H_∞ Robust Control Theory And Its Application To Double Inverted Pendulum System

In this paper, the H∞ standard control problem and state-feedback control method are researched and discussed in detail. Disturbance attenuation problem and H∞ Robust control of system with parameter uncertainty are systematically summarized. Based on this method, the H∞ state-feedback controller of double inverted pendulum system is designed.The double inverted pendulum system is a nonlinear and unstable control problem. Obviously the study of a typical, nonlinear and unstable system has the more important meaning on both the theory and methodology. Modeling for the double inverted pendulum has the instructional function to study the stability of the system. The paper analyzes the movement of a double inverted pendulum from the movement of the rigid body. The linear mathematical model of double inverted pendulum is constructed by mechanical Equation and the data of the actual plant. The H∞ state-feedback control theory based on Riccati equation is used to calculate the state-feedback control law for the double inverted pendulum. Using this approach, the key is to determine the values of the C1 , D12 matrixes and γ, which are defined in state space realization of the augmented plant of the pendulum system and Riccati equation, and to determine the method of calculating the Riccati equation. The principle and method of choosing the values of the C1, D12 matrix and y is researched and given from the experimental view. A programming method in Matlab environment is introduced, which can resolve Riccati equation. A robust controller is presented, and the resulting closed-loop system is analyzed by simulation. The results show that the double inverted pendulum equilibrium control system designed by the presented method has stronger robust stability. By contrast with LQG(Linear Quadratic Gaussian) simulation results, a conclusion can be drawn that H∞ state-feedback control theory is an effective design approach.A control program is designed and programmed in Turbo C language, which can manage the experiment of double inverted pendulum. The framework, components, datastructure, control arithmetic and function of the program are given briefly. The LQG and H∞ control law of the double inverted pendulum is tested in real equipment. The performance is not good by LQG control method, but H∞ control method can improve the control result.