Approximate Error Feedback Controller for Tracking and Disturbance Rejection for Linear Distributed Parameter Systems

In this paper we present an error feedback controller for approximate tracking and disturbance rejection for linear distributed parameter systems. The controller is approximate because it is only guaranteed to produce a small tracking error rather than an asymptotic zero tracking error. However, the asymptotic tracking error can be reduced by solving a sequence of controllers, similar in spirit to cascade controllers, where the error at one level becomes the target to track at the next level. At each step the error is reduced geometrically so that achieving a desired tracking level seldom requires more than one or two iterations. An example is given in which the plant is governed by a convection-diffusion equation with non-constant coefficients. In order to compare the effectiveness of our controller with the classical internal model controller the reference signal and disturbance are generated by a six dimensional exosystem. We note that while our approximate controller achieves a small error almost immediately the internal model controller requires much longer transient to achieve a similar level. Furthermore, our controller can handle much more general reference and disturbance signals as demonstrated in a second numerical simulation.