Dynamic Damping of Vibrations in Objects with Undefined Parameters

The paper is devoted to the automatic control problem of weakly damped systems with non-stationary parameters. Theoretical prerequisites for the suppression of oscillations in such systems based on modal controllers are considered. It is shown that the solution of the stated problem is possible if the eigenvalues of the system's characteristic matrix are divided into two groups, one of which forms the components of the desired transient process, and the other is selected from the controller robustness conditions. As a result of this division, the modal controller synthesis is reduced to solving the problem of minimizing a certain objective function, the choice of which is determined by additional requirements for the system. In particular, the work uses the requirement of the controller coefficients' compact arrangement. An observer of the object state coordinates is constructed. An analysis of the conditions for canceling the observer's zeros and poles is made. The expediency of ensuring the robust system accuracy indicators by introducing a separate astatic controller is substantiated. An example of the calculation of all robust system elements is given. Based on the analysis of the resulting system”s Gershgorin domains, the damping properties of the obtained control are demonstrated in a wide range of non-stationarity of the object's parameters.