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Multivariable Frequency-Domain Identification of Industrial Robots
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
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 [en]
Frequency-domain identification, industrial robots, nonparametric identification, nonlinear gray-box identification, multivariable systems, closed-loop identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-10149ISBN: 978-91-85895-72-4 (print)OAI: oai:DiVA.org:liu-10149DiVA: diva2:16904
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
List of papers
1. Frequency-Domain Gray-Box Identification of Industrial Robots
Open this publication in new window or tab >>Frequency-Domain Gray-Box Identification of Industrial Robots
2008 (English)In: Proceedings of the 17th IFAC World Congress, 2008, 15372-15380 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper considers identification of unknown parameters in elastic dynamic models of industrial robots. Identifying such models is a challenging task since an industrial robot is a multivariable, nonlinear, resonant, and unstable system. Unknown parameters (mainly spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. The nonlinear parametric robot model is linearized in the same positions 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). In order to accurately estimate the nonparametric FRFs, the experiments must be carefully designed. The selection of optimal robot configurations for the experiments is also part of the design. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest.

Keyword
System identification, Multivariable systems, Nonlinear systems, closed-loop identification, frequency response methods
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-12711 (URN)10.3182/20080706-5-KR-1001.02600 (DOI)978-3-902661-00-5 (ISBN)
Conference
17th IFAC World Congress, Seoul, South Korea, July, 2008
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-02-23
2. Analysis of Methods for Multivariable Frequency Response Function Estimation in Closed Loop
Open this publication in new window or tab >>Analysis of Methods for Multivariable Frequency Response Function Estimation in Closed Loop
2007 (English)In: Proceedings of the 46th IEEE Conference on Decision and Control, 2007, 4881-4888 p.Conference paper, Published paper (Refereed)
Abstract [en]

Estimation methods for the multivariable frequency response function are analyzed, both in open and closed loop. Expressions for the bias and covariance are derived and the usefulness of these expressions is illustrated in simulations of an industrial robot where the different estimators are compared. The choice of estimator depends on the signal-to- noise ratio as well as the measurement setup and a bias-variance trade-off.

Keyword
Closed loop systems, Frequency response, Industrial robots, Multivariable frequency response function estimation, Open loop, Signal-to-noise ratio, Closed loop
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-12712 (URN)10.1109/CDC.2007.4434780 (DOI)978-1-4244-1497-0 (ISBN)978-1-4244-1498-7 (ISBN)
Conference
46th IEEE Conference on Decision and Control, New Orleans, LA, December, 2007
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-09-15
3. Experimental Comparison of Methods for Multivariable Frequency Response Function Estimation
Open this publication in new window or tab >>Experimental Comparison of Methods for Multivariable Frequency Response Function Estimation
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.

Keyword
System identification, Frequency response methods, Multivariable systems, Non-parametric identification, Closed-loop identification, Industrial robots
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-12713 (URN)10.3182/20080706-5-KR-1001.02598 (DOI)978-3-902661-00-5 (ISBN)
Conference
17th IFAC Worlds Congress, Seoul, Korea, July, 2008
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-09-15
4. Estimation of nonlinear effects in frequency-domain identification of industrial robots
Open this publication in new window or tab >>Estimation of nonlinear effects in frequency-domain identification of industrial robots
2008 (English)In: IEEE Transactions on Instrumentation and Measurement, Braunschweig, Germany, 2008, 856-863 p.Conference paper, Published paper (Other academic)
Abstract [en]

A method for the detection and estimation of nonlinear distortions when identifying multivariable frequency response functions (FRF) is considered. The method is successfully applied to experimental data, which were collected in closed loop, from an industrial robot. The results show that nonlinear distortions are indeed present and cause larger variability in the FRF than the measurement-noise contributions.

Series
IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456
Keyword
closed loop systems, frequency response, frequency-domain analysis, industrial robots, nonlinear distortion, nonlinear effect estimation, multivariable frequency response function, closed loop, frequency domain identification, nonparametric identification, Frequency response functions (FRF)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-12714 (URN)10.1109/TIM.2007.911698 (DOI)
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2009-05-18
5. Experiment Design for Identification of Nonlinear Gray-Box Models with Application to Industrial Robots
Open this publication in new window or tab >>Experiment Design for Identification of Nonlinear Gray-Box Models with Application to Industrial Robots
2007 (English)In: Proceedings of the 46th IEEE Conference on Decision and Control, 2007, 5110-5116 p.Conference paper, Published paper (Refereed)
Abstract [en]

Experiment design involving selection of optimal experiment positions for nonlinear gray-box models is studied. From the derived Fisher information matrix, a convex optimization problem is posed. By considering the dual problem, the experiment design is efficiently solved with linear complexity in the number of candidate positions, compared to cubic complexity for the primal problem. In the numerical illustration, using an industrial robot, the parameter covariance is reduced by a factor of six by using the 15 optimal positions compared to using the optimal single position in all experiments.

Keyword
Covariance matrices, Industrial robots, matrix algebra, Optimisation, Fisher information matrix, Convex optimization problem, Nonlinear gray-box models, Parameter covariance
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-12715 (URN)10.1109/CDC.2007.4434059 (DOI)978-1-4244-1497-0 (ISBN)978-1-4244-1498-7 (ISBN)
Conference
46th IEEE Conference on Decision and Control, New Orleans, LA, USA, December, 2007
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-02-23
6. Nonlinear Gray-Box Identification of a Flexible Manipulator
Open this publication in new window or tab >>Nonlinear Gray-Box Identification of a Flexible Manipulator
2007 (English)In: Control Engineering Practice, ISSN 0967-0661Article in journal (Other academic) Published
Abstract [en]

A three-step procedure for time-domain nonlinear gray-box identification of an industrial manipulator containing flexibilities is studied. The aim of the first two steps is to obtain good initial values for the third prediction error minimization step. In the first step, rigid body dynamics and friction are identified using a separable least-squares method. In the second step, initial values for flexibilities are obtained using an inverse eigenvalue method. Finally, in the last step, the remaining parameters of a nonlinear graybox model are identified directly in the time domain using prediction error minimization.

Place, publisher, year, edition, pages
Elsevier, 2007
Keyword
Optimization, Gray-box identification, Flexibility, Minimization, Parameter
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-12716 (URN)
Available from: 2007-10-30 Created: 2007-10-30 Last updated: 2013-07-23

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  • en-US
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