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MIMO PID Tuning via Iterated LMI Restriction

Boyd, Stephen; Hast, Martin LU and Åström, Karl Johan LU (2015) In International Journal of Robust and Nonlinear Control
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
MIMO PID tuning Convex optimization
in
International Journal of Robust and Nonlinear Control
publisher
John Wiley & Sons
external identifiers
  • scopus:84933073535
  • wos:000374004500009
ISSN
1099-1239
DOI
10.1002/rnc.3376
project
PID
PICLU
language
English
LU publication?
yes
id
bef90200-d9c1-4c26-8479-792feeecf119 (old id 7758600)
date added to LUP
2015-08-12 11:53:08
date last changed
2017-04-23 04:44:06
@article{bef90200-d9c1-4c26-8479-792feeecf119,
  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.},
  author       = {Boyd, Stephen and Hast, Martin and Åström, Karl Johan},
  issn         = {1099-1239},
  keyword      = {MIMO PID tuning Convex optimization},
  language     = {eng},
  publisher    = {John Wiley & Sons},
  series       = {International Journal of Robust and Nonlinear Control},
  title        = {MIMO PID Tuning via Iterated LMI Restriction},
  url          = {http://dx.doi.org/10.1002/rnc.3376},
  year         = {2015},
}