A two-loop robust controller for compensation of the variant friction force in an over-constrained parallel kinematic machine

A translational parallel mechanism (TPM) with an isotropic Jacobian matrix can overcome the kinematic complexity in a traditional parallel mechanism. However, the over-constrained condition on the links of a TPM may produce a non-uniform friction force due to imperfect link assembly. In order to minimize the effects of the non-uniform friction force on precision positioning, a two-loop structure for a robust controller is proposed by adopting a disturbance observer (DOB) as the internal-loop compensator to cancel out the model error and reduce the effects of the variant friction force. Then, an external-loop 2-DOF H∞ controller is designed to provide the overall system with sufficient robustness in terms of stability and tracking performance. Experiments on the constructed parallel kinematic machine show that the proposed two-loop controller can successfully eliminate the effects of the variant friction force and achieve high positioning accuracy with a mean square tracking error within 0.02 mm, which is superior to that of the H∞ controller (0.15–0.28 mm), the PD controller (0.11–0.22 mm) and the PD controller with DOB (0.09–0.19 mm).