非線性動態逆控制應用於表面式永磁同步馬達驅動系統之轉速控制器自動調適

Abstract

本論文提出一種針對表面式永磁同步馬達(Surface Permanent Magnet Synchronous Motor; SPMSM)的非線性動態特性，所設計的新轉速與電流控制律(Control Law; 即用於決定控制器輸出的數學式)，以取代傳統上磁場導向控制(Field-Oriented Control; FOC)中使用多組比例積分(Proportional-Integral; PI)控制器的轉速及電流回授控制迴路。傳統上FOC中使用的PI控制器需要對SPMSM的非線性動態特性進行線性近似(Linear Approximation)後，才能以線性系統理論(Linear System Theory)進行設計，但如此一來控制系統的閉迴路極點(Closed-loop Pole)位置將隨著操作點遠離近似點而有所變化，使得輸出響應不如預期。本文則採用具有將非線性系統進行輸入-狀態線性化(Input-State Linearization)效果的非線性動態逆控制(Nonlinear Dynamic Inversion Control; NDIC)方法，推導出SPMSM的轉速與電流控制律。控制律中直接包含了可供自由選擇且不會隨操作點變動而改變的控制系統閉迴路極點位置，因此可以直接使用線性系統理論來設計極點位置以確保閉迴路穩定性並設計暫態響應特性，且在寬廣的操作範圍中皆會維持此設計好的暫態響應特性。而在線性系統理論之中，線性二次調節器(Linear Quadratic Regulator; LQR)即是常見的用於決定閉迴路極點位置的方法，其特點為可確保閉迴路系統穩定性和強健性(Robustness)，並可透過設定欲最佳化的二次成本函數(Cost Function)中的加權因子(Weighting Factor)來調整輸出響應。因此，在進行NDIC控制律的極點擺置時，若搭配LQR進行設計，則可透過設定少數的加權因子即得到兼具穩定性和強健性的轉速響應。這即是達到了控制器設計中，兼具穩定性與調整便利性的自動調適(Automatic-Tuning)功能。將NDIC控制律搭配LQR進行極點擺置的方法，在本論文中稱為NDICLQR。本文將針對NDIC應用於SPMSM的轉速與電流控制律進行詳細推導，並進行考慮馬達參數誤差下的穩定度分析，以及說明如何將LQR方法與NDIC控制律結合以達成自動調適的功能。最後，這些理論分析的成果將以MATLAB程式進行微分方程式數值模擬得到初步驗證，並在額定功率2kW、額定轉速2000rpm的永磁同步馬達實驗平台上獲得成功驗證。

In this paper, a feedback control technique with automatic-tuning function using nonlinear dynamic inversion control (NDIC) in the speed controller of the drive system of surface permanent magnet synchronous motors (SPMSMs) will be introduced. Conventional automatic-tuning methods for SPMSMs are mostly based on the approximation of linear time-invariant system characteristics, which would be improper when the parameters or operating conditions of the SPMSMs vary significantly with time. Especially, the moment of inertia of the mechanical load of SPMSM can change a lot during the speed control operation. Besides, due to the nonlinear characteristics of the dynamical behavior of SPMSMs, the transient response performance of the designed linear controllers operating at different speed intervals may be far from expected. Therefore, a nonlinear controller which can deal with the nonlinear dynamical behavior of SPMSMs and stabilize the system against the time-varying motor parameters is required. The control law derived using NDIC method has the above advantages while transforming the nonlinear system dynamics to a linear one at the same time, which will make the controller design problem simpler. After that, the linear quadratic regulator (LQR), which is widely used for the linear control system will be combined with NDIC in order to achieve the automatic-tuning function, and the whole control method is named after NDICLQR. The derivation and analysis of control laws of SPMSMs using NDIC will be shown, and then the automatic-tuning method using NDICLQR will be presented. Finally, the numerical simulation using MATLAB and experimental results on the SPMSM testing platform will be used to verify the proposed method.