Indirect Control of Oscillations: Elements of Theory

A brief review of the main research areas in the field of controlled vibration protection systems is given. It is shown that Vibration systems with indirect control processes of oscillations allow with a minimum expenditure of energy to ensure programmable switching parameters and structures, in which the dissipative restoring and inertial forces generated on the basis of active impact. Within synthesis of indirect control the chains of new auxiliary mathematical constructs for finding optimal synthesizing functions of the elastic-damping units parameters control are obtained. It enabled to separate a base model with intermittent damping and base model with impulse trap. As a result of the study, based on the harmonic balance method, the dynamic properties of the basic model with intermittent damping, calculation formulas are obtained for determining the parameters of the compensation effect and calculating the dynamic coefficient. It is established that, with an optimal sequence of damping switching, the resonant phenomena are eliminated, and the transient processes decay within one period of the kinematic perturbation. The basic model with a pulse trap imitates the limiting variant of intermittent damping and realizes the process of superimposing constraining bonds, the sequence and duration of which are new variables essentially increasing controllability. And for indirect pulse control, there exicts a certain minimum of power consumption independent of the achieved effect of vibration protection. A regulated increase in the duration of the application of the restraining coupling in the low-frequency region and a decrease in this duration in the high-frequency region provides a monotonically decreasing dependence on the dynamic coefficients over the entire frequency range. An example of a solution to the optimization problem of controlling the damping process for a basic model of a vibration isolation system is considered. It is established that intermittent damping is an indispensable feature of the optimality of the vibration isolation system: the damper switches on when the sign of the object's speed has changed and turns off when the object's displacement sign has changed.