精密單層雙軸氣浮運動平台之加速度曲線規劃分析

Abstract

本論文提出加速度曲線的規劃架構以改善系統產生無窮大的Jerk，此架構是基於給予系統突然的速度命令時，需要極大的加速度來實行，而突然的加速度則會產生無窮大的Jerk，並且根據牛頓第二定律F=ma也會對系統造成極大的負荷，因此進行加減速度曲線的規劃使加速度為連續曲線，不僅能夠讓運動過程維持平順的速度運動，還能使Jerk為連續的有限值，降低對系統的負荷。 此系統是以永磁無刷式線性馬達以及空氣軸承所組成的單層雙軸氣浮運動平台。將雙軸的系統解耦成三個(X、Y、Theta軸)單一輸入、單一輸出(SISO)系統。由於系統為不穩定的系統，系統識別方面採用閉迴路系統識別方法去進行數學模型的識別，並且使用Simulink內建「參數估測」搭配時域方法來得到三個(X、Y、Theta軸)單一輸入、單一輸出(SISO)系統的轉移函數。 控制架構上，主要先規劃出連續加減速度曲線，並且利用積分得出位置與時間的函數，得到位置命令的追跡(tracking)曲線，再搭配工業上常用的PID控制器以及串聯控制方法，達到控制目標。比較以往實驗室團隊所提出的「迫近及定位控制」(Access and Positioning control)架構，控制架構以同時輸入參考位置與參考速度的方式，並且利用繁複的運算使整體系統的H-infinite norm限制在一定的範圍內，最後再搭配改良後的Luenberger式狀態估測器去補償內外部的低頻干擾。加速度曲線規劃的控制架構使用較為簡單的PID控制器，在犧牲到達定位點的短暫時間，換取相較於「迫近及定位控制」架構較高的定位精度以及較低的最大超越量，在角度控制上，整體表現也比「迫近及定位控制」架構來的好。如果犧牲最大超越量，則可以換取較高的定位精度以及較快的定位時間，角度控制上，穩定性也明顯高於「迫近定位控制」架構。

This thesis addresses the fundamental problem of design of acceleration curve so that it can deal with the infinite Jerk when system starts moving. This structure is based on giving the system a sudden speed command that requires a great deal of acceleration, and a sudden acceleration produces an infinite jerk. According to Newton's second law, F=ma, this large acceleration can also cause a great load on the system. Therefore, the design of the acceleration curve is to make a continuous curve, not only let motion pro-cess maintain a smooth speed movement, but also make the Jerk a continuous finite val-ue, and reduce the load on the system. The system is a dual-axis air-bearing motion stage system consists of four perma-nent magnet brushless linear motors. For simplicity, in this thesis the complex system is decoupled to three(X, Y, Theta-axis) single input single output(SISO) systems. Because of the system is unstable, a closed-loop system identification method is used to identify the mathematical model. Finally, the transfer function of three(axis) single input, single output(SISO) system is obtained by using the embedded function, “Parameter estima-tion” under Simulink environment with time domain method. In control structure, mainly designing the continuous acceleration and deceleration curve first, and using the integral to get the position of time function. After obtaining the tracking curve of the position command which is position of time function, using PID controller and series control method to achieve the control target. Compared with the “Access and Positioning control” structure proposed by the lab team, the “Access and Positioning control” structure simultaneously inputs the reference position and ref-erence velocity, and the complicated operation makes the system’s H-infinite norm lim-ited to a range. Finally, using the augmented-Luenberger observer to compensate for the internal and external low-frequency disturbance. Design of acceleration curve structure uses simpler PID controller. If at the sacrifice of a short time to reach the location point, design of acceleration curve structure has a higher positioning accuracy and a lower maximum overshoot than “Access and Positioning control” structure. In angle control, the design of acceleration curve structure overall performance is better than “Access and Positioning control” structure. If at the sacrifice of maximum overshoot, design of ac-celeration curve structure has a higher positioning accuracy and a shorter time to reach the location point than “Access and Positioning control” structure. In angle control, the overall performance of design of acceleration curve structure is better than “Access and Positioning control” structure, too.