The Study On H_∞ Control Method Of Inverted Pendulum And Its Application

Inverted pendulums are ideal experimental platforms of study on automation control theory. It is clear when they are used to illustrate many abstract ideas in control such as stabilization of system, controllability, disturbance resistance etc. Therefore inverted pendulums have been classic tools in the control laboratoriessince the 1950s.The control of inverted pendulums is similar to the inverted performance of acrobatics sportsman and it's greatly clear and interesting, which interests many researchers of control theories in illustrating their new ideas in control by them. Because of high order, unstabilization, multivariable, nonlinear nature and strong coupling, inverted pendulums have been used to illustrate ideas in linear control such as stabilization of unstable systems. The examples in the field of nonlinear control are variable structure control, passivity based control, backstepping and forwarding, nonlinear observers, friction compensation and nonlinear model reduction. They are suited to illustrate task-oriented control such as swinging up and catching the pendulum, hybrid systems and control of chaotic systems. So this type of experimentation was called "the jewel of the crown of every control department"'-1'. Many researchers of modern control theories have been looking 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 history of inverted pendulum systems and robust control theory are discussed briefly. After that the H oo control theory (including H 皁 statement feedback control and its solutions, robust H oo control of uncertain system, disturbance resistance and robust stability) and the configurations, work principle and statement equations of single or double inverted pendulum systems are discussed respectively and following the H oo statement feedback controllers for them are designed and the MATLAB simulations are finished. The simulation results and practical control charts are also given in contrast with LQR control. In practical experiment, the swing-up of single inverted pendulum and balance control of single or double inverted pendulums got satisfying results. Then theIIinner framework, peripheral interfaces, instruction set and program developing method of four-axis motion controller GM-400(designed by Googol Technology Ltd) are thoroughly investigated. Finally the design principle of control program, program flow charts and main functions are discussed and the software platforms of inverted pendulum systems are built, which paves the way for the developing and investigating of inverted pendulum systems at a higher level.