以傅立葉函數為基底之自適應滑動模式控制應用於縮尺風力發電機葉片變旋角轉速控制之研究

Abstract

本文以改裝變旋角機構之東元2kW被動式小型風機進行大型風機的縮尺實驗，模擬大型風機在額定功率區與切出風速後之超轉區的控制，考量到風場因素，希望以功率最大化的前提下降低轉速至停機，達到風機效率的最大化。 本實驗將風力發電機立於在開放式風洞中，以傅立葉函數為基底的非線性項自適應估測滑動模式控制器對變旋角系統進行風機轉子轉速的控制。變旋角系統由伺服馬達驅動，旋角由伺服馬達之編碼器回授，風機之轉子轉速由外加之轉速計測量，風速則由固定之風速計測量，風力發電機產生之電力由電纜接至三項Y接型水泥電阻消耗。藉由改裝之變風速系統，開放式風洞可以簡易控制風速大小。 控制器使用以傅立葉函數為基底之自適應滑動模式控制器。此控制器設計是藉由回授線性化推導出系統模型，再利用以傅立葉級數為基底之函數估測法估測系統中的非線性項與未知的系統參數，其中各項傅立葉級數參數由自適應的方式進行更新。由李亞普諾夫函數證明系統穩定，誤差會收斂於零。 最後進行縮尺風機實驗驗證，將控制器應用在縮尺風力發電機實驗中的定轉速以及變轉速控制，觀察控制器在額定轉速區以及停機區控制效果，並與PID控制器比較。實驗結果可得到以傅立葉函數為基底之自適應滑動模式控制器比起PID控制器，在額定轉速區的穩態誤差以及超轉區的轉速追蹤效果皆更好。

In this dissertation, the modified TECO 2kW small horizontal axis wind turbine with variable pitch control was used to conduct a scaled-down experiment with the prototype Vesta Micon M 1100-600-PLS2. This study focuses on the rotational speed control in rated rotor speed region and the over speed region, which is over cut-off speed. This experiment was implemented in an open wind tunnel, and the wind turbine’s rotor speed is controlled by the Fourier-series based adaptive sliding mode controller via variable pitch control. The variable pitch control is driven by the servo motor, and the pitch angle feedback is by the servo motor’s encoder. The rotor speed is measured by the additional tachometer and the wind speed is measured by the anemometer. The turbine’s output electricity connects to the Y-shaped cement resistance through the power cable. The open wind tunnel can simply control the magnitude of wind speed via modified variable wind speed system. The Fourier-series based adaptive sliding mode (FSBASM) controller was applied in this dissertation, including feedback linearization, Fourier-series based function approximation and adaptive law design. The stability was proved by the Lyapunov function and the error converges to 0. Finally, the experiment was implemented in the scale-down test turbine. The proposed FSBASM controller was applied to the constant speed and variable speed control of a scaled-down wind turbine to observe the control performance in the rated rotor speed region and over-speed region in comparison with the PID controller. The experimental results show that the FSBASM controller has better steady-state error in the rated speed region and better tracking performance in over-speed region than the PID controller.