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Contouring Control for Multi‐Axis Motion Systems With Holonomic Constraints: Theory and Application to a Parallel System

In this paper, the contouring control problem for the constrained multi‐axis motion system is studied. The method of equivalent errors, previously proposed for unconstrained motion systems, is generalized to the system with holonomic constraints. It is shown that the method can be applied to the constrained system provided that the constraints satisfy a proper condition. Because of the constraints, the states in the control law are not completely independent. The unavailable states can be estimated using linear approximation from the constraint equations. As an illustrative example, the proposed method is applied to a parallel motion system with complicated dynamics. A contouring controller is designed using the method of equivalent errors incorporated with integral sliding mode control. Simulation results for contouring circular, elliptic, and square paths verify the effectiveness of the proposed method.