Determining the stability region in the plane of parameters and quality indicators of linear discrete automatic control systems by D-partitioning method

Abstract

The problem of constructing the boundary of the stability region (BSR) of linear discrete automatic control systems in the plane of the system parameters, which are linearly included in the coefficients of the characteristic equation, and quality indicators of the transient process (stability degree, fluctuation degree or attenuation factor) by the D-partition method is considered. The shifted and fictitious characteristic equations for BSR construction in the area of parameters and quality indicators are introduced. It is shown that the quality indicators are non-linearly included in the coefficients of the characteristic equation, therefore it is impossible to construct the BSR of discrete automatic control system using the classical D-partition method. Constructing of digital control system BSR of spaceship state using one coordinate in the plane of the system parameter- stability degree is considered. The BSR is obtained using the previously proposed by the authors method of constructing the region of stability in the plane of two parameters, one of which is nonlinearly included in the system equation. At the same time, the construction of the entire D-partition curve, special straight lines, and the use of Neimark hatching is excluded, and computer realization of the limit of stability region is ensured. The obtained BSR family in the plane of the parameter and at different values of another system parameter which is nonlinearly included in the coefficients of the shifted characteristic equation makes it possible to estimate, and for the parameter values on the boundary of the stability region of the BSR family, to determine the stability degree.