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Design of Low-Order Controllers using Optimization Techniques

Hast, Martin LU (2015) In PhD Theses TFRT-1106.
Abstract
In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers.



The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency... (More)
In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers.



The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort.



The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed.



For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Wik, Torsten, Signals and Systems department, Chalmers, Sweden
organization
publishing date
type
Thesis
publication status
published
subject
in
PhD Theses
volume
TFRT-1106
pages
163 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
defense location
Lecture hall B, M-building, Ole Römers väg 1, Lund University, Faculty of Engineering LTH, Lund
defense date
2015-06-05 13:15
ISSN
0280-5316
ISBN
978-91-7623-286-6
978-91-7623-285-9
language
English
LU publication?
yes
id
633824e7-c344-430a-9b80-42539cbbaf46 (old id 5368057)
date added to LUP
2015-05-12 07:31:40
date last changed
2016-12-19 16:21:57
@phdthesis{633824e7-c344-430a-9b80-42539cbbaf46,
  abstract     = {In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers.<br/><br>
<br/><br>
The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort.<br/><br>
<br/><br>
The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. <br/><br>
<br/><br>
For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation.},
  author       = {Hast, Martin},
  isbn         = {978-91-7623-286-6},
  issn         = {0280-5316},
  language     = {eng},
  pages        = {163},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {Design of Low-Order Controllers using Optimization Techniques},
  volume       = {TFRT-1106},
  year         = {2015},
}