Active nonlinear partial-state feedback control of contacting force for a pantograph-catenary system.

In this paper, a nonlinear partial-state feedback control is designed for a 3-DOF pantograph-catenary system by using backstepping approach, such that the contacting force of the closed-loop system is capable of tracking its reference profile. In the control design, the pantograph-catenary model is transformed into a triangular form, facilitating the utilization of backstepping. Derivatives of virtual controls in backstepping are calculated explicitly. A high-order differentiator is designed to estimate the unknown time derivatives of elasticity coefficient; and an observer is proposed to reconstruct the unmeasurable states. It can be proved theoretically that, with the proposed nonlinear partial-state feedback control, the tracking error of the contacting force is ultimately bounded with tunable ultimate bounds. Theoretical results are demonstrated by numerical simulations.