Research On Control Algorithm Of Linear Inverted Pendulum System

Inverted pendulum is a typical fast, multivariable, non-linearity, strong-coupling and naturally unstable system. During its control process,it can reflect many crucial questions in the control theory, such as calm question, non-linear problem, robust question as well as tracking question and so on. It is the favorate problem in the control theory and tests the modern control theory,and also the control technique and idea is useful in average industrial process. The research on inverted pendulum system has the profound significance in theory and project application.The correlative scientific research achievement has already applied to astronautics science technology and subject of robot and so many domains.In this paper, the research object was the linear inverted pendulum system and the experimental tool was solid line inverted pendulum control device which provided by the Googol companies. The author studied the stability of double inverted pendulum and triple inverted pendulum system by the use of the device. The main work was as follows: firstly, the author described the significance of the study on the stability of inverted pendulum system, and also included the development history and future. Secondly, according to the characteristics of linear inverted pendulum system, the author established mathematical model of double inverted pendulum and triple inverted pendulum system by using of linear Lagrange equations, and got the linear state space equation near the equilibrium point of the system. Lastly, the author made the qualitative analysis of double inverted pendulum and triple inverted pendulum system by the linear control theory and the Conclusion was that the inverted pendulum system was a linear open-loop unstable system which was controllable and observable.In this paper, the author designed a Two-dimensional fuzzy controller based on fusion of fuzzy controller function by using of the fuzzy control algorithm. At first, the paper explained the process of fuzzy controller design; established a complete fuzzy controller based on the characteristics and control requirements of the Inverted pendulum system. The double inverted pendulum system was simulated and physical control by using Matlab/Simulink and compared the experimental results with the results of classical PID controller. Through the compared analysis, we could conclude that both the system of Simulink and physical control, fuzzy control have achieved good control results and showed the superiority of intelligent control. And then, the author designed a linear quadratic optimal controller for triple inverted pendulum system and was simulated by Matlab/Simulin. And also the author analyzed the results of the experiments and how the matrix Q affected the system.Finally, the author tried to the physical control of triple inverted pendulum system, and the results indicated that it was much more difficult to control triple inverted pendulum than double inverted pendulum.