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Two-state GMS-based friction model for precise control applications

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Abstract

The capability of a model to represent the complex friction behavior is particularly important for systems where friction has a major impact on motion precision. In this work a GMS-based model is proposed which would require only two states, aiming to simplify the implementation of control laws that require friction models capable of representing presliding friction. Simulations of the proposed model are provided, showing that it keeps the main properties of the GMS model, like hysteresis with nonlocal memory, non-drifting behavior and friction lag. Also, an experimental comparison of the performance of model-based compensation for the proposed two-state model and for the complete GMS model is presented for a linear motor system with linear guides, showing promising results.

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Abbreviations

F f :

friction force

x :

position

v :

velocity

F i :

single GMS element force

ν i :

weight factor associated to the contribution of a single GMS element to net friction force

k i :

single GMS element stiffness

σ 2 :

viscous friction coefficient

C :

GMS attraction parameter

s(v):

Stribeck curve without viscous term

l i :

transition to slip parameter for element i

t c :

time at which a loop is closed

t s,i :

time at which element i starts slipping

Δx :

displacement from initial position

kΔx :

displacement from point of motion reversal k

F s :

sticking force

F d :

slipping force

F γ :

correction for varying s(v)

F h :

hysteresis and Stribeck contribution to friction force

F l :

friction lag contribution to friction force

κ():

nonlinear spring stiffness function

Π():

nonlinear spring function

γ():

slipping fraction function

φ i :

Deviation of elementary force from s(v) for slipping elements

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Authors and Affiliations

  1. Facultad de Ingeniería, UNLPam-CONICET, 9 y 110, General Pico, La Pampa, 6360, Argentina

    Fernando Villegas & Rogelio Lorenzo Hecker

  2. Instituto de Automática, UNSJ-CONICET, Av. San Martín 1109(O) San Juan, San Juan, 5400, Argentina

    Miguel Peña

Authors
  1. Fernando Villegas
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  2. Rogelio Lorenzo Hecker
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  3. Miguel Peña
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Correspondence to Fernando Villegas.

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Villegas, F., Hecker, R.L. & Peña, M. Two-state GMS-based friction model for precise control applications. Int. J. Precis. Eng. Manuf. 17, 553–564 (2016). https://doi.org/10.1007/s12541-016-0068-y

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  • DOI: https://doi.org/10.1007/s12541-016-0068-y

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