Experimental implementation and validation of a novel minimal control synthesis adaptive controller for continuous bimodal piecewise affine systems

Abstract

This paper presents the first digital implementation of a novel model reference adaptive scheme for the control of continuous bimodal piecewise affine systems. The algorithm is based on the minimal control synthesis algorithm, originally developed as a MRAC for smooth systems. The resulting adaptive algorithm is a switched feedback controller able to cope with uncertain continuous PWA systems. The analogue continuous-time control law is implemented by using a digital low-cost commercial microcontroller. The aim is to control a piecewise-linear electrical circuit. The experimental validation process is made challenging by the presence of measure uncertainties, noise, quantization errors, unmodeled nonlinear dynamics and computational delays. Experiments confirm the effectiveness of the controller to cope with switching in the circuit dynamics, establishing the strategy as a viable control tool. Nevertheless, the experimental analysis provides a first insight into the robustness of the algorithm.