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PID synthesis under probabilistic parametric uncertainty

Mercader, Pedro; Soltesz, Kristian LU and Banos, Alfonso (2016) 2016 American Control Conference, ACC 2016 In 2016 American Control Conference, ACC 2016 p.5467-5472
Abstract

In many system identification methods, process model parameters are considered stochastic variables. Several methods do not only yield expectations of these, but in addition their variance, and sometimes higher moments. This paper proposes a method for robust synthesis of the proportional-integral-derivative (PID) controller, taking parametric process model uncertainty explicitly into account. The proposed method constitutes a stochastic extension to the well-studied minimization of integrated absolute error (IAE) under H∞-constraints on relevant transfer functions. The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost. In this work, the... (More)

In many system identification methods, process model parameters are considered stochastic variables. Several methods do not only yield expectations of these, but in addition their variance, and sometimes higher moments. This paper proposes a method for robust synthesis of the proportional-integral-derivative (PID) controller, taking parametric process model uncertainty explicitly into account. The proposed method constitutes a stochastic extension to the well-studied minimization of integrated absolute error (IAE) under H∞-constraints on relevant transfer functions. The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost. In this work, the problem is instead approximated by a deterministic one, through the unscented transform (UT), and its conjugate extension (CUT). The deterministic approximations can be solved efficiently, as demonstrated through several realistic synthesis examples.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
2016 American Control Conference, ACC 2016
pages
5467 - 5472
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
2016 American Control Conference, ACC 2016
external identifiers
  • scopus:84992031572
ISBN
9781467386821
DOI
10.1109/ACC.2016.7526527
language
English
LU publication?
yes
id
fa03ae04-60c9-43f0-b7c2-1aa232c510fa
date added to LUP
2017-01-12 09:52:47
date last changed
2017-08-21 16:29:10
@inproceedings{fa03ae04-60c9-43f0-b7c2-1aa232c510fa,
  abstract     = {<p>In many system identification methods, process model parameters are considered stochastic variables. Several methods do not only yield expectations of these, but in addition their variance, and sometimes higher moments. This paper proposes a method for robust synthesis of the proportional-integral-derivative (PID) controller, taking parametric process model uncertainty explicitly into account. The proposed method constitutes a stochastic extension to the well-studied minimization of integrated absolute error (IAE) under H∞-constraints on relevant transfer functions. The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost. In this work, the problem is instead approximated by a deterministic one, through the unscented transform (UT), and its conjugate extension (CUT). The deterministic approximations can be solved efficiently, as demonstrated through several realistic synthesis examples.</p>},
  author       = {Mercader, Pedro and Soltesz, Kristian and Banos, Alfonso},
  booktitle    = {2016 American Control Conference, ACC 2016},
  isbn         = {9781467386821},
  language     = {eng},
  month        = {07},
  pages        = {5467--5472},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {PID synthesis under probabilistic parametric uncertainty},
  url          = {http://dx.doi.org/10.1109/ACC.2016.7526527},
  year         = {2016},
}