Investigation on the car of the inverted pendulum systemAbstractpendulum control system is a complex, uncertain, nonlinear systems, control theory teaching and various control experiment is ideal experiment platform. Study on inverted pendulum system can effectively reflect in control of many of the typical issues : such as nonlinear problems, robustness, stabilization, servo and tracking problems. Through the control of inverted pendulum, used to verify that the new control method of strong ability to handle nonlinear and instability problems. At the same time, its control method in the robot for military, aerospace, and General in the field of industrial processes have a wide range of uses, such as in the process of walking robot balance control, vertical control in the rocket and satellite attitude control in flight.Keywords : nonlinear, pendulum, balance control, servo1. IntroductionInverted pendulum is in multiple areas of robotics, control theory, computer- controlled, multi-technology organic Combination, the controlled system is an absolute instability, higher-order, multivariable, strongly coupled nonlinear System can be used as a typical control object to study it. The initial study began in the twentieth century 1950s, the Massachusetts Institute of Technology (MIT), cybernetics experts, based on the principle of rocket launch booster design the equipment of an inverted pendulum. In recent years, a new control method, people are trying to test new control methods have a strong handle multivariate, nonlinear, and absolutely unstable system capacity through a typical inverted pendulum control object, and thus from which to find the best control methods. Inverted pendulum system as a control theoretical research in an ideal experimental tool for the teaching of automatic control theory, experiment and research to build an experimental platform to some kind of control theory or method used to test a typical program to promote control system theory, the development of new ideas. Due to the extensive application of control theory, thus the system of methods and techniques in the semiconductor and precision instrument processing, robot control technology, artificial intelligence, missile intercept control system, aviation docking control technology, rocket launchers vertical control the satellite flight attitude control, and general industrial applications, has a broad development prospects. Planar inverted pendulum can be more realistic simulation of the rocket flight control and walking robot stability control.2 .Control ResearchInverted pendulum swing-up problem is a classic experiment in the control theory, the essence of the inverted pendulum system from a stable equilibrium state in the role of external forces automatically transferred to another state of equilibrium. In this process, we demand from the swing fast, but not too much overshoot.Main sliding mode control for inverted swing-up control method, Di color predictive control, partial state feedback control, optimal control, energy control, supervision and control of anthropomorphic control, neural network control, evolutionary control, but the main focus In the energy control, optimal control, intelligent control.Do not apply to non-linear input and output, and many commonly used linear control theory based on nonlinear theory, the head ljif the following several methods have been successfully inverted pendulum starting to swing control.1976, MoiltIJ, who proposed a control system contains two controllers, one controller to automatically swing, and the other to stabilize into the inverted pendulum system near equilibrium. In general, the swing-up controller by shaking the inverted pendulum movement to a specified range, then the controller switches to another responsible for the stable part. 1996, Torres. PomalesJ design a simple sliding mode controller for inverted pendulum swing-up.Based on the simple control of the energy terms is to control the energy of the pendulum rather than control the position and velocity of the pendulum. Yoshida using the energy of the linear inverted pendulum swing-up control, the FantoniE41 energy control, but the controlled object the controlled object is a plane motion of a pendulum. The Astrom detailed account of the energy control theory, the control object is a straight line an inverted pendulum. Fu Ying, Zhang Guangli energy feedback method to complete the inverted pendulum swing-up control, similar to the above method, relatively speaking, more experienced, and successful implementation of a kind of a straight line for inverted pendulum swing-up control.Numerical algorithms for optimal control, the calculation of the optimal control law in the state variables when there are fewer, but more for the state variables, especially the problem with endpoint constraints are difficult to achieve. Hou Xianglin 71 based on the optimal method of fast swing-princ