微型陀螺儀的強健控制器設計

Abstract

隨著微機電科技的進步，微型陀螺儀的應用日益廣泛，如在汽車的導航及安全控制、遊戲主機、手機等都可發現其蹤跡。對於目前的微機電式陀螺儀而言，製造過程中的誤差及使用過程中的磨損會造成成品與設計間存在差異，以至於無法滿足原先系統的規格。本研究的重點在於設計一控制器，能在微型陀螺儀的特性參數發生變異時，還能保有一定的系統性能。 因為陀螺儀本身屬於多輸入多輸出系統 (multi-input multi-output, MIMO)，且驅動軸與感測軸間有耦合的情形，若系統特性有變異時，無法利用一般的PID控制設計方法來達成規格要求。因此，我們必須設計一個既可以控制MIMO系統又可以忍受特性參數變異的穩健控制器(robust controller)。在此論文中我們會先忽略系統變異並利用pole placement的控制理論設計出PID控制器，之後再利用穩健控制理論中的H∞理論結合量化迴授理論(quantitative feedback theory, QFT)設計出穩健控制器，最後比較不同控制器的性能和穩健特性等差異。 論文中，我們先找出受控體的特性矩陣P(s)和權重函數，並使用MATLAB輔助完成控制器的設計。當系統的共振頻率和阻尼係數存在10%變異量時，加入PID控制的系統響應變異量為24%，而加入QFT/H∞控制器的變異量為5.6%，且暫態響應的特性仍能符合規格，包含安定時間小於0.2ms，最大超越量低於10%，可知利用QFT/H∞的控制方法設計出的控制器在穩健性上有明顯的改善。此外和一般H∞控制器相比，系統迴路由狀態回授變為輸出回授，因而在實現上也較為容易。

With the progress of the MEMS technology, the application of micro-gyroscopes becomes more and more extensive. Examples can be found in automobile navigation and safety control, game hosts, mobile phones, etc.. However, fabrication errors and operation wearout will cause difference in component characteristics between the expected value and the actual value in real devices. The objective of this research is focused on the design of a controller which can maintain certain system performance in the presence of the system characteristic parameter variation. The gyroscope is a multi-input multi-output (MIMO) system with possible variations in system characteristics. Therefore, the common PID controller design method can not be used in controller design to meet the specification. A robust controller which can be used to control a MIMO system and endure parameter variation is required. In this thesis, the pole placement method is applied to design a PID controller without considering the system variation. Then the H∞ theory and quantitative feedback theory (QFT) are applied to design the controller. The performance and the robustness of the controllers are compared. After determining the characteristic matrix P of the plant and the weighting functions, the controller is calculated by MATLAB. When the natural frequency and the damping coefficient both have variation of 10%, the variation of the system response is 5.6% in QFT/H∞ controller and 24% in PID controller. Therefore, the QFT/H∞ control method has better robustness. Compared with conventional H∞ controller, the QFT/H∞ control loop uses output feedback and is easier to realize.