Path: SC/Actuator
% Friction model. This model uses a bristle state.
F = sigma0*z + sigma1*zDot + sigma2*v
zDot = v - |v|*z/g(v)
g(v) = (fC + (fS - fC)*exp(-(v/vS)^2))/sigma0;
The maximum damping coefficient |v|/g(v) is an input. This prevents
numerical instabilities. When the damping coefficient is set to the
maximum value and
zDot = max(|v|/g(v))*(zSS - z)
so it damps to the equilibrium value which is
zSS = sign(v)*g(v)/sigma0
The maximum damping constant should be set to a number that is
consistent with the time step. For example: 1/dT.
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Form:
[zDot, f, cDamp] = FrictionBristle( z, t, d )
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Inputs
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z (:) State
t (1,1) Time (not used)
d (:) Data structure
.v - velocity
.fStatic - Static friction
.fCoulomb - Coulomb friction maximum
.vStribeck - Stribeck velocity
.sigma0 - Bristle stiffness
.sigma1 - Bristle damping
.sigma2 - Viscous friction coefficient
.maxC - Maximum damping constant
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Outputs
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zDot (:) Bristle state derivative
f (:) Friction
cDamp (:) The damping coefficient
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