/control systems technology @TUeCST

LRM for multivariable and position-dependent mechanical systems

nD-LRM for position-dependent models

/department of mechanical engineering

key mechanism: exploit smoothness over frequencies

[1] R. Pintelon, J. Schoukens, System System identification: a frequency domain aproach, 2nd ed. Wiley-IEEEpress, Hoboken, NJ, USA, 2012.

[2] E. Geerardyn, Development of user-friendly system identification techniques, PhD thesis, VUB-ELEC, Brus-sels, Belgium, 2016.

[3] T. Mckelvey, G. Guérin, Non-parametric frequency response estimation using a local rational model, 16thIFAC Symposium on System Identification, pp. 49-54, 2012.

[4] R. Voorhoeve, A. v.Rietschoten, E. Geerardyn, T. Oomen, Identification of high-tech motion systems: An activevibration isolation benchmark, 17th IFAC Symposium on System Identification, pp. 1250-1255, 2015.

[5] R. v.d.Maas, A. v.d.Maas, T. Oomen, Accurate frequency response function identification of LPV Systems:A 2D local parametric modeling approach, 54th IEEE Conference on Decision and Control, pp. 1465-1470,2015.

• user friendly algorithms

• parametric modeling and control (poster Rozario A16)

Robbert VoorhoeveTom Oomen

r.j.voorhoeve@tue.nlControl Systems Technology

Dept. of Mechanical EngineeringERNSI workshop 2016

FRFs have a central role in identification and control ofmotion system and are used for:

1. obtaining basic information on the system:resonances, nonlinearities, etc.,

2. direct controller tuning and validation, and

3. as an intermediate step in parametric identification.

New class of methods for improved FRF identification⇒Local parametric approaches [1].

• LRM [2,3]: improved quality around lightly dampedresonances compared to LPM

• MIMO LRM⇒ open aspect: parametrization

MIMO LRM parametrizations

Different parametrizations for G (w) = D−1(w)N (w)

• MISO: D (w) = diag(di (w))

• Common denominator: D (w) = Inu dc(w)

• full MFD D (w) = D0 + D1w + . . .

• integer (low) order MFD

Acknowledgments: Rick van der Maas, Annemiek van der Maas, Egon Geerardyn, Dieter Verbeke, Johan Schoukens and Maarten Steinbuch are gratefully acknowledged for their contributions to this work.This research is supported by NWO/STW VENI grant “Precision Motion: Beyond the Nanometer” (no. 13073), ASML research and the TUE Impulse program

⇒ analyze methods on simulations and benchmark data

key mechanism: exploit smoothness in scheduling domain [5]

θ2

zy

θ1

θ2

z

yθ1

Frequency

Scheduling Parameter

Ampl

itud

e

Frequency

Scheduling Parameter

Ampl

itud

e

FRF identification

Ongoing work

References

Mechanical systems often position-dependent due to motion⇒ nonlinear / LPV behavior.

Here: local modelig, i.e., “frozen” in fixed operating point⇒ behavior smooth over frequency and scheduling domain.

2D: D (w, z) =ND∑

i=0

ND−i∑i=0

Di ,j w j z i , N (w, z) =NN∑

i=0

NN−i∑i=0

Ni ,j w j z i

300

θ2

50

0

-50

20Frequency [Hz]

15105

-80

-60

-40

Ampl

itud

e[d

B]

LPM: G22 := u2 → θ2

θ2

50

0

-50

20Frequency [Hz]

15105

-80

-60

-40

Amp l

itud

e[d

B]

2D-LPM: G22 := u2 → θ2

101

102

-200

-150

-100

-50

Frequency [Hz]

Mag

nitu

de[d

B]

• 4× 4 simulated system

• MFD variant overall bestperformance, especiallyaround resonances

• All LRM variants outper-form spectral analysisand LPM estimates

• Experimental benchmarkdata of AVIS [4]

• Analyse efficiency ofMIMO LRM compared tostandard techniques

50 100 150 200 2500

2

4

6

8

Npar

ML -

cost

common den.MISOMFD

common den.full-MFDlow order MFD

0 5 10 15 205

10

15

20

25

30

Measurement time [s]

Cost

LRMSpectral analysis