Controlled vibration protection systems: optimization and energy efficiency

The energy efficiency of controlled vibration protection systems is defined as the ratio of the vibration safety indicator they achieve to the cost of energy resources necessary to achieve the desired indicator. To solve the optimization problems of controlled vibration protection, a sufficient condition for the optimality of the accepted functional and, accordingly, the minimum principle, was used, the step-by-step implementation of which, in the course of numerical integration of the initial equations of the state of the system, makes it possible to reproduce the optimal control numeric arrays and the related components of the system state. The algorithm of the step-by-step procedure of the minimum principle was used to optimize the dynamic processes in the vibration protection system with indirect control of the viscous resistance damper and the potential energy recuperator. It has been established that the optimal controls that allow eliminating resonant phenomena in these systems are positional functions of a singular type, the relay switching of which in vibration protection systems with a controlled damper and recuperator is associated with a change in the sign of the absolute and relative velocity of the object and with a change in the sign of the velocity and relative displacement of the object.