UDC 681.5.01

S.V. Ippolitov, О.N. Choporov, D.V. Lopatkin, A.V. Sizov

The work is devoted to the solution of the actual scientific and technical problem related to ensuring the required accuracy of control in a group in the automatic mode. The technique for synthesizing an algorithm for automatic control of fast moving dynamic objects in their joint motion based on the theory of covariance control is presented. The essence of the theory is to provide a given steady-state value of the covariance matrix of the state of a linear system by means of feedback. The approach is substantiated and a numerical algorithm for determining the achievable covariance matrix of the system formalizing the specified requirements for the accuracy of control in the group flight mode in terms of the RMS errors of the controlled parameters is developed. The numerical algorithm for solving the synthesis problem of an achievable covariance matrix is based on the method of solving linear matrix inequalities (LMI), using the cvx package of the Matlab system. A general linearized model of the relative motion in the group is developed, taking into account external perturbations of the turbulence of the atmosphere and the random wind and internal disturbances associated with the dynamics of the control system drives. To take into account the influence of a random wind, the Dryden model, which describes the turbulence of the atmosphere, is used. On the basis of the described mathematical model and the developed algorithm, numerical modeling is carried out to evaluate the accuracy of control under the influence of perturbations.

Keywords: dynamic objects, synthesis, algorithm, control, matrix, modeling.

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