Vibration protection system with controlled inertial damper

As a result of applying the theory of dynamic programming to vibration protection systems as cyclic control objects, relations were obtained that, by linking the components of the system state vector and control, allow implementing the procedure of the local minimum principle to find the optimal positional control function in relation to typical quality indicators that are clearly independent of control. Examples of finding the optimal positional control function for oscillations of an active vibration protection system are given. It is shown that, in the case of harmonic oscillations, for the adopted basic model with two degrees of freedom, the necessary adjustment of the amplitude and phase is carried out by means of discrete-type control signals, which ensures the achievement of the required vibration safety indicators for the protected object according to the adopted functional criterion.