MIMO PID tuning via iterated LMI restriction

• Published in: International journal of robust and nonlinear control Vol. 26; no. 8; pp. 1718 - 1731
• Main Authors: Boyd, Stephen, Hast, Martin, Åström, Karl Johan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 25.05.2016; Wiley Subscription Services, Inc
• Subjects: Constrictions; Control Engineering; controller design; Controllers; Convergence; convex optimization; Design optimization; Electrical Engineering, Electronic Engineering, Information Engineering; Elektroteknik och elektronik; Engineering and Technology; Inequalities; linear matrix inequalities; MIMO PID; MIMO PID tuning Convex optimization; Optimization; Proportional integral derivative; Reglerteknik; Teknik; Tuning
• ISSN: 1049-8923; 1099-1239; 1099-1239
• DOI: 10.1002/rnc.3376

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.