Multibody modeling and nonlinear control of the pantograph/catenary system

In this paper, a closed-chain multibody model of a pantograph/catenary system is developed and used for the optimal design of a nonlinear controller based on an open-loop control architecture. The goal of the nonlinear controller is the reduction of the contact force arising from the pantograph/catenary interaction and, at the same time, the suppression of the mechanical vibrations of the pantograph mechanism. The analytical formulation employed in this paper for describing the nonlinear dynamics of the pantograph/catenary multibody system considers a Lagrangian approach and is based on a redundant set of generalized coordinates. The contact forces generated by the pantograph/catenary interaction are modeled in this work employing an elastic force element collocated between the pantograph pan-head and a moving support. The external support follows a prescribed motion law that simulates the periodic deployment of the catenary system. On the other hand, in this investigation, the algebraic constraints arising from the closed-loop topology of the pantograph multibody system are enforced employing a method based on the Udwadia–Kalaba equations recently developed in the field of analytical dynamics. Furthermore, the problem of the determination of an effective feedforward controller for reducing the pantograph/catenary contact force is formulated in this work as a nonlinear optimal control problem. For this purpose, the solution of the control optimization problem is carried out by using an adjoint-based computational procedure. Numerical simulations demonstrate the effectiveness of the nonlinear controller obtained in this investigation for the pantograph/catenary multibody system.

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