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Relay feedback and multivariable control

Johansson, Karl Henrik LU (1997) In PhD Theses TFRT-1048.
Abstract (Swedish)
Popular Abstract in Swedish

Återkoppling är en fundamental princip inom reglertekniken. Genom att mäta vissa variabler kan andra påverkas så att ett system uppför sig på önskat vis. Denna doktorsavhandling behandlar två typer av återkoppling: reläåterkoppling och flervariabel återkoppling.



Reläåterkoppling är den enklaste formen av återkoppling. Endast tecknet på en uppmätt variabel återkopplas: +1 om mätvariabeln är positiv och -1 om den är negativ. Detta kallas ofta för på-av-reglering och är mycket vanligt, till exempel i termostater. I avhandlingen beskrivs nya intressanta fenomen som kan erhållas i reläåterkopplade system. Ett exempel illustreras av kurvan på avhandlingens framsida. Fenomenen... (More)
Popular Abstract in Swedish

Återkoppling är en fundamental princip inom reglertekniken. Genom att mäta vissa variabler kan andra påverkas så att ett system uppför sig på önskat vis. Denna doktorsavhandling behandlar två typer av återkoppling: reläåterkoppling och flervariabel återkoppling.



Reläåterkoppling är den enklaste formen av återkoppling. Endast tecknet på en uppmätt variabel återkopplas: +1 om mätvariabeln är positiv och -1 om den är negativ. Detta kallas ofta för på-av-reglering och är mycket vanligt, till exempel i termostater. I avhandlingen beskrivs nya intressanta fenomen som kan erhållas i reläåterkopplade system. Ett exempel illustreras av kurvan på avhandlingens framsida. Fenomenen analyseras matematiskt och kriterier bestäms för när de kan dyka upp.



I många system används flervariabel återkoppling, dvs flera variabler mäts och regleras samtidigt. En vanlig dusch är ett exempel på ett sådant system: flödet och temperaturen regleras samtidigt med hjälp av varm- och kallvattenkranen. Det är betydligt svårare och dyrare att konstruera och underhålla flervariabla reglersystem. Det är därför viktigt att kunna avgöra om en flervariabel regulator verkligen är nödvändig. Detta diskuteras i avhandlingen och ett resultat som talar om när flervariabla regulatorer är överflödiga ges. Dessutom beskrivs en ny laborationsprocess, som har tagits fram för att illustrera detta och andra resultat. Processen består av fyra sammankopplade vattentankar, som trots sin enkelhet kan visa flera intressanta egenskaper hos flervariabla reglersystem.



Sist i avhandlingen beskrivs hur reläåterkoppling kan användas för att ställa in flervariabla regulatorer. Genom att koppla in ett relä på ett speciellt ställe i ett existerande reglersystem och studera svaret från experimentet, kan en enkel modell för systemet bestämmas. Modellen kan sedan användas för att förbättra inställningen hos den flervariabla regulatorn och på så sätt höja prestanda hos systemet. (Less)
Abstract
This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems.



Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes.

... (More)
This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems.



Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes.



Performance limitations in linear multivariable control systems is the second topic. It is proved that if the top left submatrices of a stable transfer matrix have no right half-plane zeros and a certain high-frequency condition holds, then there exists a diagonal stabilizing feedback that makes a weighted sensitivity function arbitrarily small. Implications on control structure design and sequential loop-closure are given. A novel multivariable laboratory process is also presented. Its linearized dynamics have a transmission zero that can be located anywhere on the real axis by simply adjusting two valves. This process is well suited to illustrate many issues in multivariable control, for example, control design limitations due to right half-plane zeros.



The third topic is a combination of relay feedback and multivariable control. Tuning of individual loops in an existing multivariable control system is discussed. It is shown that a specific relay feedback experiment can be used to obtain process information suitable for performance improvement in a loop, without any prior knowledge of the system dynamics. The influence of the loop retuning on the overall closed-loop performance is derived and interpreted in several ways. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Prof Nijmeijer, Hendrik, Dept. of Applied Mathematics, University of Twente, the Netherlands
organization
publishing date
type
Thesis
publication status
published
subject
keywords
robotics, Automation, Frequency methods, Process control, Sequential control, Automatic tuning, Control education, Laboratory process, Performance limitations, Decentralized control, Multivariable zero, Multivariable systems, Hybrid control, Nonlinear dynamics, Limit cycles, Oscillations, Relay feedback, Sliding modes, control engineering, Automatiska system, robotteknik, reglerteknik
in
PhD Theses
volume
TFRT-1048
pages
176 pages
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
defense location
Room M:B, M-building, Lund Institute of Technology.
defense date
1997-11-25 10:15
ISSN
0280-5316
language
English
LU publication?
yes
id
0ac5c7ef-5c3c-4de7-a635-7a8812d01182 (old id 29739)
date added to LUP
2007-06-14 11:21:51
date last changed
2016-09-19 08:44:54
@phdthesis{0ac5c7ef-5c3c-4de7-a635-7a8812d01182,
  abstract     = {This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems.<br/><br>
<br/><br>
Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes.<br/><br>
<br/><br>
Performance limitations in linear multivariable control systems is the second topic. It is proved that if the top left submatrices of a stable transfer matrix have no right half-plane zeros and a certain high-frequency condition holds, then there exists a diagonal stabilizing feedback that makes a weighted sensitivity function arbitrarily small. Implications on control structure design and sequential loop-closure are given. A novel multivariable laboratory process is also presented. Its linearized dynamics have a transmission zero that can be located anywhere on the real axis by simply adjusting two valves. This process is well suited to illustrate many issues in multivariable control, for example, control design limitations due to right half-plane zeros.<br/><br>
<br/><br>
The third topic is a combination of relay feedback and multivariable control. Tuning of individual loops in an existing multivariable control system is discussed. It is shown that a specific relay feedback experiment can be used to obtain process information suitable for performance improvement in a loop, without any prior knowledge of the system dynamics. The influence of the loop retuning on the overall closed-loop performance is derived and interpreted in several ways.},
  author       = {Johansson, Karl Henrik},
  issn         = {0280-5316},
  keyword      = {robotics,Automation,Frequency methods,Process control,Sequential control,Automatic tuning,Control education,Laboratory process,Performance limitations,Decentralized control,Multivariable zero,Multivariable systems,Hybrid control,Nonlinear dynamics,Limit cycles,Oscillations,Relay feedback,Sliding modes,control engineering,Automatiska system,robotteknik,reglerteknik},
  language     = {eng},
  pages        = {176},
  publisher    = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {Relay feedback and multivariable control},
  volume       = {TFRT-1048},
  year         = {1997},
}