臺灣博碩士論文加值系統

為了控制單軸滾珠導螺桿進給系統，本論文推導單軸滾珠導螺桿進給系統之運動方程式並建立運動模型，以特徵值及特徵向量觀察運動模型頻率響應峰值之組成。結合PID控制器、疊代學習控制器和零相位巴特沃斯低通濾波器並使用IPSO (改良式粒子群演算法)以及HPSO(混合粒子群演算法)模擬控制，模擬結果顯示控制器能有效的控制系統位移。在模擬中可以發現循跡誤差有明顯的降低，其誤差降低且頻寬隨著疊代次數增加而自動調整大小，再利用經驗模態分析誤差訊號，拆解成數個內稟模態函數，結果顯示控制器可以在重覆學習控制下消除循跡誤差，計算疊代內稟模態函數與快速傅立葉的訊號分析，了解誤差如何逐次降低的相關性，藉以得知系統在隨疊代次數增加開發的控制器如何處理誤差訊號於低頻至高頻的問題。

To control a single-axis ball screw feed system, this thesis establishes the model first and derives linear equation of motion and solves in frequency response. Solution of the eigenvalues and eigenvectors shows the feed system consists of several peaks in different mode shape frequency responses. Improved particle swarm optimization and hybrid particle swarm optimization are used to tune the gains of PID controller, iterative learning control gain and the bandwidth of zero phase Butterworth filter for reducing the tracking error with repetitions. Simulation results show that the developed controller can effectively lower the RMS tracking error with as iterations. Intrinsic mode functions of empirical mode decomposition are used to demonstrate the mechanism of eliminated tracking error as repetitive learning process. Correlation coefficient of intrinsic mode functions with tracking errors will examine the shift of compensated low-frequency error signals to high-frequency error signals as repetitive learning.

中文摘要 I
Abstract II
謝誌 III
目錄 IV
表目錄 VII
圖目錄 VIII
第一章 緒論 1
1-1研究動機 1
1-2 文獻回顧 2
1-3 論文架構 4
第二章 理論基礎 5
2-1單軸滾珠導螺桿進給驅動數學模型 5
2-1-1 進給剛性計算 7
2-2數值模擬 11
2-3 PID控制器 14
2-4 疊代學習控制器(Iterative Learning Control, ILC)15
2-5粒子群最佳化演算法(Particle Swarm Optimization, PSO)20
2-5-1收縮係數 24
2-5-2 線性時變加速係數 25
2-6被動學習因子 26
2-7改良式粒子群優化演算法(Improved Particle Swarm Optimization, IPSO) 27
2-8混合粒子群演算法(Hybrid Particle Swarm Optimization)31
2-9巴特沃斯濾波器(Butterworth Filter) 32
2-10經驗模態分解法(Empirical Mode Decomposition Method, EMD) 35
2-11系統響應評估法則 38
2-12 相關性計算 38
第三章 實驗架構 41
3-1單軸滾珠導螺桿進給驅動系統架構 41
第四章 數值模擬結果 44
4-1 PSO-ILC-PID-filter 控制器模擬 44
4-2 PSO演算法模擬比較 46
4-3 系統收斂性能與循跡誤差 48
第五章 結論與展望 85
5-1 結論 85
5-2 未來研究 85
參考資料 86

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