Wavelet-based adaptive sliding-mode control with H ∞ tracking performance for pneumatic servo system position tracking control

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Abstract
An adaptive sliding-mode controller developed from an orthogonal Haar wavelet is proposed for a pneumatic servo control system experiment to overcome its non-linear and time-varying characteristics. To achieve real-time control of the pneumatic servo system, the orthogonal Haar wavelet is employed to quickly and accurately fit a non-linear function, thus bypassing the model-based prerequisite. The adaptive laws for the coefficients of the Haar wavelet series are derived from a Lyapunov function to guarantee system stability. One of the authors’ purposes is to enhance the stability, reliability and working performance of the pneumatic servo system. Hence, the H∞ tracking technique is incorporated into the conventional adaptive sliding-mode control method [Haar wavelet-based adaptive sliding-mode controller with H∞ tracking performance (HWB-ASMC + H∞)] to attenuate the vibration of servo valve, which is caused by the chattering effect. The authors also show that the proposed HWB-ASMC + H∞ is robust against approximated errors, un-modelled dynamics and disturbances, and can reduce the control chattering problem. The advantages of the proposed method include that no system dynamic models being required to achieve the controller design and no trial-and-error efforts are needed in selecting an approximation function. Consequently, practical experiments on a pneumatic servo system are successfully implemented with different position tracking profiles, which validates the proposed method.

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