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Dynamic Systems Control with Symmetrization of Phase Limitations

Vladimir N. Pilishkin, Ingmar Tollet
For the wide class of technical systems (i.e. aircrafts, technological processes, manipulator robots etc.) one of the most important problems is a problem of providing limitations on motion parameters. Many already known methods are ineffectual because of this problem’s salvation difficulty. The possible method which allows to solve such problems is given in this work.
Synthesis of a regulator (robust, in general case) for a linear dynamic system with the condition of providing given phase limitations is investigated. Limitations are brought to a symmetrical to the point of origin figure (rectangular parallelepiped). In this case it is shown that for the meeting given limitations closed system matrix’s rows must belong to some adjusted cones, that are symmetrical to positive semiaxis of a state space. Derived correlations are being reduced to the system of linear equations of n^2-order.
The solvability of this system is investigated. The method of regulator’s synthesis is shown. The more “strict” case of “truncated” cones, for which the synthesis procedure is more simple is shown.
The conditions of problem’s solvability are given. The correlations for a synthesis of robust regulators regarding internal and external indeterminacies are derived.
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