極配置における区分的定数サンプル値ホールド関数の最適化

抄録

In pole assignment of linear time invariant (LTI) continuous time systems by using output feedback, the control of using generalized sampled-data hold function (GSHF) is more advangeous in theoretical aspects comparing with the conventional sampled-data approaches of using e. g., ZOH. However GSHF, which is an analog continuous-time function in general, is impossible to be implemented as sampled-data output feedback gain in application by using digital computer.
In this paper, we consider a new sampled-data output feedback of using piecewise constant sampled data hold function (PCSHF) in pole assignment of LTI systems. We show that the closed-loop poles can be arbitrarily assigned by using PCSHF, if the plant is controllable and observable. In general, such PCSHF control is not uniquely determined in pole assignment, and the difference between the PCSHFs appears in different intersample behavior. Therefore, it is necessary to choose the PCSHF in an optimal way with respect to the intersample behavior. In this paper, we investigate the optimal PCSHF in pole assignment, where the performance index is of LQR form related to the intersample behavior. The existence and uniqueness of the PCSHF are shown, under the assumption that the plant is contollable and observable. Finally, a numerical example is given to illustrate the PCSHF, comparing with the approaches of using ZOH and GSHF.