臺灣博碩士論文加值系統

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 我們都知道當系統有適當的相位邊限以及增益邊限的話，將會使系統有良好的強健性，因此在本研究中，我們主要是將探討如何以相位邊限以及增益邊限這兩個頻域規格來設計控制器，而其中所探討的控制器類型包含了比例-微分控制器(Proportional-Derivative Controller) 、比例- 積分控制器(Proportional-Integral Controller) 、比例- 積分- 微分控制器(Proportional-Integral-Derivative Controller)、以及相位領先或落後補償器(Phase Lead or Lag Compensator)這幾種形式。由於整個控制器的設計流程中，為了要使得整個系統同時達到我們所要求的相位邊限以及增益邊限的規格將會是非常複雜且需要不斷以嘗試錯誤(tryand error)的方式來設計，因此我們利用增益-相位邊限測試方法(Gain-PhaseMargin Tester Method)來實現。增益-相位邊限測試方法是一種非常快速且直覺的控制器設計方法，可以將控制器的解轉換成二維平面，只要讀取圖上的值即可找出解來。而在一些情況下，控制器的解可能會超過二維平面，因此我們利用穩態誤差(steady-state error)的條件限制，進而不增加控制器設計上的複雜度。最後我們也利用幾個簡單的例子來作模擬及測試。
 In control theorems, gain margin and phase margin are important specificationsin the frequency domain for the analysis and design of practical control systems andhave served as important measures of robustness analysis. In this thesis, we willdiscuss how to design of controllers to satisfy required gain and phase marginspecifications, and the controllers are proportional-integral (PI) controller,proportional-derivative (PD) controller, proportional-integral-derivative (PID)controller, and phase lead or lag compensator.In the procedure of controller design, it is very hard and complicated to let thesystem achieve our required gain and phase margin specifications, simultaneously.So we utilize gain-phase margin tester method to achieve this goal. The gain-phasemargin tester method can transform the solutions of the controller intotwo-dimension surface, and we can find solutions on the figure. In some cases, thesolutions of the controller will exceed two-dimension surface, so we utilize thecondition of steady-state error to constrain the dimension of solutions, and avoid toincrease the complexity of controller design. Finally, the effectiveness of themethod is demonstrated by examples.
 Chapter 1 Introduction .........................11-1 Motivation .........................11-2 Organization of this thesis .........................2Chapter 2 Fundamental Concept and Research Method .........................32-1 Gain margin and Phase margin .........................32-1-1 Gain margin .........................32-1-2 Phase margin .........................62-2 Steady-state error .........................92-3 Kharitonov theorem [7, 8] .........................14Chapter 3 Main Method and Simulation Results .........................163-1 PI Controller .........................173-2 PI controller with uncertain plant .........................253-3 PD controller: .........................323-4 PID controller .........................363-5 Phase Lead or Lag compensator: .........................43Chapter 4 Conclusions .........................50Reference......................... 51
 [1] B. C. Kuo, “Automatic Control Systems”, Addison-Wesley, 8th ed., 2002.[2] C. H. Chang, and K. W. Han, “Gain Margin and Phase Margin Analysis of a Unclear Reactor Control System with Multiple Transport Lags”, IEEE Transactions on Nuclear Science., vol. 36, no. 4, pp. 1418-1425, 1989.[3] G. F. Franklin, J. D. Powell, and A. E. Naeini, “Feedback control of dynamic systems”, Addison-Wesley, 3rd ed., 1994.[4] H. W. Fung, Q. G. Wang, and T. H. Lee, “PI tuning in Terms of Gain and Phase Margins,” Automatica, vol. 34, No. 9, pp. 1145-1149, 1998.[5] J. H. Lee, “A New Phase-Lead Design Method Using the Root Locus Diagrams”, IEEE Trans. On Automatic Control, vol. 50, No. 11, pp. 1887-1891, 2005.[6] K. S. Yeung, K. Chen, ”A Non-Trial-and-Error Method for Lag-Lead Compensator Design,” IEEE Transaction on Education, Vol. 41, pp.76-80, Feb. 1998[7] K. S. Yeung, and S. S. Wang, “A simple proof of Kharitonov''s theorem”, IEEE Trans. Automat. Control, vol. 32, no. 9, pp. 822-823, 1987.[8] N. K. Bose, and Y. Q. Shi, “A Simple General Proof of Kharitonov’s Generalized Stability Criterion”, IEEE Transactions on Circuits and Systems, vol. 34, no. 8, pp. 1233-1237, 1987.[9] N. Tan, I. Kaya, C Yeroglu, and DP. Atherton , “Computation of stabilizing PI and PID controllers using the stability boundary locus”, Energy Conversion and Management, Vol.47, No.18-19, pp. 3045-3058, 2006[10] Q. G. Wang, H. W. Fung, and Y. Zhang, "PID Tuning with Exact Gain and Phase Margins," ISA Transactions, Vol. 38, pp. 234-249, 1999.[11] Q. G. Wang, Z. Ye, and C. C. Hang, “Tuning of phase-lead compensator for exact gain and phase margins”, Automatica, vol. 42, No. 2, pp. 349-352, 2006[12] S. Sujoldzic and J. Watkins, “Stabilization of an Arbitrary Order Transfer Function with Time Delay using PI and PD controllers,” Proceedings of the American Control Conference, Minneapolis, MN, 14-16 June 2006 Page(s):6[13] S. Y. Chu and C. C. Teng, “Tuning of PID controllers Based on Gain and Phase Margin Specifications Using Fuzzy Neural Network,” Fuzzy sets and Systems, 101, pp. 21-30, 1999.[14] W. K. Ho, C.C. Hang, and L.S. Cao, “Tuning of PID Controllers Based on Gain and Phase Margin Specifications”, Automatica, vol. 31, no. 3, pp. 497-502, 1995[15] W. Tang, Q. G. Wang, Z. Ye, Z. Zhang, “PID tuning for dominant poles and phase margin”, Asian Journal of Control, 2006[16] Y. J. Huang and Y. J. Wang, “Robust PID controller design for non-minimum phase time delay systems”, ISA Transactions., vol. 40, no. 1, pp. 31-39, 2001.[17] Y. J. Huang and Y. J. Wang, “Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem”, ISA Transactions., vol. 39, no. 4, pp. 419-431, 2000.
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