The Research On Robust Control For Inverted Pendulums

Inverted pendulums are ideal experimental platforms of study on automation control theory. It is clear that they are used to illustrate many abstract ideas in control such as stabilization of system, controllability, disturbance resistance etc. Since the 1950s, many researchers of moderns control theories all have looked them as objects, and new control theories and methods are discovered, which are broadly used in the fields of astronautics and robotics. From which we can see great values in theory and practical engineering by studying inverted pendulums.In this paper, the robust control methods of the single, double and triple inverted pendulum were studied for the experiment equipment made by Gu-Gao Company. First, by using kinetic equations and Lagrange equations, the nominal models of the single, double, triple inverted pendulum and their uncertain models were established. Then, based on the theory of LMI, the design method of robust H_∞state-feedback controller was deduced for the inverted pendulum system. In order to compare with other methods, PID and state-feedback control methods were used for the single inverted pendulum system, LQR method was applied for the double inverted pendulum system, and the genetic algorithm, robust LQ methods were used for the triple inverted pendulum system. Robust H_∞state-feedback method was compared with these methods. By the simulation comparisons, we can know that robust H_∞control method has a better anti-jamming and robustness than the other methods. Therefore, using this method to design the controllers of the inverted pendulum can further improve the control performance of the system.