Study On The Stability Control Of Double Inverted-pendulum System

The inverted pendulum system as a typical higher order system with multi-variable,non-linear, fast and strong coupling is the ideal device to study various control theory andmethods.In the controlling process, it can effectively reflect many key problems such asrobustness, nonlinear and tracking in control, so researching of inverted pendulum systemhas the important meaning in theory. On the other hand, any phenomenon with fulcrumunder its barycenter is similar to an inverted pendulum system, the study on stability controlof inverted pendulum has an important practical significance in the biped robot, Rocketvertical posture and direction of the satellite control.In this thesis, linear inverted pendulumsystem as the research object, using a variety of control methods for the stability control ofinverted pendulum. Main research work is declared below:1) the paper introduces the research profile of the inverted pendulum system as well asvarious control methods. Using Lagrange Equation for the System Modeling, derivation itstransfer function and State-space equations, moreover, analysis of its stability,controllability and observability.2) Designed the controller that based on the linear quadratic (LQR) optimal controltheory to control the inverted pendulum system, and studied the effect of the control thatwas parameter settings impacted. But LQR is Mainly for the Linear systems, in processingdouble inverted pendulum this serious nonlinear system, it must be linearization themathematical model of the system, So, LQR’s control range is not enough.3)The paper focused on the mathematical foundations of fuzzy control and methods,designed the fuzzy controller to control the system. Contrany to the “rules explosion”, thepaper designed the fusion function to reduce the dimension of the fuzzy controller, therebyreducing the control of the controller rules, to make it more concise and effective.4) Simulation the control effect in the MATLAB/SIMULINK. Simulation results showthat: the controller has better robustness and stability.