Undershoot Reduction for Plants with Real Unstable Zeros by Time-Varying Controller Design

Abstract

It is well known that undershoot phenomena are inevitable for plants having real unstable zeros. In this paper, we first investigate the undershoot phenomena caused by real ustable zeros of the plant to be controlled theoretically. We then propose methods of reducing the undershoot amount for a plant with real unstable zeros. The ideas are an introduction of exponential decay factor in the performance index in optimal LQR, and time-varying controller (digital control) with piecewise constant hold, where in this design enables us to change the inter-sample control input. We can confirm the effectiveness by simulations.