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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 26(8). p.1718-1731
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
; and
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
volume
26
issue
8
pages
1718 - 1731
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:84933073535
  • wos:000374004500009
ISSN
1099-1239
DOI
10.1002/rnc.3376
project
PID Control
PICLU
language
English
LU publication?
yes
id
bef90200-d9c1-4c26-8479-792feeecf119 (old id 7758600)
date added to LUP
2016-04-04 11:48:24
date last changed
2024-05-11 21:28:18
@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}},
  keywords     = {{MIMO PID tuning Convex optimization}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{1718--1731}},
  publisher    = {{John Wiley & Sons Inc.}},
  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}},
  doi          = {{10.1002/rnc.3376}},
  volume       = {{26}},
  year         = {{2015}},
}