應用強健多項式時延系統之雙向轉換器研製

Design and Implementation of a Bidirectional Converter Applying Robust Polynomial Systems with Time-Delay

王淳煥(CHUN-HUAN WANG)

指導教授 ： 余國瑞

國立中正大學/工學院/電機工程學系/碩士(2016年)

摘要

本論文應用多項式時延系統，設計直流/直流雙向轉換器之強健H∞控制器，此雙向轉換器結合升壓轉換器與降壓轉換器於同一架構，因此具有高效率與低成本之優勢。由於轉換器之控制為一調變問題，本論文在系統狀態空間方程式中增加誤差積分的狀態變數，使雙向轉換器得以穩定在目標電壓。除此之外，降壓與升壓轉換器皆存在二極體偏壓，本論文將二極體偏壓視為一固定之外在干擾訊號以H∞指標抑制干擾的影響，同時考慮因元件特性所造成的時間延遲回授訊號，應用 Lyapunov-Krasovskii泛函數推導雙向轉換器之H∞多項式時延控制系統穩定定理，並以SOS(Sum of Squares)表示。接著，為了克服實際電路因元件老化導致控制性能降低的問題，進一步考慮系統模式不確定性，推導雙向轉換器之強健多項式時延控制系統SOS穩定定理。最後將所設計之強健多項式時延控制器以自行研製的TI控制板實現，並應用於自行研製額定功率2kW之雙向轉換器，透過輸入電壓變動、干擾訊號、負載變動與電感變動測試，驗證所設計控制器的強健性能。實測結果顯示，相較於其他未考慮時延訊號之控制器，所設計之強健多項式時延控制系統無論在安定時間或最大超越量之性能皆更優異。

關鍵字

雙向轉換器 ； 多項式

並列摘要

In this thesis, the polynomial systems with time-delay are applied to design a robust H∞ controller for a bidirectional converter, which combines a buck converter and a boost converter. The circuit of the bidirectional converter possesses the advantages of high control efficiency and low implementation cost. Since the control of a converter is a kind of regulation problems, the integral of tracking error signal is defined as a new state variable added to the state-space equations of the bidirectional converter to achieve a desired value. The model of this bidirectional converter takes into account of time-delay signals caused by state feedback signals. In addition, both buck and boost modes of the bidirectional converter contain diode bias, which will be regarded as a fixed external disturbance signals in this paper. The first theorem and stability conditions for the polynomial time-delay system which satisfies the H∞ performance index are derived based on the Lyapunov-Krasovskii functional to guarantee external disturbances could be attenuated to a certain level. Moreover, in order to overcome the problem of non-ideal properties due to the actual circuit resulting in control performance degradation, the parameter uncertainty will be considered. The second theorem and stability conditions in the SOS form of the robust polynomial time-delay system are derived. Finally, the designed robust controller is realized via control board with a TI microprocessor, and is applied to the bidirectional converter with 2kW rated power in this paper. This thesis compares the proposed controller with other controllers which time-delay signals are not considered to verify the robust performance through the experiments of input voltage variations, external perturbations, load variations and inductance variations. Experimental results show that the proposed robust polynomial control systems with time-delay achieve better performances in both settling time and the maximum overshoot.

並列關鍵字

converter ； polynomial

參考文獻

[4] X.P. Liu, M. Ding, J.H. Han, P.P. Han and Y.L. Peng, “Dynamic economic dispatch for microgrids including battery energy storage,” in Proc. IEEE PEDG, 2010, pp. 914-917

[5] Z. Liao and X. Ruan, “Control strategy of bi-directional DC-DC converter for a novel stand-alone photovoltaic power system,” in Proc. IEEE VPPC, 2008, pp. 1-6.

[6] H. Bai and C. Mi, “The impact of bidirectional DC-DC converter on the inverter operation and battery current in hybrid electric vehicles,” in Proc. IEEE ICPE, 2011, pp. 1013-1015.

[7] S. C. Tan, Y. M. Lai and C. K. Tse, “General design issues of sliding-mode controllers in dc–dc converters,” IEEE Trans. Industrial Electronics, vol. 55, no. 3, pp. 1160-1174, 2008.

[8] T. F. Wu, C. H. Chang and Y. K. Chen, “A fuzzy-logic-controlled single-stage converter for PV-powered lighting system applications,” IEEE Trans. Industrial Electronics, vol. 47, no. 2, pp. 287-296, 2000.