Abstract
Linear automatic regulation systems are described by differential equations of the type (a0pn + a1pn-1 + … + an-pp + an)x* = (b0pv + . .. + bv-ip + bv)f(t). Therefore, when it is necessary to find the transient curve caused by an input step or impulse f(t) = cl(t) or f(t) = cl’ (t), the problem reduces to solution of the homogeneous equation: (aopn + a1pn-1 + … + an-1p + an)x = 0. This chapter describes useful procedure for calculating the arbitrary constants developed by A. I. Sud-Zlochevskii. In the usual solution, two most cumbersome computations are encountered: (1) finding the roots of the characteristic equation and (2) determining the arbitrary constants for given initial conditions. The first of these operations may be carried out by the simple numerical method. Therefore, it is necessary to obtain a simpler method of determining the arbitrary constants of integration.
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