Research On LQR-Fuzzy Control Algorithm Of Inverted Pendulum System

Inverted pendulum system is multivariable, nonlinear, strong-coupling and instability naturally. The research of inverted pendulum has many important realistic meaning in the research such as, the walking of biped robot, the lunching process of rocket and flying control of helicopter, and many correlative productions has applications in the field of technology of spaceflight and subject of robot.LQR&Fuzzy control theory is introduced to study simulation and the controlling problem in realtime of three inverted pendulum in this paper. Success of control of hardware pendulum system, and success of simulation proves that this controller has very good stability, robustness and adaptability. Main research work is declared below:The mathematical model of three inverted pendulum is proposed. It is proved that open control inverted pendulum system is instability, but it is controllable and observable on equilibrium point. At same time the controllability of three inverted pendulum is very small, so control of three inverted pendulum is very difficult.Research on LQR control algorithm of inverted pendulum system. By using optimization control theory, The selection of matrix Q and R is dicussed. It is introduced how to realize the simulation of the inverted pendulum system by the Matlab. Three inverted pendulum LQR controller is designed and emulated. LQR control model is programmed by Simulink5.0, control of double inverted pendulum hardware system is realized. Moreover, the response curves of each state variable and the curve of control quantity when the pendulum is stable or being disturbed are presented. At last, a photo when the pendulum is stable is shown.Research on LQR&Fuzzy control algorithm of inverted pendulum system. The dimension of input varieties of fuzzy controller is depressed by designing a optimal state variables synthesis function using optimization control theory, and it can reduce the rules of fuzzy sharply, 'rule explosion' problem is solved. The infection of quantification factors to effect of control is studied. The quality of LQR&fuzzy controller is improved by adding auto switching quantification factors.The simulation of LQR&Fuzzy control of three inverted pendulum system is discussed . It is introduced how to realize the simulation of the inverted pendulum system by the Matlab. It makes simulation model more agility, simulation work become more convenient. Simulation experiment of the LQR&Fuzzy control of inverted pendulum is very well implemented by using LQR&Fuzzy control theory, that the result shows that it not only has quite good stability, but also is able to make the cart of the pendulum moving to the place where it is appointed by us in advance, along the orbit.