超音速風洞之穩健控制系統及錯誤診斷系統之設計

Abstract

本論文提出一穩健多變數PI控制器以及穩健錯誤診斷系統之較直接的設 計方法, 主要應用於下吹式超音速風洞系統進行吹試環境建立之控制及診 斷. 此系統對實際存在模式不準度, 外在干擾及可能發生錯誤之情形下能 提供穩健可靠的控制及診斷結果. 在PI控制設計上, 本文提出兩階段式的 設計方法. 在第一階段中經由適當的模式化將PI控制系統之模式整理成與 LQG/LTR 設計相近之模式, 代入所發展的模式近似公式, 以達成穩定及具 解耦性輸出行為之初步設計. 在第二階段則利用提出之增益修正法以達成 指定之輸出阻尼行為.在診斷系統設計上, 經由推導我們可建構出一餘值 產生器(residual generator), 使產生之餘值與未知輸入(unknown input) 無關, 而僅與欲偵測之錯誤有關. 我們引用一動態加權矩陣於餘 值產生器上以增加設計自由度, 並符合所需之錯誤偵測和區分(FDI) 性能 要求. 在風洞應用上, 我們首先推導出風洞之數學模型, 並根據指定工作 點之線性名義模式(nominal model) 以進行該風洞之控制及診斷系統設 計. 就大尺度風洞, 我們採用史密斯預測器(Smith predictor) 進行顯著 延時性之補償. 而對較小尺度風洞, PI控制器即可提供滿意之控制結果, 此由實驗結果可得驗證. 另一方面, 我們提出之錯誤診斷系統亦可在顯著 模式不準度下成功的達成風洞系統之感測器及致動器之FDI 工作需求. 其 中感測器FDI 系統可達成主要感測器之多重錯誤偵測及區分. 由於未知輸 入與控制輸入方向相近, 無法直接設計致動器之FDI 系統. 然而藉由錯誤 方向性之觀念, 感測器FDI 系統亦可應用於致動器之FDI 工作上, 達成穩 健之單一錯誤偵測與區分之工作要求. A robust multivariable PI design and a straightforward method for robust faultdetection and isolation system design are proposed in this thesis, they are applied to achieve a reliable control system for supersonic intermittent blowdown-type wind tunnels subjected to uncertainty, disturbance as well as fault. Inthe PI controller design, by reformulating the PI controlled process similar to the LQG/LTR design problem, the proposed model matching theorem in the firstdesign stage successfully results in a robust PI controller with well-decoupled output behavior and sufficient stability. Moreover, control performance can be further improved to achieve well-damped response by modifying the PI gain matrices. In the diagnostic system design, by exploiting the properties of a nominal model structure, a basic set of residual is formed which is independent of the unknown input but dependent on the measurements. A dynamic weighting matrix is appended to the residual to meet the required detection and isolationperformance. In the wind tunnel application, mathematical models for two different structured wind tunnels are derived, its linearized nominal model at a specific operating point is chosen for both control and diagnostic system design. The Smith predictor is employed in the control system for a large scale wind tunnel to compensate the significant time delay effects. For the smaller sizewind tunnel system which is in more complex dynamics, the proposed simple- structured PI controller sufficiently provides desirable control performance. In the diagnostic system design for wind tunnel, the unknown input distribution matrix corresponding to the linear model of the wind tunnel is estimated, and the proposed FDI system with the unknown input decoupling are developed for sensor and actuator of the wind tunnel system. Results indicated that the proposed control system has successfully achieved the desired responses of pressure and temperature in the system. Also, the proposed FDI system achieves mutual fault isolation in sensor FDI for principal sensors. Moreover, although the proposed robust FDI cannot be directly applied to actuators because of the similarity between unknown input and control input directions, the robust FDI which is originally designed for sensor can be also employed for achieving actuator F DI tasks for wind tunnel system.