Abstract
This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.
Highlights
The significance of the deadzone problem lies in the fact that it affects many physical and practical systems
The advances reached in the area of adaptive compensation and control theory gave rise to increased interest in handling the deadzone problem
The PD controller resulted in limit cycles where as the adaptive controller proved to be stable with no limit cycles and improved performance with a zero approaching tracking error
Summary
The significance of the deadzone problem lies in the fact that it affects many physical and practical systems. How to cite this paper: Ahmad, N.J., et al (2015) Robust Adaptive Control for a Class of Systems with Deadzone Nonlinearity. The approach of designing an inverse adaptive deadzone compensator was thoroughly investigated in [2] and [3] which was shown to improve performance. Lewis et al in [4] proposed a fuzzy logic type inverse deadzone compensator, a neural network inverse compensator was designed in [5] Both approaches show clear improvement in reducing the tracking error. An adaptive sliding mode control scheme used to offset a non-symmetrical deadzone nonlinearity in continuous time was presented in [7]. The proposed method does not require any knowledge of the deadzone parameters or the specialized design of an inverse deadzone controller and only an upper bound of the deadzone spacing which is determined a priori
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