Optimal impulse response tracking and disturbance rejecting controllers

The tuning of PID controllers can essentially be posed as the problem of selecting open-loop zeros such as to obtain a desired system response. In this paper, the general case wherein stable open-loop system zeros can be cancelled is considered, allowing more freedom in placing open-loop zeros, as opposed to just two zeros in the case of a PID controller. Subsequently, optimal open-loop zeros are computed such as to minimize the deviation from a desired reference impulse response, while maintaining the relative degree and the type of the reference system, thus giving the controlled system desired input tracking and disturbance rejection properties. Further, due to the inverse compensation of the plant zeros, the controller is in general causal when the relative degree of the plant and the reference system are similar.