Research of Minimum-time erect & position control for an inverted pendulum

• Main Authors: Liu, Ke-Qiang, 劉克強
• Other Authors: Wu, Chang-Hui
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/89419501305431203053

碩士 === 元智大學 === 機械工程研究所 === 86 === Resulting from the industrial development, it is very important about the "TIME". It says, "Time is money". Therefore, to improve our future industrial development, applications for saving more time of the optimization in engineering will be a good field of further study. In this thesis, the focus is on the inverted pendulum system, which allows swing the bar from the bottom to the top in a shortest time and stays at the standing position for the longest time. Usually, the problem of the time-controlled system will be solved by the analytical method for it''s minimum time in the 2nd order mode. The inverted pendulum system, thus, is the 4th order nonlinear system and is not capable to adopt the analytical method. Therefore, Iteration method is used to approach the minimum and solve this problem. Since the more iteration takes, the more time convergence will increase, Mr. Wu, Chia-Ju (etc., 1992) propose a numerical method to solve this problem. That is to improve the iteration method of convergence speed to save the process time. In 1995, Mr. Wu published the application of this Method on inverted pendulum system at "Journal of In telligent and Robotic Systems: Theory & Applications". However, in the document of Mr. Wu''s study, the big angle control and the possibility of the implement in high order non-linear system was not discussed.Due to there are varies and wide-rang of possible solutions, a numerical method is developed in this study to find out the solution of high order nonlinear system of inverted pendulum system. and from the result of this study, the numerical method applies to linear system will save about 20% CPU running time.In addition, the state-feedback control theorem is used to solve the problem of balance position. By using the angle variable to switch those two methods to implement the inverted pendulum system completely. This enhances the bar from bottom to top in very short time, and keeps the bar in / around the balance position. At the end of this research, the numerical simulation method will be used to verify this control law is universality and superiority.