Pole assignment for control of flexible link mechanisms

Although the dynamics of flexible link mechanisms and manipulators is nonlinear, motion and vibration control often relies on linear or piecewise-linear controllers based on linearized models in order to ensure real-time implementability. Keeping such an objective in mind, this paper proposes a general receptance-based method for pole assignment in flexible link mechanisms with a single rigid-body degree of freedom (dof) using a single control force (i.e. rank-one control). A chief advantage of the approach proposed is that it makes use of the second-order system model representation through the receptance matrix of the symmetric part of the asymmetric model. The asymmetric terms in the stiffness and damping matrices arise from the coupling between rigid-body motion and elastic motion. The proposed receptance-based formulation ensures numerical reliability and efficiency also for large dimensional and ill-conditioned system models originating from the simultaneous presence of high-frequency and weakly controllable oscillating modes, and of rigid-body motion low-frequency dynamics, which may also be unstable. The validation of the proposed technique is carried out by performing pole assignment through position and velocity feedback or acceleration and velocity feedback on a mechanism. Integral control is also introduced to improve the steady state system response. Numerical results indicate that the proposed method is more accurate and robust than two popular established methods.