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PID Syntehsis under Probabilistic Parametric Uncertainty

Mercader, Pedro; Soltesz, Kristian LU and Baños, Alfonso (2016) American Control Conference, 2016 In Proceedings of the 2016 American Control Conference
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. (Less)
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Proceedings of the 2016 American Control Conference
pages
6 pages
conference name
American Control Conference, 2016
language
English
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yes
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9ee5d28e-dbe2-4a0d-958b-27af17e9f5e4 (old id 8570948)
date added to LUP
2016-01-28 16:53:05
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@misc{9ee5d28e-dbe2-4a0d-958b-27af17e9f5e4,
  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 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.},
  author       = {Mercader, Pedro and Soltesz, Kristian and Baños, Alfonso},
  language     = {eng},
  pages        = {6},
  series       = {Proceedings of the 2016 American Control Conference},
  title        = {PID Syntehsis under Probabilistic Parametric Uncertainty},
  year         = {2016},
}