ESTIMATION OF THE TOLERANCE AREA FOR CORRECTION PARAMETERS IN INDUCTION ACCELERATION SYSTEMS

Abstract

The general statements of the problems of the normal functioning of the object in real modes are considered, within which the problems of evaluating the area of admissible parameters are formulated. The issues of formalizing the formulation of problems for calculating tolerances for parameters in the presence of dynamic restrictions with respect to fluctuations of the state vector of a real object are studied. For the purpose of numerical implementation of this kind of inverse problems, the application of practical stability algorithms for systems of differential equations dependent on parameters is proposed. For linear dynamic constraints on the spread of the vector of phase coordinates, a necessary and sufficient condition for the corresponding estimate of the area of deviations of the system parameters in a given structure is given. It is shown that in this concretization the problem of tolerance estimation is completely covered by the statements of stability problems. A class of problems related to the estimation of deviations of the vector of parameters from the calculated ones in the presence of a variation in the quality index is singled out. For the numerical implementation of the formulations of such problems, a linear system of differential equations depending on parameters with fixed initial conditions is studied. The analysis of the corresponding system of differential equations with respect to the spread of the state vector and parameters was carried out by methods of practical stability. Provided that the deviations of the values of the vector of parameters from the nominal are small enough, and the change in the vector of parameters within the tolerance field is linear, the expression for the variation of the quality indicator is presented in the form of a linear form. Within the framework of the formulations formulated, the area of tolerances for parameters is specified structurally in the form of an ellipsoid. The range of admissible parameters was estimated by finding the maximum of the linear form on the ellipsoid. A more complicated variant of the problem of estimating the maximum range of allowable values of the spread of the vector of parameters by the methods of practical directional stability is considered. The algorithms are extended to the case of a nonlinear change in the vector of parameters within the tolerance field and non-fixed initial conditions of the original system. In the applied plan, the considered problem statements are extended to a discrete model of an induction acceleration system for estimating the tolerance range for the correction parameters under given restrictions on the spread of the quality criterion.