Процедура оптимізації лінійних параметричних кіл у середовищі UDF MAOPCs

Abstract

Наведено процедуру оптимізації лінійних параметричних кіл, яка основана на частот- ному символьному методі та реалізована у середовищі системи UDF MAOPCs. Особливість оптимізації полягає у тому, що попередньо оцінюють стійкість досліджуваного лінійного параметричного кола в заданих межах зміни параметрів та визначають області допустимої їх зміни, у яких коло є стійким. Виключно у цих областях відбувається оптимізація.

The paper presents the procedure of optimization of linear periodically time-variable circuits based on the calculation of circuit parametric transfer functions by the frequency symbolic method. The parametric transfer function is approximated according to the frequency symbolic method by the Fourier trigonometric polynomial, in which some or all parameters of circuit elements are given by symbols. These parameters act as variables while performing procedures mentioned. The peculiarity of optimization consists in the fact that the previously the assessment of stability (asymptotic) of investigated linear periodically time-variable circuits circuit within the prescribed limits of changing parameters is carried out and the permissible areas of their change in which circuit is stable are determined. Exclusively in these areas optimization occurs. The assessment of circuit stability is carried out by the real parts of the denominator roots of a normal parametric transfer function, which also is defined by the frequency symbolic method in the form of approximation by the Fourier trigonometric polynomials. For the optimization of linear periodically time-variable circuits the general additive criterion of optimality is selected, which represents the sum of squared deviations of output characteristics from the technical requirements. This paper proposes the optimization procedure of the linear periodically time-variable circuit with two varied parameters of elements. The assessment of stability in this case is carried out by the denominator of the normal parametric transfer function. The results of this assessment are the areas of stability, whose limits are described mathematically, and which, being expressed in the form of inequalities, are the conditions for carried optimization. Performing the procedures of tolerance analysis and optimization of linear periodically time-variable circuits, while assessing the asymptotic stability, provides adequacy of the results and increases the efficiency of further design stages.