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This paper presents a design method of optimal servo systems based on sliding mode for an active pantograph with flexibility subject to the stiffness variation of the catenary. It is pointed out through our analysis that the flexibility makes the control problem much harder, because it increases not only the freedom of motion but also the relative degree between the control input and the contact force to be controlled. However, it is shown by employing the optimal control theory, especially SRL (Symmetric Root Locus), together with sliding mode theory that pole-zero cancellations play an important role in the controller design. Some numerical simulations in a practical situation, where the actuator dynamics and sensor noise are taken into account, show the effectiveness of the proposed design method.

An optimal servo system based on sliding mode for the contact force of an active pantograph