｜軸向磁通永磁馬達之模型建構與向量控制設計

摘要：近幾年來，軸向磁通永磁馬達（Axial-Flux Permanent Magnet Motor, AFPM）因具有高效率、緊密結構與高轉矩密度等特性，吸引著工業界的注目，並已廣泛應用在電動車與飛輪儲能等系統上。在這些應用中，需要馬達平穩的運轉，以避免震動與噪音干擾，因此，精確的馬達模型與其控制器設計，使其性能優化是非常重要的。本文建立一個軸向磁通永磁馬達之模型並設計其向量控制器，首先推導此軸向磁通永磁馬達在三相靜止座標之數學模型，其中電磁轉矩方程式具有頓轉矩漣波，再利用PSIM模擬軟體所具備的電路元件、數學運算與轉移函數等功能來建構與驗證此模型，此模型具有三相電壓輸入端與負載轉矩輸入端，可以很方便直接地將此模型方塊連接到整體馬達驅動器的PWM變頻器；並做負載轉矩與馬達參數不準度和變化等整體馬達驅動器性能的評估與模擬，轉矩響應模擬結果並與利用ANSYS Maxwell有限元素分析法之結果做比較，以驗證其正確性。之後，進一步推導在同步旋轉座標之d-q軸模型，依此軸模型設計以轉子磁場為導向的向量控制器，包含PI解耦電流控制器與二自由度轉速控制器，模擬結果顯示所設計的控制器對轉速命令與負載轉矩的瞬間加入皆有理想的轉速響應，並且馬達轉動慣量參數在 60 %的不準度時，仍有穩定的轉速響應，但在低轉速時可看出轉速響應上有明顯的漣波，是頓轉矩所造成，有待進一步設計更高階的控制器來消除此頓轉矩漣波效應。。

Abstract: In recent years, Axial-Flux Permanent Magnet Motor (AFPM) motors have received increased attention due to their high efficieny, compact construction, and high torque density. They have been utilized in a wide range of applications such as electrical vehicles and flywheel energy storage systems. Most of these applications require smooth motor running in order to avoid vibration and acoustic noise. Thus, an accurate model for controller design to optimize the performance of the AFPM motors is very important. This paper presents the modeling and vector control design of an axial-flux permanent magnet (AFPM) motor. Firstly, the mathematic model of the AFPM motor in the three-phase stationary frame is derived, in which the electro-magnetic torque of the motor has cogging torque ripple. The model block was constructed and verified in PSIM which contains circuit components, mathematic operation components, and transfer function blocks. The constructed model has three-phase voltage and load torque input ports which facilitate the coupling of the model to the PWM inverter and the load torque input for integrated performance evaluation and simulation of the motor drives. The model has also been verified by comparing the torque response with the simulation result using ANSYS Maxwell finite element analysis. In addition, the model of the motor in the d-q synchronously rotating frame is derived, based on which the rotor-flux oriented vector controller is then designed. This controller contains PI-decoupling current controllers and a two-degree-of-freedom speed controller. Simulation results show that the proposed controller provides good speed response to the speed reference, sudden change of the load torque, and still provides good response at moment inertia uncertainty, respectively. However, at low speeds, ripples are apparent in the response due to the cogging torque. The authors are encouraged to design more advanced controllers to reduce the cogging torque ripple effect in the near future.

關鍵詞：軸向磁通永磁馬達、模型建構、向量控制

Keywords：Axial-Flux Permanent Magnet Motor (AFPM), Modeling, Vector Control

前言
近幾年來，軸向磁通永磁馬達（Axial-Flux Permanent Magnet Motor, AFPM）因具有高效率、緊密結構與高轉矩密度等特性，吸引著工業界的注目，並已廣泛應用在電動車與飛輪儲能等系統上[1,2]。在這些應用中，需要馬達平穩的運轉，以避免震動與噪音干擾，這些干擾往往是馬達轉動時其轉子與定子間的磁力吸引所產生的週期性頓轉矩漣波所造成的[3]。因此，精確的馬達模型與其控制器設計，使其性能優化是非常重要的。

在文獻上有許多關於永磁馬達建模的報導[4-8]，可分為兩大類，其中一類是建構在以數學方程式為基礎[4,5]；另一類是建構在以電路元件為基礎[6,7,8]。以上前者具有不能直接連接到外部電路的問題，後者具有不易加入負載轉矩與模擬馬達參數變化的問題，因此兩者皆有礙於馬達驅動器整體性能的評估與模擬。

本文提出以PSIM模擬軟體建構一個AFPM馬達在靜止座標系之相變數（phase variable）模型，在其三相輸入端以電路元件來建構其模型，仿如一實際的馬達操作，在模型內部加入頓轉矩漣波（cogging torque ripple）的作用，外部並含以數學方程式建構的負載轉矩（load torque）輸入端，可以很方便直接地將此模型方塊連接到整體馬達驅動器的PWM變頻器（inverter）；並做負載轉矩與馬達參數不準度或變化等整體馬達驅動器性能的評估與模擬。雖然在MATLAB/Simulink與PSIM模擬軟體中已有內建的永磁馬達模型，但是很不方便在此內建的永磁馬達模型上加入頓轉矩漣波與馬達參數變化的功能。

除此，本文進一步推導在同步旋轉座標系之d-q模型，依此設計其向量控制器，可得到抵抗負載轉矩瞬間變化的轉速響應，並探討頓轉矩漣波對轉速響應的影響。雖然文獻上已有不少關於與永磁馬達向量控制器設計的報導[9,10]，但很少探討頓轉矩漣波效應的問題。