Two degree optimal robust steady-state tracking controller design for plant with time-varying uncertainty

This paper addresses the robust steady-state tracking problem when the system under consideration is subject to norm bounded time-varying uncertainty as well as unknown external bounded disturbances. With the help of two-degree control scheme and Youla parametrization, we propose an exact formula for computing the worst-possible steady-state absolute value of the control error. Using this formula, we show that the problem of designing a controller that minimizes the worst case steady-state controller error is reduced to a finite dimensional l1 optimization problem. Hence, the proposed controller can be obtained by solving a standard linear programming problem. We also demonstrate that the proposed controller ensures both optimal robust stability and optimal steady-state tracking performance. The experimental results manifest the approach's effectiveness.