Abstract
This paper presents a continuous-time adaptive control scheme for systems with uncertain non-symmetrical deadzone nonlinearity located at the output of a plant. An adaptive inverse function is developed and used in conjunction with a robust adaptive controller to reduce the effect of deadzone nonlinearity. The deadzone inverse function is also implemented in continuous time, and an adaptive update law is designed to estimate the deadzone parameters. The adaptive output deadzone inverse controller is smoothly differentiable and is combined with a robust adaptive nonlinear controller to ensure robustness and boundedness of all the states of the system as well as the output signal. The mismatch between the ideal deadzone inverse function and our proposed implantation is treated as a disturbance that can be upper bounded by a polynomial in the system states. The overall stability of the closed-loop system is proven by using Lyapunov method, and simulations confirm the efficacy of the control methodology.
Highlights
The problem of deadzone nonlinearity has been addressed by many researches with great success by utilizing adaptive control methods to eliminate the undesirable effects on the output of a plant [1]-[5]
An adaptive inverse deadzone controller is compared with a robust adaptive controller for systems with output deadzone nonlinearity
The proposed deadzone inverse controller has greatly improved the performance of the system over the robust controller
Summary
The problem of deadzone nonlinearity has been addressed by many researches with great success by utilizing adaptive control methods to eliminate the undesirable effects on the output of a plant [1]-[5]. One of the earliest investigations of output nonlinearities such as deadzone was presented by [4] Their proposed methodology was based on output matching control which involved the design of an adaptive deadzone inverse used to reshape the input reference trajectory to negate the effect of the deadzone. Motivated by the success in producing successful results in handling input deadzone, we present an extended method to reduce the errors caused by output deadzone nonlinearity. The proposed method relies on the premise that by pre-shaping the input trajectory to mimic an inverse form of the deadzone nonlinearity, the combined effect will reduce if not completely eliminating the effect of output deadzone.
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