Deadbeat control system with time-varying uncertainty: Minimization of worst case steady-state tracking error

This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.