Independence of convergence rate of the wave tracking error on structures of feedforward controllers

Abstract

Although the fundamental problem of asymptotic tracking and disturbance rejection in control theory has been well studied, the independence of convergence rate of the tracking error on structures of feedforward controllers has been overlooked. In such control design, many feedforward controllers can be constructed and it is of practical importance to know whether all feedforward controllers actually achieve the same performance. Using the wave equation as an example, we show that the wave tracking error exponentially converges to zero and its convergence rate is indeed independent of the structures of feedforward controllers as the rate is completely determined by a stabilization system. This is generally true for other control systems.