-shaped layer. The states will always enter the state-dependent boundary layer and the choice of the sliding mode will be seen to determine the ultimate system performance. A proof of stability shows ultimate boundedness. The controller is applied to a nonlinear simulation model of a cart-pendulum and exhibits a high degree of robustness. The new boundary layer in connection with a novel dynamically changing, state-dependent gain can be used to obtain a narrow boundary-layer shape in the operating region of interest. This permits rejection of disturbances without chattering of the control and improves on the performance expected of a sliding-mode control with constant boundary layer.

Keywords: Sliding-mode control; boundary layers; robust control; Lyapunov analysis (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9045-4

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