VFC – Variational Feedback Controller and its application to semi-active suspensions

Active and semi-active control of oscillating devices and structures is a challengingfield and this paper proposes an original investigation based on variational controls that can be successfully applied to mechanical systems. The method produces a general class of new controllers, named VFC–Variational Feedback Controllers, that is the main theoretical contribution of the paper. The value of the theory relies on using a reformulation of the Variational Optimal Control Theory, that has in general the limit of producing control program strategies and not directly feedback control methods. The difficulties are in fact related to the intrinsic nature of the variational optimal control, that must solve initial and final boundary conditions. A special definition of the class of the considered objective functions, permits to skip this difficulty, producing a pure feedback control. The presented theory goes beyond with respect to the most acknowledged LQR variational-based tech- niques, in that VFC can be applied to more general nonlinear dynamical systems, even with finite time horizon. To test the effectiveness of the novel approach in real engi- neering problems, a deep investigation on nonlinear suspension systems treated by VFC is proposed in this paper. To this aim, VFC is systematically compared with the most recent methods available in this field and suitable to deal with nonlinear system control of car suspensions. In particular, the comparative analysis is made in terms of both comfort and handling key performance indexes, that permits to easily and significantly compare dif- ferent control logics, such as the Sky-hook and Ground-hook control families, the Accel- eration and Power Driven Dampers. The results of this comparison are collected in a performance plane, having comfort and handling indexes as coordinate axes, showing that VFC controllers completely cover the regions reached by the other mentioned control logics in this plane, but reveal to have access to new valuable areas of unexplored different performance combinations.