利用數值最佳化方法估測系統之干擾分佈矩陣

Estimate the Unknown Input Distribution Matrix by Using the Optimal Design Procedure

為了維持控制系統的完整性及安全性，故障監視與診斷的技術已被考慮使用於各個工程應用領域。在各種故障診斷系統設計的方法中，以模式為基礎的設計被廣泛的注意。由於動態系統中不可避免出現干擾或模式不準度，其將可能影響到診斷系統的正常運作，因此診斷系統必須具備足夠的強健性，讓診斷結果只與故障有關，而不會受到模式模式不準度的干擾。其中使用未知輸入觀測器的故障診斷設計是穩健式故障診斷系統的重要設計方法。不過，此種強健式的診斷系統設計的先決條件是要有已知的干擾分佈矩陣E， Patton等人曾提供了一套E矩陣的估測方法，但是僅限使用於感測器的數目等於系統狀態的數目，亦即輸出矩陣為可逆方陣的動態系統中，此項限制條件阻礙了矩陣E 之估測技術的運用與發展，本論文提出一套新的E 矩陣估計方法，即便是感測器的數量少於狀態的數目，其亦可藉由最佳化之步驟以估測出E 矩陣。透過應用例的模擬結果，可說明了本設計方法是可行且有效的。

To ensure control system integrity and hence maintain safety, fault monitoring and diagnostic techniques are employed in many engineering areas. In all approaches of fault diagnostic system design, the model-based design method has received great attention. Since modeling error is inevitable which may deteriorate the function of a model-based fault diagnostic system, therefore, robustness of the fault diagnostic system is an important issue such that the diagnostic results should be immune to the disturbance or modeling error, only related to the present faults. Unknown Input decoupling approach is an important method for designing a robust fault diagnostic system. However, the robust fault diagnostic design required that the disturbance distribution matrix should be known in a priori. Patton et al provide a design procedure for the estimation of the disturbance distribution matrix, but this approach can only be used in the system with the output matrix is square and invertible, which means the number of independent sensors should be the same as the number of process states. This restriction obstructs the use and development of the estimation technique. In this paper, we provide a new design procedure to relax this restriction such that the disturbance distribution matrix can be estimated with lesser sensors. Simulation results demonstrate that the developed approach is practicable and effective.