STABILIZATION OF ROCKET MOTION UNDER UNCERTAINTY

Abstract

The article deals with the support of the guaranteed stability factor of a stabilizing system (SS) for the rocket motion under uncertainty of coefficients in the mathematical model and absence of their stable statistical characteristics. The aim consists of development the verify methodology of SS stability degree by the presence of limited deviations of coefficients of the disturbance motion equations and choice of a control law on the basis of the standard Butterworth’s polynomials where the roots of a characteristic polynomial (CP) are placed on a semicircle of the given radius. Goal: formalize the sequence of steps to control the stability degree in a set of uncertainty (SUn) coefficients of equations in conditions of control law construction for their nominal values and consider all coordinates of state vector within the limits of the accepted model. It is applied the methods of automatic control theory and iterative procedure of a function’s extremum research in multidimensional space. The following results were obtained. It is developed the algorithm for verifying the guaranteed stability degree of SS for the rocket motion when the coefficients of its mathematical model are in SUn, i.e. they have limit deviations from the basic values. The element of novelty is Sun’s construction that passing from any of its tops to a neighbor one, the extreme value changes in only one coefficient, that gives an opportunity to trace its influence on the selected system indicator. It was also offered a function which took on the negative value in the point of six-dimensional space of equations coefficients, where the given stability degree is not provided. The application of this function in comparison with the iterative calculation of CP roots leads to the substantially fewer expenses of machine time. The table of SUn’ tops also allows to determine the constellation of errors in which the chosen indicator (the degree of SS stability on the space of CP roots) takes on the least value. Conclusions. The introduced algorithm can be applied for the correlation between the assured degree of stability and limitations of coefficient deviations when their steady statistical characteristics are absent or the volume of experimental data is insufficient

Keywords

• множина невизначеності
• закон регулювання
• ступінь стійкості