Design of an error-based robust adaptive controller

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 K_p(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 K_p(e, t), for large error K_p(e, t) is kept large, thus increasing the bandwidth of the system which yields a fast response, whereas for decreasing errors, K_p(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 K_v(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 K_p(e, t) and the velocity feedback K_v(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.