不確定系統之H_∞──量化迴授管限追蹤控制設計

The H_∞-QFT Sphere-Tracking Control Design for Uncertain Systems

大部分具有物理意義的系統都含不確定性因素，諸如在建構數學模型時，便是一個不確定性生成；這些未知不確定性，像系統參數變動或系統結構改變的不確定性（uncertainties），可能會因為環境因素導致系統性能變差，在更糟糕的情況下，可能造成閉迴路系統不穩定。本文考慮一個有界但具有不確定性之參考輸入，而受控系統為合參數不確定之系統，結合H_∞量化回授理論（quantitative feedback theory, QFT）來確保在不確定系統的干擾下，系統輸出誤差可控制在預設的管限範圍之內。為了匹配所需的規格，由落後領先補償器P_l (s)、及伺服補價器S_C (s)進行設計，再經由H_∞控制器選擇權重函數W_S (s)、W_U (s)、W_T (s)的迴路整型方法，壓低系統受到外在干擾及系統內部不確定性之影響，再搭配量化回授理論，使系統輸出在受到不確定性影響下，還能夠達到預定之管限追蹤性能。最後，本研究以一個高度參數不確定之系統和水下無人載具系統為例子，做為電腦模擬對象，以驗證所推導之見H_∞-QFT管限追蹤控制器之性能，電腦模擬結果顯示此控制器除能保證不確定性系統之暫態響應能達到預設的性能規範之外，並能有效降低系統不確定參考輸入及外在干擾的影響。 Most mathematical model of physical system contains various uncertainties, which may be presented in the form of system parameter variation. These uncertainties may make the closed-loop system unstable or result in poor system performance. In this study, an uncertain system containing bounded parameter variation with a sphere-bounded reference input is considered. The composite design methodology of the H_∞-control and the Quantitative Feedback Theory is then proposed in this research for the above system to ensure that the system output is bounded in the pre-specified sphere, which matches the desired performance. To match the desired specifications, three weighting matrices W_S(s), W_U(s), WT(s) and a lag-lead compensator P_l(s) that contains servo mechanism S_C(s) are added to the augmented plant so that the proposed H_∞-QFT controller is able to minimize the H; norm of the matrix between the exogenous inputs and the controller outputs to reduce the ill-effects caused by disturbances and plant uncertainties on the tracking errors and the control energy while the desired system performance can be guaranteed by examining the Nichols chart through the QFT process. Finally a physical system of an underwater vehicle is used as an example to demonstrate the feasibility of the proposed control structure.