Алгоритмы анализа робастных свойств многоцелевых законов управления подвижными объектами

Abstract

The problems of analyzing robust properties for control systems of moving objects are of significant importance in modern control theory. This is because the mathematical models used in the synthesis of control laws are almost always inaccurate and only approximately represent the dynamics of moving objects. At the same time, one of the requirements for control systems in practice is the preservation of their dynamic properties, when the parameters and structure of mathematical models can vary within certain limits. If the developed control system does not have this property, then it can not be considered workable. The article deals with the analysis of robust stability and robust quality for multi-purpose control laws of moving objects. The multi-purpose approach is chosen as the basis for designing the control system, since it allows to provide the desired quality of the control system operation in various regimes, including under the influence of external disturbances. In this case, the choice of tunable elements of the multi-purpose control law determines the robust properties of the closed-loop system. The formalized statement of the problem of robust properties analysis for control laws with a multi-purpose structure is considered taking into account the limited admissible variations of the mathematical model. Frequency-domain approach to the analysis of robust stability and optimization approach to the analysis of robust performance are proposed. On the basis of the obtained results, computational algorithms for the analysis of robust properties are formed. As a practical example, the system of ship motion control is considered. The analysis of its robust properties is performed taking into account the admissible variation of the linear model coefficients in the given ranges. Examples of simulation modeling in MATLAB environment are demonstrated.