A Design Method for Smith Predictor for Non-Minimum-Phase Time-Delay Plants with Multiple Time-Delays

Abstract

In this paper, we examine a design method for modified Smith predictor for non-minimum-phase time-delay plants with multiple time-delays. The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time-delay, and several papers on the modified Smith predictor have been published. The parametrization of all stabilizing modified Smith predictors for minimum-phase time-delay plants is obtained by Yamada and Matsushima. Yamada et al. expand the result by Yamada and Matsushima and propose the parametrization of all stabilizing modified Smith predictor for non-minimum-phase systems. In some cases, the plant includes multiple time-delays. For minimum-phase timedelay plants with multiple time-delays, the parametrization of all stabilizing modified Smith predictors is solved by Yamada and Takenaga. However, they do not examine the parametrization of all stabilizing modified Smith predictors for non-minimum-phase time-delay systems with multiple time-delays. The purpose of this paper is to expand the result by Yamada and Takenaga and to propose the parametrization of all stabilizing modified Smith predictors for non-minimum-phase time-delay plants with multiple time-delays.

Robust stability condition for a class of time-delay plants with uncertainty

“…In this section, we present a design method for robustly stabilizing controller satisfying Theorem 3 using the parametrization of all stabilizing modified Smith predictor [16][17][18].…”

“…According to [16,17], the parametrization of all stabilizing modified Smith predictor for minimumphase plant G m (s)e −sT is written by…”

“…Using the result in Section 4., in Section 5., we examine the robust stability condition in the case that the number of poles of the nominal time-delay plant in the closed right half plane is not equal to that of the time-delay plant. In Section 6., a design method for robustly stabilizing controller using the parametrization of all stabilizing modified Smith predictor [16][17][18] is presented. In Section 7., we show a numerical example to illustrate the effectiveness of the proposed method.…”

A Design Method for Modified Smith Predictive Control System to Attenuate Periodic Disturbances

“…From [23][24][25], the parameterization of all stabilizing modified Smith predictors C(s) is written by…”

“…Since the parameterization of all stabilizing modified Smith predictors for minimumphase time-delay plants was obtained, we could express previous studies of modified Smith predictors for minimum-phase time-delay plants in a uniform manner and could design modified Smith predictors for minimum-phase time-delay plants systematically. Yamada et al expanded the result in [23,24] and proposed the parameterization of all stabilizing modified Smith predictors for non-minimum-phase time-delay plants [25]. However, they do not examine a design method for modified Smith predictive control system using the parameterization of all stabilizing modified Smith predictors to achieve desirable control specification.…”