Research On Control System For Multistage Inverted Pendulum Based On Fuzzy Logic

Inverted pendulum system is a typical model of single-input and multi-outputs, multivariable, nonlinearity, strong-coupling and absolutely instability naturally. The research on the accurate control of the inverted pendulum has great engineering value to the control of the complex industrial object. What is more, the research of inverted pendulum has many important realistic meaning in the research such as, the walking of biped robot, the launching process of rocket and flying control of helicopter. This paper is based on the linear inverted pendulum of GUGAO Company. The main works in this paper are the following:1. After concisely introducing the structure and moving characters of inverted pendulum system, the mechanism and mathematical models of double and triple inverted pendulum are presented, employing newton-oula analysis and Lagrange equation method respectively. It is proved that open control system of multistage inverted pendulum system is instability, but it is controllable and observable on equilibrium point. At the same time, we caculated that the comparative controllability of triple inverted pendulum is much smaller than that of double inverted pendulum, so it is more diffcult to control a triple inverted pendulum successfully.2. Linear quadratic optimal controller is designed for double inverted pendulum. The thought of obtaining fuzzy control rule base based on the ideal response curve of closed-loop system, which reduces the subjective error in obatining the fuzzy control rule list employing traditional methods, is presented. On this basis, the state synthesis fuzzy controller and hierarchy fuzzy controller are designed for double inverted pendulum. The simulation results are given and the infection of quantification factors to effect of control is studied.3. As for triple inverted pendulum, the LQR conreoller is designed; the essence of variable universe fuzzy control is stated and its control performance for linear and non-linear system is deeply studied. The algorithm of input-variables weight variable fuzzy control is detail explained and the expansion-contract factor based on fuzzy inference machine is constructed in detail. At the same time, the adjustment-factor of output variables is designed based on the ideal output curve. Under matlab/simulink circumstance, control effects of fore-mentioned fuzzy controllers for triple inverted pendulum are realized. Some contrast analysis between different controllers is done carefully. 4. The main components and control mechanism of double inverted pendulum hardware systems are briefly introduced. The program of fuzzy control algorithm for double inverted pendulum is scheduled. The response curves of numerical control system when the pendulum is stable, changing some parameters or being disturbed are obtained. In order to test the robustness and the capacity of resisiting disturbance, lots of experiments are done and the rusluts are analysised in very great detail.Results of simulation and experiments proved that the controllers designed in this paper have a good stability, robustness and adaptability.