Premium
MIMO PID tuning via iterated LMI restriction
Author(s) -
Boyd Stephen,
Hast Martin,
Åström Karl Johan
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3376
Subject(s) - pid controller , iterated function , linear matrix inequality , mathematics , convergence (economics) , control theory (sociology) , mathematical optimization , simple (philosophy) , matrix (chemical analysis) , controller (irrigation) , quadratic equation , computer science , control (management) , engineering , control engineering , temperature control , mathematical analysis , artificial intelligence , philosophy , agronomy , materials science , geometry , epistemology , economics , composite material , biology , economic growth
Summary We formulate multi‐input multi‐output proportional integral derivative 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 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 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 multi‐input multi‐output proportional integral derivative controllers. The method is readily extended in many ways, for example, to the design of more complex, structured controllers. Copyright © 2015 John Wiley & Sons, Ltd.