Design of an Error-Based Robust Adaptive Controller

Abstract

Design of an adaptive controller for complex dynamic systems is a big challenge faced by the researchers. In this paper, we propose a novel method for the design of an error- based robust adaptive controller to make the system response reasonably fast with no overshoot. Here the control action is designed by introducing the notion of `error-based adaptive controller' (EB-AC). In the design of this feedback adaptive controller, parameters of the controller are designed as a function of the system error. For example, the position feedback parameter Kp(e, t), which controls the bandwidth of the system as well as the dynamic response, is a function of the system error e(t). In the design of the position feedback parameter Kp(e, t), for large error Kp(e, t) is kept large, thus increasing the bandwidth of the system which yields a fast response, whereas for decreasing errors, Kp(e, t) is continuously decreased to a small value. Thus, during the dynamic response of the system, the bandwidth of the system is continuously controlled by the system error e(t). Similarly, the velocity feedback parameter Kv(e, t) which controls the damping of the system is kept very small for large errors, and continuously increased to a large value for decreasing value of error. Hence, in the design of the proposed adaptive controller, the position feedback Kp(e, t) and the velocity feedback Kv(e, t) are formulated as a function of the system error, and this approach for formulating the adaptive controller yields a very fast response with no overshoot. In this paper, we present an error-based robust adaptive control design methodology for a linear system.