應用於時滯系統之輸出回授積分型順滑模態控制

Abstract

基於線性多輸入多輸出系統，在部分參數不確定且受到外界未知干擾之環境，本論文提出一動態輸出回授積分型順滑模態控制法則，使受控系統穩定並抑制非匹配干擾之影響。順滑模態控制為一強健非線性的控制方法，先設計一穩定之順滑平面，再設計控制輸入使系統在有限時間內進入該平面，具有設計簡單、可消除匹配性雜訊等優點。當系統只有部分狀態或是輸出訊號可量測，應用於此類系統之傳統輸出回授順滑模態控制器存在著受限於系統結構的控制器合成問題，且只能滿足區域性的逼近與順滑條件。本論文採用積分型順滑平面，可保留順滑模態控制原有之優點，並解決控制器合成問題，當系統進入順滑平面後也可提供一自由度去抑制非匹配型干擾之影響。另外為了滿足全域逼近與順滑條件，在控制輸入中設計了一個適應性法則，計算部份未知量的範數上限。此動態輸出回授積分型順滑模態控制法則，經過修正後亦可應用於參數不確定且受到外界未知干擾之時滯系統。針對於固定但未知延遲時間之狀態延遲時滯系統，沿用輸出回授積分型順滑平面之結構，並加入一全階補償器以完成動態控制器之設計。當系統進入順滑平面，利用一強健干擾抑制分析技術可以推理出一線性矩陣不等式作為穩定性與保證干擾抑制效能的充分條件；若修正補償器結構，則該線性矩陣不等式可分解為兩個維度較小之代數Riccati不等式以利計算，兩種不等式之解皆可用來決定順滑平面、補償器、控制器之參數。當延遲時間未知且時變，讓系統在某些延遲時間造成不穩定，使得控制難度大幅提升。利用上述動態輸出回授積分型順滑模態控制器架構，本論文亦針對此複雜系統完成穩定性充分條件分析與控制器設計。

For linear multi-input multi-output uncertain systems with external unknown disturbances, this thesis proposed a dynamic output feedback integral sliding mode control method to stabilize the system and suppress the effect of mismatched disturbances. The advantages of sliding mode control are its simple design procedure, great robustness against matched disturbances, etc. As part of system states or outputs are only measurable, conventional output feedback sliding mode controllers involved a synthesis problem by a structural constraint and ensured the approaching and sliding condition locally. The thesis adopted an integral sliding surface to improve the controller synthesis problem, reserved inherent benefits of sliding mode control, and offered an extra degree of freedom to suppress the effect of mismatched disturbances when the system is in the sliding mode, simultaneously. For satisfying the approaching and sliding condition globally, an adaption law was added in the controller to estimate the bound of part of unknown terms. The proposed control method can be modified to apply to uncertain time-delay systems with disturbances. For state delays with a fixed and unknown delay time, combined the output feedback integral sliding mode technique with a full-order compensator can complete the dynamic controller design. Since the system is in the sliding mode, using the property of robust disturbance attenuation can derive a linear matrix inequality as a sufficient condition for the stability; this linear matrix inequality can be decomposed into two smaller algebraic Riccati inequalities by modifying the structure of compensator. Solutions to two types of inequalities can both determine parameters of sliding surface, compensator, and controller. In the case of time-varying and unknown delay time, some delay times caused the instability of system and worsened the difficulty designing the controller. The proposed structure of dynamic sliding mode control can also complete the stability analysis and control law design for systems with time-varying delay.