倒單擺最短時間豎起及定位控制之研究

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

劉克強(Ke-Qiang Liu)

指導教授 ： 吳昌暉

元智大學/工程學院/機械工程學系/碩士(1997年)

摘要

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.

關鍵字

最短時間 ； 控制 ； 倒單擺 ； 機械工程 ； 工程

並列摘要

無資料

並列關鍵字

Minimum-time ； control ； inverted pendulum ； MECHANICAL-ENGINEERING ； ENGINEERING