Loop shaping for PID controller design based on time and frequency specifications

Clarisse Pétua Bosman Barros, Péricles Rezende Barros, José Sergio da Rocha Neto

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)
7 Downloads (Pure)


In this paper it is described a new method to design PID controllers using a linear programming approach for optimizing performance subject to robustness constraints. It is based on the shaping of a reference loop gain transfer function which forms a convex region on the Nyquist diagram which contains and bounds the designed loop gain Nyquist plot. The convex region is approximated by a set of lines in order to formulate a linear optimization problem. It is also presented an optional performance specification related to the crossover frequency of the designed loop gain. The class of stable linear time-invariant single-input simple-output (SISO) systems is considered and the optimization problem is proposed, solved and analyzed.

Original languageEnglish
Pages (from-to)592-597
Number of pages6
Issue number4
Publication statusPublished - 1 Jan 2018
Externally publishedYes
Event3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control PID 2018 - Ghent, Belgium
Duration: 9 May 201811 May 2018


  • Linear programming
  • Multiobjective optimization
  • Optimization problems
  • Parameter optimization
  • PID control


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