MIMO PID Tuning via Iterated LMI Restriction
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7758600
- author
- Boyd, Stephen ; Hast, Martin LU and Åström, Karl Johan LU
- organization
- publishing date
- 2015
- 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
- 2022-04-16 03:59:03
@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}},
}