粒子群演算法於二階時變系統穩定分析與穩定化設計

Stability and Stabilization for Second-Order Time-Varying Systems Based on PSO Algorithm

董聖龍(Shen-Lung Tung)

指導教授 ： 莊堯棠

國立中央大學/資訊電機學院/電機工程學系/博士(2011年)

摘要

本論文係研究二階向量微分線性時變系統之指數穩定性分析及穩定化控制設計，研究的範疇包含奇異與非奇異等兩大系統，而且系統中含有的非線性擾動因子，也在本文的探討之列。本研究之技術關鍵，乃藉由估算線性時變系統狀態軌跡大小的邊界，將時變系統的穩定問題，轉換為非時變系統的穩定問題。進而，推導出時變系統的指數型穩定性分析及穩定化設計準則。而且為解出最佳的指數型穩定分析準則與穩定化控制器，本論文也提出一種命名為「適應性模糊粒子群最佳化演算法」(AFPSO)。此AFPSO乃是利用模糊理論，適應性地動態調整粒子群最佳化演算法(PSO)之兩個加速度參數，以改善粒子搜尋的精準度與效率性。而AFPSO又可彈性的衍生出多種的變種演算法則，進一步地改善粒子全域搜尋的能力與效率。例如，結合二次插補交叉的計算，形成AFPSO-QI演算法；或併入限制因子，形成AFPSO-cf演算法。最後，本論文提出的穩定化設計法則，應用至三個自由度(3DOF)的雙軸拖曳車之前軸避震系統上。經由模擬的結果顯示，本法可使得車輛的震動及擺動狀態，快速達到指數式的衰減穩定，改善駕駛的舒適感與車輛的操控性。

關鍵字

時變系統 ； 二階向量 ； 粒子群最佳化演算法

並列摘要

Stability and Stabilization for Second-Order Time-Varying Systems Based on PSO Algorithm
Abstract

In this dissertation, uniformly exponential stability analysis and stabilization design of linear time-varying systems represented by the second-order vector differential equations are concerned. The systems with a singular or a nonsingular leading coefficient matrix and with bounded nonlinear uncertainties are all discussed. Using bounding techniques on the trajectories of linear time-varying systems, the stability problem of linear time-varying systems is transformed to that of linear time-invariant systems. Then the sufficient conditions for uniformly exponential stability and stabilization are derived. Besides, an adaptive fuzzy particle swarm optimization (AFPSO) algorithm is also proposed for solving the optimization problems of uniformly exponential stability and stabilization. The proposed AFPSO utilizes fuzzy set theory to adjust the PSO acceleration coefficients adaptively to improve the search accuracy and efficiency. Two variants of AFPSO are constructed by incorporating with the quadratic interpolation and the crossover operator called the AFPSO-QI as well as integrating with a constriction factor called the AFPSO-cf, these may further improve global searching ability and effectiveness. Finally, the proposed method is applied to active suspension systems for a three-degree-of-freedom (3-DOF) twin-shaft vehicle of front axle suspension. The simulation results show that all the states of vehicle can be guaranteed in an optimal exponential decay in nearly real-time.

並列關鍵字

time-varying system ； second-order vector ； PSO

參考文獻

[1] Y. Fujisaki, M. Ikeda, and K. Miki, “Robust stabilization of large space structures via displacement feedback,” IEEE Transactions on Automatic Control, vol. 46, no. 12, pp. 1993-1996, 2001.

[2] K. Inoue, S. Yamamoto, T. Ushio, and T. Hikihara, “Torque-based control of whirling motion in a rotating electric machine under mechanical resonce,” IEEE Transactions on Control Systems Technology, vol. 11, no. 3, pp. 335-344, 2003.

[3] S. L. Campbell and N. J. Rose, “A second order singular linear system arising in electric power systems analysis,” International Journal of Systems Science, vol. 13, no. 1, pp. 101-108, 1982.

[4] H. Tasso, “On Lyapunov stability of dissipative mechanical systems,” Physics Letters A, vol. 257, no. 5-6, pp. 309-311, 1999.

[5] H. Tasso and G. N. Throumoulopoulos, “On Lyapunov stability of nonautonomous mechanical systems,” Physics Letters A, vol. 271, no. 5-6, pp. 413-418, 2000.