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Robust PID Design by Chance-Constrained Optimization

Mercader, Pedro; Soltesz, Kristian LU and Baños, Alfonso (2017) In Journal of the Franklin Institute 354(18). p.8217-8231
Abstract
A method for synthesizing proportional-integral-derivative (PID) controllers for process models with probabilistic parametric uncertainty is presented. The proposed method constitutes a stochastic extension to the well-studied maximization of integral gain optimization (MIGO) approach, i.e., maximization of integral gain under constraints on the H-infinity norm of relevant closed-loop transfer functions. The underlying chance-constrained optimization problem is solved using a gradient-based algorithm once it has been approximated by a deterministic optimization problem. The approximate solution is then probabilistically verified using randomized algorithms (RAs). The proposed method is demonstrated through several realistic synthesis... (More)
A method for synthesizing proportional-integral-derivative (PID) controllers for process models with probabilistic parametric uncertainty is presented. The proposed method constitutes a stochastic extension to the well-studied maximization of integral gain optimization (MIGO) approach, i.e., maximization of integral gain under constraints on the H-infinity norm of relevant closed-loop transfer functions. The underlying chance-constrained optimization problem is solved using a gradient-based algorithm once it has been approximated by a deterministic optimization problem. The approximate solution is then probabilistically verified using randomized algorithms (RAs). The proposed method is demonstrated through several realistic synthesis examples. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
PID control, Probability, Uncertainty, Sparse grid
in
Journal of the Franklin Institute
volume
354
issue
18
pages
8217 - 8231
publisher
Elsevier
external identifiers
  • scopus:85033231461
  • wos:000417001200012
ISSN
0016-0032
DOI
10.1016/j.jfranklin.2017.10.017
language
English
LU publication?
yes
id
fc9dc96f-2a07-4a43-a06d-53994ae571c9
date added to LUP
2017-10-05 21:00:01
date last changed
2018-01-16 13:21:09
@article{fc9dc96f-2a07-4a43-a06d-53994ae571c9,
  abstract     = {A method for synthesizing proportional-integral-derivative (PID) controllers for process models with probabilistic parametric uncertainty is presented. The proposed method constitutes a stochastic extension to the well-studied maximization of integral gain optimization (MIGO) approach, i.e., maximization of integral gain under constraints on the H-infinity norm of relevant closed-loop transfer functions. The underlying chance-constrained optimization problem is solved using a gradient-based algorithm once it has been approximated by a deterministic optimization problem. The approximate solution is then probabilistically verified using randomized algorithms (RAs). The proposed method is demonstrated through several realistic synthesis examples.},
  author       = {Mercader, Pedro and Soltesz, Kristian and Baños, Alfonso},
  issn         = {0016-0032},
  keyword      = {PID control,Probability,Uncertainty,Sparse grid},
  language     = {eng},
  number       = {18},
  pages        = {8217--8231},
  publisher    = {Elsevier},
  series       = {Journal of the Franklin Institute},
  title        = {Robust PID Design by Chance-Constrained Optimization},
  url          = {http://dx.doi.org/10.1016/j.jfranklin.2017.10.017},
  volume       = {354},
  year         = {2017},
}