Controller design for optimal tracking response in discrete-time systems

O. A. Sebakhy*, H. A. Yousef

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)381-391
Number of pages11
JournalOptimal Control Applications and Methods
Issue number5
Publication statusPublished - Sept 2007
Externally publishedYes


  • Controller design
  • Deadbeat control
  • Optimal control
  • Tracking

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Control and Optimization
  • Applied Mathematics


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