Dissipative Control For A Class Of Linear Output Tracking Systems

Dissipative theory plays an important role in the stability research of control systems since it was brought forward in1970s. Especially for the input-output systems, the dissipative theory provides a frame in system designing and analyzing. The essence of dissipative theory is that, there exists a non-negative storage function, such that the rate of energy consuming is always less than the rate of energy supplying. Dissipative theory can contact some mathematic tools with physical phenomenon, and has been applied to many control problems. Dissipative theory has been approved to be a kind of effective method in electromechanical system, robot control and adaptive control, nonlinear H∞control and so on.Output tracking control is an important problem in control theory, its essence is making the controlled output approach the reference output. Output tracking control is closely related to our daily life. It has been applied to many realms including aircraft, missile interception, and so on. The traditional methods to solve the output tracking problem are PID control, optimal control and H∞control. Currently, there exists no research on solving the tracking control problem by dissipative theory.This paper studies the dissipative control problem for the output tracking systems. Firstly, according to transforming the tracking system into augmented form, the dissipativity and passivity of the augmented tracking system are defined. Secondly, the conditions that the closed loop augmented tracking system is dissipative and passive are given, and the dissipative and passive state-feedback controller for the tracking system and time-delay tracking system are designed respectively, such that the closed-loop systems are dissipative and passive. Finally, numerical examples are given to verify the effectiveness of the theorems, and the tracking process is simulated by Matlab. The simulation result shows that the dissipative controller is effective in the tracking process. Eventually, compare the tracking performance between the control system with dissipative controller and controller.