MIMO PID Tuning via Iterated LMI Restriction

Research output: Contribution to journalArticle


We formulate multi-input multi-output (MIMO) proportional-integral-derivative (PID) controller design as an optimization problem that involves nonconvex quadratic matrix inequalities. We propose a simple method that replaces the nonconvex matrix inequalities with a linear matrix inequality (LMI) restriction, and iterates to convergence. This method can be interpreted as a matrix extension of the convex-concave procedure, or as a particular majorization-minimization (MM) method. Convergence to a local minimum can be guaranteed. While we do not know that the resulting controller is globally optimal, the method works well in practice, and provides a simple automated method for tuning MIMO PID controllers. The method is readily extended in many ways, for example to the design of more complex, structured controllers.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Control Engineering


  • MIMO PID tuning Convex optimization
Original languageEnglish
Pages (from-to)1718–1731
JournalInternational Journal of Robust and Nonlinear Control
Issue number8
Publication statusPublished - 2015
Publication categoryResearch

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