On the stability of inverse dynamics control of flexible-joint parallel manipulators in the presence of modeling error and disturbances
Inverse dynamics control is considered for flexible-joint
parallel manipulators in order to obtain a good trajectory tracking
performance in the case of modeling error and disturbances. It is known
that, in the absence of modeling error and disturbance, inverse dynamics
control leads to linear fourth-order error dynamics, which is asymptotically
stable if the feedback gains are chosen to make the real part of the
eigenvalues of the system negative. However, when there are modeling errors
and disturbances, a linear time-varying error dynamics is obtained whose
stability is not assured only by keeping the real parts of the frozen-time
eigenvalues of the system negative. In this paper, the stability of such
systems is investigated and it is proved that the linear time-varying system
can be rendered stable by selecting the feedback gains such that the
variation of the system becomes sufficiently slow. To illustrate the
performance of the control method, deployment motion of a 3-RPR
planar parallel manipulator subject to impact is simulated. For the impact
model, the impulse-momentum and the coefficient of restitution equations for
the system are derived.
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