Contouring control for constrained motion system with application to a parallel system

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 equally 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. 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 both circular and elliptic contouring verify the proposed method.