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

Author

Listed:
  • G. Herrmann

    (University of Leicester)

  • S. K. Spurgeon

    (University of Leicester)

  • C. Edwards

    (University of Leicester)

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.

Suggested Citation

  • G. Herrmann & S. K. Spurgeon & C. Edwards, 2006. "On Robust, Multi-Input Sliding-Mode Based Control with a State-Dependent Boundary Layer," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 89-107, April.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:1:d:10.1007_s10957-006-9045-4
    DOI: 10.1007/s10957-006-9045-4
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