A Cascading Method for Reducing Asymptotic Errors in Feedback Control of Nonlinear Distributed Parameter Systems

This paper presents an error feedback controller for approximate tracking and disturbance rejection for nonlinear distributed parameter systems. The controller is error feedback because the only information available to the controller is the error given as the difference between the reference signal to be tracked and the measured output of the plant. In particular, the controller cannot directly access the output data. Also, the unknown disturbance corrupting the plant is unavailable to the controller. The controller is "approximate" in the sense it only guarantees 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 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 achieving the desired tracking level seldom requires more than one or two iterations. We present a numerical example to demonstrate the utility of the method.