A robust approximate constraint-following control method based on the fundamental equation of Udwadia–Kalaba approach is designed to control the permanent magnet linear motor. The control scheme consists of three parts: the nominal part to suppress any tendency of deviating from the constraints, the second part to deal with any possible initial condition deviation from the constraint manifold and drive the system toward the constraints, and the robust part to compensate for the effect due to uncertainty. Theoretical proof, numerical simulation, and experimental validation have been done to verify the effectiveness of this control method.
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