Controller design for optimal tracking response in discrete‐time systems

The problem of designing a controller, which results in a closed‐loop system response with optimal time‐domain characteristics, is considered. In the approach presented in this paper, the controller order is fixed (higher than pole‐placement order) and we seek a controller that results in closed‐loop poles at certain desired and pre‐specified locations; while at the same time the output tracks the reference input in an optimal way. The optimality is measured by requiring certain norms on the error sequence—between the reference and output signals—to be minimum. Several norms are used. First, l₂‐norm is used and the optimal solution is computed in one step of calculations. Second, l_∞‐norm (i.e. minimal overshot) is considered and the solution is obtained by solving a constrained affine minimax optimization problem. Third, the l₁‐norm (which corresponds to the integral absolute error‐(IAE)‐criterion) is used and linear programming techniques are utilized to solve the problem. The important case of finite settling time (i.e. deadbeat response) is studied as a special case. Examples that illustrate the different design algorithms and demonstrate their feasibility are presented. Copyright © 2007 John Wiley & Sons, Ltd.