Improving transient performance of adaptive control via a modified reference model and novel adaptation

• Published in: International journal of robust and nonlinear control Vol. 27; no. 8; pp. 1351 - 1372
• Main Authors: Na, Jing, Herrmann, Guido, Zhang, Kaiqiang
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2017
• Subjects: adaptive control; Adaptive systems; Compensators; Computer simulation; Control systems; Convergence; Design parameters; Dynamical systems; Excitation; Mathematical models; Model reference adaptive control; Nonlinear dynamics; nonlinear system; Nonlinear systems; Nonlinearity; Parameter estimation; robustness; System dynamics; Transient performance
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3636

Summary This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed‐loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high‐gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.