ADAPTIVE MODEL-REFERENCE CONTROL FOR A CLASS OF UNCERTAIN NONLINEAR SYSTEMS USING A SIMPLE SYSTEMATIC LYAPUNOV-BASED DESIGN

Abstract

This paper proposes an adaptive design of nonlinear feedback controllers for a class of complex nonlinear applications that have ill-defined mathematical models due to the effects of uncertainties and external disturbances. The design is aimed at estimating the uncertain parameters of the system while using a feedforward-like technique to cancel the effect of disturbances and unwanted nonlinearities. This is being achieved using a combination of state feedback and Lyapunov-based techniques that can guarantee the asymptotic stability of the closed loop system. The controller is synthesized such that it will follow the performance of a reference model via satisfying a certain criterion. The control law is demonstrated to be easily achievable for applications that can be modeled by low-order dynamics, e.g., industrial processes (level, flow, pressure, etc.) and some automotive applications (active suspension). The key factor in the design is arriving at the best parameter update law that guarantees both stability and satisfactory transient performance. The application of the proposed controller is extended to higher-order systems via proposing a low-order nonlinear model that is capable of encapsulating the dominant dynamics of the system without using linearization techniques. Trade-offs between stability and performance are carefully studied along with comparisons with a nonmodel-based PID controller to highlight the superiority of the proposed design. A simulated nonlinear Duffing oscillator and a continuous stirred tank reactor are used to exemplify the suggested technique. Finally, a conclusion is submitted with comments regarding feasibility of the controller along with its advantages and limitations.