The Optimal Control Of Inverted Pendulum System With Delay

Optimal control theory is an important part of the control theory. Generally, theactual perturbation of the system that we study is ignored, for example, the timedelay. This paper studies the optimal control of inverted pendulum system with timedelay. In the practical problems, it will constitute a delayed control of the entiresystem, because of the reaction time of the system and the calculating time of thecomputer, etc. In addition of the inverted pendulum system is a simple model incontrol theory. Therefore, it is very necessary to study the optimal control of invertedpendulum system with time delay.The control of the computer system is discrete, but both the general system thatwe study and the performance index function corresponding to the given system arecontinuous. To get the optimal control of the system, it is necessary to discretize thedifferential equation of the system and its performance index function. Then thecontrol scheme can be calculated by the computer. In this paper, the delay time canbe not considered integer multiple of the sampling time. We classify all kinds ofdelay time and give the different optimal controls corresponding to the differentdelay time.