本論文提出了一個新的具有最優化PID濾波之長輸入時延線性系統的精確數位再設計的追蹤器，所以受控的系統輸出將可以最佳化地追蹤到高度隨時間變化的輸入軌跡。首先，針對非方陣的多輸入多輸出(MIMO)系統，提出了一種新且有系統的方法來設計非方陣最優化且具有低通濾波特性的PID控制器，且保證其非方陣PID控制器具有抗飽和特性，再來，針對具有長輸入時延特性的模擬系統，提出了新的最優化線性二次模擬追蹤器（LQAT），最後，基於修改過的精確數位再設計結合數位PID控制器與最優化二次數位追蹤器，在本論文中被創新地利用在控制具有長輸入時延特性的資料採樣系統中，所以受控系統的輸出將可以追蹤到預先指定的高度隨時間變化的輸入軌跡。

A new exactly digitally redesigned optimal tracker for the proportional-integral-differential (PID) controller-embedded linear sampled-data systems with a long input delay is presented in this thesis, so that the controlled system output will optimally track the highly time-varying input trajectory. First, a new systematic way to design the optimal low-pass filter-based analog PID controller for the square/non-square multi-input multi-output (MIMO) systems is proposed to improve the performance of the MIMO plant and to achieve the anti-windup objective for the PID controller. Then, the new optimal linear quadratic analog tracker (LQAT) is proposed for the servo control of a long input time-delay analog system, in which the system matrix might be singular. Finally, based on a modified version of the exact digital-redesign approach, a digital PID controller together with an optimal linear quadratic digital tracker (LQDT) is newly proposed in this thesis for the long input-delay sampled-data linear systems, so that the controlled system output will optimally follow the pre-specified highly time-varying reference input.

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