Dual‐rate control system extension using the null space of a closed‐loop system

Abstract

The present paper discusses a design method for a single‐input single‐output linear time‐invariant dual‐rate sampled‐data control system, where the sampling interval of a plant output is longer than the holding interval of a control input. In such a control system, intersample output oscillation, called ripple, can occur even if the sampled output converges to the reference input. In order to resolve this problem, two design methods have been proposed such that the existing sampled output response is maintained: an open‐loop system design method and a closed‐loop system design method. However, the open‐loop design method cannot be applied to systems for which the gain matrix of the control input is full rank. On the other hand, the closed‐loop design method can be used for such systems, but the sampled output response is maintained only in the steady state. The present study proposes a new closed‐loop design method in which ripples are eliminated and both the transient and steady‐state responses are maintained. The effectiveness of the proposed method is demonstrated through numerical examples. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.