Robust Indirect Adaptive Control for a Class of Nonlinear Systems and Its Application to Shape Memory Alloy Actuators

In this paper, a new robust adaptive control method has been proposed for nonlinear systems with uncertainties. This method combines the advantages of self-tuning control and sliding mode control. A simple parameterization model is first derived based on a linear dynamic model and unmodeled dynamics. Based on a modified sliding surface, the design procedure is based on the indirect adaptive control concept. This controller consists of four parts: 1) the system parameters estimation; 2) the unmodeled dynamics estimation; 3) the weighting polynomials updating; and 4) the control law calculation. The key merits of this controller are as follows: 1) the controller is applicable to non-minimum phase and open-loop unstable systems; 2) the estimation of the unmodeled dynamics is introduced as a feedback compensation control to improve the response; and 3) the strict stability condition is eliminated and a desirable performance is ensured during a wide operation region. Moreover, the control problem of a shape memory alloy actuator system is considered. In the literature, the mechanism model-based controllers have been extensively reported to address this issue. As an alternative, we describe this plant as a gray-box model. The adaptation algorithm and the control law have been implemented through the Beckhoff controller. The experimental results have demonstrated that the proposed controller has wider applicability than some existing methods.