Dynamic Sliding Mode Control Design for Nonlinear Systems Using Sliding Mode Observer

Authors

1 Faculty of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran

2 Faculty of Electrical and Robotic Engineering, Sharood University of Technology, Shahrood, Iran

Abstract

In this paper, dynamic sliding mode control (DSMC) of nonlinear systems using sliding mode observer is proposed. In DSMC the chattering is removed due to the integrator (or a low pass filter) which is placed before the input control signal of the plant. However, in DSMC the augmented system (system plus the integrator) is one dimension bigger than the actual system (if the integrator is used) and then to stabilize the system, the plant model should be completely known. To solve this problem, we suggest a sliding mode observer to identify and to obtain a model for the uncertain nonlinear system and then, chattering free control signal is calculated to have desired properties. Stability of the proposed observer and controller is based on Lyapunov theorem and moreover the upper bound of the system dynamic is not used which is important in practical applications. To verify the proposed approach, Duffing-Holmes chaotic system with comparison to usual sliding mode control is used. To have a rightful comparison, we use from the same observer (the proposed sliding mode observer) in two methods. With comparison of the equations, we can see the simplicity of the usual SMC while one can also see the simple concepts of DSMC. Moreover, from equations and simulations, it is clear that in usual SMC chattering is available, while in DSMC chattering is removed completely.

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