具瑕疵補償與直接角度量測之微機電陀螺儀系統

Abstract

本研究採用回授控制(軟體計算)同時補償機械結構瑕疵及感測電路瑕疵所造成的影響，在搭配適當的控制與訊號處理方法下，可以不透過角速度積分的方式，直接得到物體轉動角度。本論文詳細探討：(1)瑕疵所造成的系統響應在哪些條件下能被正確估測；(2)如何利用控制輸入營造出此條件，進而補償其瑕疵響應；(3)如何由補償過後的陀螺儀動態直接獲得角度資訊。本文設計的控制器可藉由 Lyapunov直接法來證明系統的參數收斂性與系統穩定性。此方法所能補償的機械結構瑕疵包括因為微結構設計、製程關係所造成的振動質量塊質量未知、系統剛性係數未知、系統阻尼係數未知、跨軸動態耦合、感測介面的差分電容對不匹配；感測電路瑕疵包括：寄生電容(Parasitic capacitance)、運算放大器的輸入偏壓(Offset voltage)、電路雜訊。 本論文所提出的方法亦可與其它狀態觀察器進行整合，擷取其它狀態觀察器的優點。在角速度估測的部份，本文利用擴增型卡曼濾波器降低雜訊干擾的能力來提升系統參數與動態估測的品質。在數值模擬印證中，相較於以開路方式操作下的「理想陀螺儀」(無機械結構瑕疵與感測電路瑕疵)，本方法可在陀螺儀的所有結構參數都未知(或變動)且感測介面與電路存在瑕疵下，改善感測精確度達六倍；此外，再加入｢記憶褪去法｣後，對於角速度的感測頻寬改善達十倍。在直接角度估測部分，在角速度以200sin(2*pi*10t)°/sec快速變動下，相較於同樣條件下以角速度積分的結果，本方法可有效避免誤差累積的問題。此外，系統阻尼係數在操作過程因環境變異而出現40%以上的變動時，本方法仍可在0.1秒內完成補償，並繼續角度估算的工作，無須進行離線校正。

In this dissertation, we proposed using control techniques to estimate and compensate the effects from both mechanical structure imperfections and interface circuit imperfections. Accompanied with proper feedback controls and signal processing techniques, the compensated system dynamics can be used to obtain the rotation angle without integrating the angular rates. The mechanical structure imperfections discussed in this report including unknown proof mass, unknown system stiffness, unknown system damping coefficients, undesired cross-axis coupling, and mismatch of the differential capacitive position sensing. The sensing circuit imperfections discussed in this report including parasitic capacitance, offset voltage of a charge amplifier, circuit noise. This dissertation discussed in detail under what conditions that the effect resulting from the imperfections can be correctly estimated. Furthermore, how to create these conditions and compensate those imperfection effects by control inputs. The stability and effectiveness of the proposed method can be theoretically proven by the Lyapunov direct method. The proposed method can work with various existing observer algorithms and benefit from their features. For instance, the extended Kalman filter can estimate system dynamics when the measured signals are noisy. This observer algorithm can be used to work with the proposed method to improve the angular rate estimation accuracy. Comparing to the “open loop” operation method, wherein most of system parameters must be known, simulation results indicated that the proposed method can improve the angular rate sensing accuracy by eight times and the sensing bandwidth by ten times, when those imperfections exist. For the angle measurements, the proposed method does not show obvious signal drifts in a simulation case that the angular rate to be measured is 200sin(2*pi*10t)°/sec. Besides, the simulation results show that the proposed method can sustain sudden system parameter variations (40% damping coefficient variations) without an offline calibration process.