Sequential Closing Method for Modes of Movement for Multidimensional, Multilinked Dynamical Systems

Currently one of the fastest growing areas of applied control theory is the development of analytical and numerical methods of modal control by roots of multidimensional dynamical systems by means close loop of multilinked feedbacks. Interest to the problem of modal placement poles of close loop dynamical system and to the calculation of the components of feedback matrix as well as the coefficients of feedback matrix hasn’t been decreasing already for several decades. In this paper a method of modal control by roots of the characteristic polynomial of multilinked systems, based on the principle of sequential closing is proposed. Detailed description of the closing algorithm and the calculating both feedback matrices and matrices of weight coefficients for problems of control definition with incomplete composition of measurements is carried out. Efficiency of the algorithm has been demonstrated using the problem of synthesis of algorithms control of spacecraft motion with double rotation (rolling solar sail with compensating gyro) and the other problem of seeking and maintaining the equilibrium attitude position of the International Space Station.

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