臺灣博碩士論文加值系統

本文主要是針對馬達-肘節機構的節能運動軌跡規劃方法進行研究。首先在系統建模方面分別是對馬達-肘節機構系統建立電氣方程式和機械方程式，並且考慮真實射出成型機在鎖模過程是具有衝擊力的，因而建立其衝擊力模型來加以描述馬達-肘節機構的鎖模過程。本文在系統鑑別方面是使用兩階段式鑑別方法，其鑑別過程乃是使用實數型基因演算法(RGA)來對系統進行兩階段式鑑別，分別是對鎖模前和鎖模後，設計兩種不同的適應函數來對系統進行參數鑑別，目的是在提高參數鑑別之精度及節省鑑別時間，經由數值模擬與實驗結果已得驗證。在本文中，我們主要的研究工作是在設計點對點（PTP）的節能運動軌跡，經由高階多項式的定義，使其滿足在最初和最後時間所設定之拘束條件(位移，速度，加速度和急跳度)而產生之最節能的運動軌跡，文中主要是使用永磁同步伺服馬達(PMSM)-肘節機構之機電系統的電氣方程式和機械方程式，來設計輸入絕對值電能（IAEE）的高階多項式運動軌跡，並使用實數型基因演算法(RGA)來確定高階多項式的係數值，以達到節能的目的，然而，高階多項式的階數是規劃節能運動軌跡的問題之一。經由數值模擬與實驗結果驗證，馬達-肘節機構機電系統的單次運動，在所提出設計的30階多項式速度運動軌跡比傳統的梯形速度運動軌跡，可節省12 %之能量輸出。本文經由收斂分析也驗證使用24階多項式，即可得到最節能之運動軌跡。本文主要是提出最小輸入絕對值電能節能軌跡的規劃方法，其方法可以應用到任何一種需要節能的點對點運動軌跡之機電系統。

The purpose of this study was to find an energy-saving trajectory for a motor-toggle mechanism. The effects of clamping forces on a motor-toggle mechanism are dynamically modeled in this study. The clamping unit used was a simple spring-damper model. Based on a real application, an impulse model associated with clamping effectiveness had to be considered for the process of clamping. A two-stage identification method also had to be developed to validate the dynamic responses of the unclamping and clamping motions. The two-stage identification method for the system parameters was carried out through a real-coded genetic algorithm (RGA) with two different fitness functions. The purpose was to improve the accuracy of parameter identification and identify the amount of saved time, both of which were obtained by the results of numerical simulations and experimentation. The point-to-point (PTP) trajectory is described by a high-degree polynomial, which satisfies the end conditions of displacement, velocity, acceleration and jerk at the initial and final times. Planning an energy-saving trajectory through the use of a high-degree polynomial for a toggle mechanism driven by a permanent magnet synchronous motor (PMSM) is quite useful. However, it was essential to find a sufficient degree for the polynomial that would produce an energy-saving trajectory. The real-coded genetic algorithm (RGA) method was employed to determine the coefficients of the polynomial, and its fitness function was the inverse of various input energy values. Comparisons of the results of the numerical simulations and experiments for polynomials of differing degrees during the whole operation of motion were analyzed. Finally, it was found that the minimum input absolute electrical energy (IAEE) value was produced when the highest-degree polynomial was used. From the percentage of relative error with respect to the input absolute electrical energy value of a trapezoidal trajectory, it was found that the percentage of relative error was -12% when the 30th-degree polynomial trajectory was used with a sufficient minimum input energy value for a single movement of the motor-toggle mechanism system. From convergent analysis, it was found that the 24th-degree polynomial was efficient in designing the energy-saving trajectory. The proposed methodology can be applied to any mechatronic system which requires the design of a minimum-energy point-to-point trajectory.

摘 要 i
Abstract ii
Acknowledgements iv
Contents v
Figure Captions viii
Table Captions xi
Nomenclature xii
Greek Letters xvi
Chapter 1 Introduction 1
1.1 Background 1
1.2 Content organization 6
Chapter 2 Mathematical Model 8
2.1 PMSM drive system 9
2.2 Impulse model 14
2.3 Motor-toggle mechanism model 15
2.4 Reduced formulation of differential equations of motion 19
Chapter 3 System Identification 22
3.1 Two-stage fitness functions 22
3.2 RGA 25
3.3 Swept-frequency sinusoid waveform 27
Chapter 4 Trajectory Planning 28
4.1 Trapezoidal trajectory planning 28
4.2 Polynomial trajectory planning 30
4.3 Input absolute electrical energy (IAEE) 32
4.4 Increasing function definition 35
4.5 RGA of trajectory planning 36
4.6 Energy-saving trajectory planning algorithm 37
Chapter 5 Numerical Simulations and Experiments 39
5.1 Experimental setup 39
5.2 Results of system identification 40
5.3 Results of minimum IAEE 47
5.4 Results of convergent analysis 52
5.5 Results of quadratic and minimum IAEE values 53
5.6 Comparison of trapezoidal and polynomial trajectories 57
5.7 Discussion 63
Chapter 6 Conclusion 64
References 65
Appendix A Dynamic Formulations for the Motor-Toggle Mechanism with a Clamping Unit 71
Appendix B Details of Equation (18) 84
Appendix C Details of Equation (22) 86

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