The Design For Optimal Robust Steady-state Tracking Controller

l₁ optimal control theory as complementary and parallel to H_∞ theory has obtained extensive attention and many meaningful research fruits. l₁ robust stability and robust performance has become an important and significant research subject. Many research problems about l₁ control were handled with truncation. The paper mainly analysis the robust performance of plants with fixed-order controller.Recently l₁ optimal control has been used to research optimal tracking problems. Steady-state error is one of important indexes of a tracking system. Some previous papers gave necessary and sufficient conditions of obtaining optimal steady-state tracking and the other gave exact formula of the worst-case robust steady-state tracking error of a system under coprime factor perturbations. These results have focused on robustness analysis of a given system, and unfortunately there has been no discussion nor description on the controller synthesis.The paper mainly consider the robust steady-state tracking problem when the system under consideration is subject to multiply and coprime factor perturbations as well as external disturbance. With the help of Youla parameterization, we propose an exact formula for computing the worst-possible steady-state absolute value of the control error. Using this formula, we show that under multiply perturbation the problem of designing a controller that minimizes the worst case steady-state controller error is reduced to the optimal robust stability. The proposed controller eventually can be obtained by solving a standard linear programming problem. Under coprime factor perturbation the problem of designing a controller is reduced to l₁ optimal robust controller design problem ensuring robust stability. The proposed controller eventually can be obtained by solving an optimal problem. The method can also be used to consider optimal steady-state tracking problem of fixed-order controller.