MIMO PID Tuning via Iterated LMI Restriction

Research output: Contribution to journalArticle


title = "MIMO PID Tuning via Iterated LMI Restriction",
abstract = "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.",
keywords = "MIMO PID tuning Convex optimization",
author = "Stephen Boyd and Martin Hast and {\AA}str{\"o}m, {Karl Johan}",
year = "2015",
doi = "10.1002/rnc.3376",
language = "English",
volume = "26",
pages = "1718–1731",
journal = "International Journal of Robust and Nonlinear Control",
issn = "1099-1239",
publisher = "John Wiley and Sons",
number = "8",