Restricted structure control loop performance assessment for state-space systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

1 Citation (Scopus)

Abstract

A novel H2 optimal control performance assessment and benchmarking problem is considered for discrete-time state-space multivariable systems, where the structure of the controller is assumed to be fixed a priori. The controller structure may be specified to be of reduced order, lead/lag, or PID forms. The theoretical problem considered is to represent the state-space model in a discrete polynomial matrix form and then to obtain the causal, stabilising controller of a prespecified form, that minimises an H2 criterion. This then provides the performance measure against which other controllers can be judged. The underlying practical problem of importance is to obtain a simple method of performance assessment and benchmarking low order controllers. The main theoretical step is to derive a simpler cost-minimization problem whose solution can provide both the full order and restricted structure optimal benchmark cost values. This problem involves the introduction of spectral factor and diophantine equations and is solved via a Wiener type of cost-function expansion and simplification. The numerical solution of this problem is straightforward and involves approximating the simplified integral criterion by a fixed number of frequency points. The main benchmarking theorem applies to multivariable systems that may be unstable, non-minimum phase and non-square.
LanguageEnglish
Title of host publicationProceedings of the 20th American Control Conference, 2002
PublisherIEEE
Pages1633-1638
Number of pages6
ISBN (Print)0-7803-7298-0
DOIs
Publication statusPublished - May 2002
Event20th Annual American Control Conference (ACC) - Anchorage, United States
Duration: 8 May 200210 May 2002

Conference

Conference20th Annual American Control Conference (ACC)
CountryUnited States
CityAnchorage
Period8/05/0210/05/02

Fingerprint

Benchmarking
Controllers
Multivariable systems
Cost functions
Costs
Lead
Polynomials

Keywords

  • condition monitoring
  • discrete time systems
  • multivariable systems
  • optimal control

Cite this

Grimble, M. J. (2002). Restricted structure control loop performance assessment for state-space systems. In Proceedings of the 20th American Control Conference, 2002 (pp. 1633-1638). IEEE. https://doi.org/10.1109/ACC.2002.1023256
Grimble, M.J. / Restricted structure control loop performance assessment for state-space systems. Proceedings of the 20th American Control Conference, 2002. IEEE, 2002. pp. 1633-1638
@inproceedings{5dc50eebd99a480db81c4b27a1ec8fda,
title = "Restricted structure control loop performance assessment for state-space systems",
abstract = "A novel H2 optimal control performance assessment and benchmarking problem is considered for discrete-time state-space multivariable systems, where the structure of the controller is assumed to be fixed a priori. The controller structure may be specified to be of reduced order, lead/lag, or PID forms. The theoretical problem considered is to represent the state-space model in a discrete polynomial matrix form and then to obtain the causal, stabilising controller of a prespecified form, that minimises an H2 criterion. This then provides the performance measure against which other controllers can be judged. The underlying practical problem of importance is to obtain a simple method of performance assessment and benchmarking low order controllers. The main theoretical step is to derive a simpler cost-minimization problem whose solution can provide both the full order and restricted structure optimal benchmark cost values. This problem involves the introduction of spectral factor and diophantine equations and is solved via a Wiener type of cost-function expansion and simplification. The numerical solution of this problem is straightforward and involves approximating the simplified integral criterion by a fixed number of frequency points. The main benchmarking theorem applies to multivariable systems that may be unstable, non-minimum phase and non-square.",
keywords = "condition monitoring, discrete time systems, multivariable systems , optimal control",
author = "M.J. Grimble",
year = "2002",
month = "5",
doi = "10.1109/ACC.2002.1023256",
language = "English",
isbn = "0-7803-7298-0",
pages = "1633--1638",
booktitle = "Proceedings of the 20th American Control Conference, 2002",
publisher = "IEEE",

}

Grimble, MJ 2002, Restricted structure control loop performance assessment for state-space systems. in Proceedings of the 20th American Control Conference, 2002. IEEE, pp. 1633-1638, 20th Annual American Control Conference (ACC), Anchorage, United States, 8/05/02. https://doi.org/10.1109/ACC.2002.1023256

Restricted structure control loop performance assessment for state-space systems. / Grimble, M.J.

Proceedings of the 20th American Control Conference, 2002. IEEE, 2002. p. 1633-1638.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

TY - GEN

T1 - Restricted structure control loop performance assessment for state-space systems

AU - Grimble, M.J.

PY - 2002/5

Y1 - 2002/5

N2 - A novel H2 optimal control performance assessment and benchmarking problem is considered for discrete-time state-space multivariable systems, where the structure of the controller is assumed to be fixed a priori. The controller structure may be specified to be of reduced order, lead/lag, or PID forms. The theoretical problem considered is to represent the state-space model in a discrete polynomial matrix form and then to obtain the causal, stabilising controller of a prespecified form, that minimises an H2 criterion. This then provides the performance measure against which other controllers can be judged. The underlying practical problem of importance is to obtain a simple method of performance assessment and benchmarking low order controllers. The main theoretical step is to derive a simpler cost-minimization problem whose solution can provide both the full order and restricted structure optimal benchmark cost values. This problem involves the introduction of spectral factor and diophantine equations and is solved via a Wiener type of cost-function expansion and simplification. The numerical solution of this problem is straightforward and involves approximating the simplified integral criterion by a fixed number of frequency points. The main benchmarking theorem applies to multivariable systems that may be unstable, non-minimum phase and non-square.

AB - A novel H2 optimal control performance assessment and benchmarking problem is considered for discrete-time state-space multivariable systems, where the structure of the controller is assumed to be fixed a priori. The controller structure may be specified to be of reduced order, lead/lag, or PID forms. The theoretical problem considered is to represent the state-space model in a discrete polynomial matrix form and then to obtain the causal, stabilising controller of a prespecified form, that minimises an H2 criterion. This then provides the performance measure against which other controllers can be judged. The underlying practical problem of importance is to obtain a simple method of performance assessment and benchmarking low order controllers. The main theoretical step is to derive a simpler cost-minimization problem whose solution can provide both the full order and restricted structure optimal benchmark cost values. This problem involves the introduction of spectral factor and diophantine equations and is solved via a Wiener type of cost-function expansion and simplification. The numerical solution of this problem is straightforward and involves approximating the simplified integral criterion by a fixed number of frequency points. The main benchmarking theorem applies to multivariable systems that may be unstable, non-minimum phase and non-square.

KW - condition monitoring

KW - discrete time systems

KW - multivariable systems

KW - optimal control

U2 - 10.1109/ACC.2002.1023256

DO - 10.1109/ACC.2002.1023256

M3 - Conference contribution book

SN - 0-7803-7298-0

SP - 1633

EP - 1638

BT - Proceedings of the 20th American Control Conference, 2002

PB - IEEE

ER -

Grimble MJ. Restricted structure control loop performance assessment for state-space systems. In Proceedings of the 20th American Control Conference, 2002. IEEE. 2002. p. 1633-1638 https://doi.org/10.1109/ACC.2002.1023256