單相換流器已被廣泛應用於不斷電系統、光伏能量系統以及燃料電池系統。換流器之輸出電壓必須被控制來追隨正弦參考波形，因而其設計可被視為典型的追蹤問題。傳統滑動模式控制為一有效的強健追蹤控制技術且已成功使用於單相換流器系統，但是其系統狀態收斂到平衡點的時間通常是漸進的。為了達成高精確的追蹤控制，近來終端滑動模式控制提供有限的系統狀態收歛時間。然而終端滑動模式控制由於不確定值的過度估測或被估測不足時，仍然可能引起顫動以及穩態誤差的問題，這些問題將造成換流器輸出電壓的高總諧波失真以及慢的動態響應。
本論文提出灰色模糊終端滑動模式控制以及積分補償終端滑動模式控制兩個策略應用於單相換流器。此兩種策略可克服傳統終端滑動模式控制的顫動以及穩態誤差的問題，使得換流器在不同負載狀況下，具有低總諧波失真及快速響應的特性。灰色模糊終端滑動模式控制策略使用數學簡單及計算快速之灰色預測來處理傳統終端滑動模式控制之顫動以及穩態誤差問題，然後再由模糊控制來微調灰色預測之預測值。模擬與實驗結果顯示，灰色模糊終端滑動模式控制策略在非線性負載下電壓總諧波失真低於2%以及在負載暫態下可得到快速動態響應。積分補償終端滑動模式控制策略則是結合積分控制與終端滑動模式控制，積分控制器使用於負載高度非線性時來消除穩態誤差，而終端滑動模式控制仍具有限時間收斂之特性。模擬與實驗結果顯示，在非線性負載狀況下，積分補償終端滑動模式控制策略可建立電壓總諧波失真在1.5%以下，優於美國電機與電子工程師協會 (IEEE) Standard 519之諧波管制。以此兩種控制策略應用於單相換流器設計，使換流器之輸出具有優異的穩態與動態性能，可應用於精密的定位系統與光學系統中，如半導體製程、精密加工、硬式磁碟機與光碟機等場合。

Single-phase inverters have been extensively applied in uninterruptible power supply (UPS) systems, photovoltaic (PV) energy systems and fuel cell (FC) systems. Output voltage of the inverter is controlled to follow a sinusoidal reference waveform, and thus the design of the inverter can be treated as a typical tracking problem. Classic sliding-mode control (SMC) is an effective robust-tracking control technique that has been used successfully for single-phase inverter systems, but the system states’ convergence to equilibrium is normally asymptotic. For high-precision tracking control, terminal sliding-mode control (TSMC) provides finite system-state convergence time. However, TSMC still suffers from chattering and steady-state error problems when uncertainty values are overestimated or underestimated. These problems will result in high total harmonic distortion (THD) of the inverter output voltage and slow dynamic response.
This dissertation proposes grey-fuzzy TSMC and integral-compensation TSMC strategies for applications to single-phase inverter design. These control methods can overcome classic TSMC chattering and steady-state error problems and produce low THD and fast response for single-phase inverters under various load conditions. The grey-fuzzy TSMC strategy uses a mathematically simple and computationally fast grey prediction (GP) methodology to deal with chattering and steady-state error problems. Then fuzzy control is used to fine-tune the GP forecasting value. Simulation and experimental results reveal that the grey-fuzzy TSMC strategy achieves voltage THD of less than 2% in the face of nonlinear load conditions and fast dynamic response in the face of transient load conditions. The integral-compensation TSMC strategy combines integral control and TSMC. The integral controller is used to eliminate steady-state errors when the load is in a highly nonlinear condition, and TSMC still offers the property of finite-time convergence. Simulation and experimental results under nonlinear load conditions indicate that the integral-compensation TSMC strategy leads to voltage THD of less than 1.5%, which is superior to the IEEE Standard 519. Single-phase inverters using the proposed control strategies have excellent steady-state and dynamics performance characteristics. These inverters are suitable for use in precise-positioning systems and optical systems, such as semiconductor processing, precise machining, hard disk drives, optical disk drives, and so on.

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