Undershoot reduction for plants with real unstable zeros

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 unstable zeros of the plant to be controlled theoretically. We then propose methods of reducing the undershoot amount for a plant with real unstable zeros by digital control. The ideas are an introduction of exponential decay factor in the performance index in optimal LQR, using piecewise constant hold instead of ZOH, and a switching gain policy. We can confirm the effectiveness by simulations.