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Experimental Comparison of Methods for Multivariable Frequency Response Function Estimation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2008 (English)In: Proceedings of the 17th IFAC World Congress, 2008, 15359-15366 p.Conference paper, Published paper (Refereed)
Abstract [en]

Nonparametric estimation methods for the multivariable frequency response function are experimentally evaluated using closed-loop data from an industrial robot. Three classical estimators (H1, joint input-output, arithmetic mean) and two estimators based on nonlinear averaging techniques (harmonic mean, geometric/logarithmic mean) are considered. The estimators based on nonlinear averaging give the best results, followed by the arithmetic mean estimator, which gives a slightly larger bias. The joint input-output estimator, which is asymptotically unbiased in theory, turns out to give large bias errors for low frequencies. Finally, the H1 estimator gives the largest bias for all frequencies.

Place, publisher, year, edition, pages
2008. 15359-15366 p.
Keyword [en]
System identification, Frequency response methods, Multivariable systems, Non-parametric identification, Closed-loop identification, Industrial robots
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-12713DOI: 10.3182/20080706-5-KR-1001.02598ISBN: 978-3-902661-00-5 (print)OAI: oai:DiVA.org:liu-12713DiVA: diva2:16900
Conference
17th IFAC Worlds Congress, Seoul, Korea, July, 2008
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-09-15
In thesis
1. Multivariable Frequency-Domain Identification of Industrial Robots
Open this publication in new window or tab >>Multivariable Frequency-Domain Identification of Industrial Robots
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [sv]

Industrirobotar är idag en väsentlig del i tillverkningsindustrin där de bland annat används för att minska kostnader, öka produktivitet och kvalitet och ersätta människor i farliga eller slitsamma uppgifter. Höga krav på noggrannhet och snabbhet hos robotens rörelser innebär också höga krav på de matematiska modeller som ligger till grund för robotens styrsystem. Modellerna används där för att beskriva det komplicerade sambandet mellan robotarmens rörelser och de motorer som orsakar rörelsen. Tillförlitliga modeller är också nödvändiga för exempelvis mekanisk design, simulering av prestanda, diagnos och övervakning.

En trend idag är att bygga lättviktsrobotar, vilket innebär att robotens vikt minskas men att den fortfarande kan hantera en lika tung last. Orsaken till detta är främst att minska kostnaden, men också säkerhetsaspekter spelar in. En lättare robotarm ger dock en vekare struktur där elastiska effekter inte längre kan försummas i modellen om man kräver hög prestanda. De elastiska effekterna beskrivs i den matematiska modellen med hjälp av fjädrar och dämpare.

Denna avhandling handlar om hur dessa matematiska modeller kan tas fram genom systemidentifiering, vilket är ett viktigt verktyg där mätningar från robotens rörelser används för att bestämma okända parametrar i modellen. Det som mäts är position och moment hos robotens alla motorer. Identifiering av industrirobotar är ett utmanande problem bland annat eftersom robotens beteende varierar beroende på armens position. Den metod som föreslås i avhandlingen innebär att man först identifierar lokala modeller i ett antal positioner. Var och en av dessa beskriver robotens beteende kring en viss arbetspunkt. Sedan anpassas parametrarna i en global modell, som är giltig för alla positioner, så att den så väl som möjligt beskriver det lokala beteendet i de olika positionerna.

I avhandlingen analyseras olika metoder för att ta fram lokala modeller. För att få bra resultat krävs att experimenten är omsorgsfullt utformade. För att minska osäkerheten i den globala modellens identifierade parametrar ingår också valet av optimala positioner för experimenten. Olika metoder för att identifiera parametrarna jämförs i avhandlingen och experimentella resultat visar användbarheten av den föreslagna metoden. Den identifierade robotmodellen ger en bra global beskrivning av robotens beteende.

Resultatet av forskningen har även gjorts tillgängligt i ett datorverktyg för att noggrant kunna ta fram lokala modeller och identifiera parametrar i dynamiska robotmodeller.

Abstract [en]

Industrial robots are today essential components in the manufacturing industry where they are used to save costs, increase productivity and quality, and eliminate dangerous and laborious work. High demands on accuracy and speed of the robot motion require that the mathematical models, used in the motion control system, are accurate. The models are used to describe the complicated nonlinear relation between the robot motion and the motors that cause the motion. Accurate dynamic robot models are needed in many areas, such as mechanical design, performance simulation, control, diagnosis, and supervision.

A trend in industrial robots is toward lightweight robot structures, where the weight is reduced but with a preserved payload capacity. This is motivated by cost reduction as well as safety issues, but results in a weaker (more compliant) mechanical structure with enhanced elastic effects. For high performance, it is therefore necessary to have models describing these elastic effects.

This thesis deals with identification of dynamic robot models, which means that measurements from the robot motion are used to estimate unknown parameters in the models. The measured signals are angular position and torque of the motors. Identifying robot models is a challenging task since an industrial robot is a multivariable, nonlinear, unstable, and resonant system. In this thesis, the unknown parameters (typically spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified, mainly in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. Each nonparametric FRF then describe the local behavior around an operating point. The nonlinear parametric robot model is linearized in the same operating points and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized parametric robot model).

Methods for estimating the nonparametric FRF from experimental data are analyzed with respect to bias, variance, and nonlinearities. In order to accurately estimate the nonparametric FRF, the experiments must be carefully designed. To minimize the uncertainty in the estimated parameters, the selection of optimal robot configurations/positions for the experiments is also part of the design. Different parameter estimators are compared in the thesis and experimental results show the usefulness of the proposed identification procedure. The identified nonlinear robot model gives a good global description of the dynamics in the frequency range of interest.

The research work is also implemented and made easily available in a software tool for accurate estimation of nonparametric FRFs as well as parametric robot models.

Place, publisher, year, edition, pages
Institutionen för systemteknik, 2007. 204 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1138
Keyword
Frequency-domain identification, industrial robots, nonparametric identification, nonlinear gray-box identification, multivariable systems, closed-loop identification
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-10149 (URN)978-91-85895-72-4 (ISBN)
Public defence
2007-11-30, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2009-05-18

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Wernholt, ErikMoberg, Stig

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