Patent GB-1083912-A (GB)
Title: Computing apparatus
IPC: G06G7/625
Filed: 1965-01-04
Abstract: 1,083,912. Testing dynamic response characteristics. NORTH AMERICAN AVIATION Inc. Jan. 4, 1965 [Jan. 27, 1964], No. 309/65. Heading G1U. [Also in Division G4] The dynamic response characteristic of a unit under test (U. U. T.) 20 which has an output related to the input by a linear expression containing derivatives of various orders, in this case is evaluated by providing electrical networks connected to both the input and output of the device so as to provide integral functions of both the inputs and output which are then compared to provide an indication of the response of the unit. In the arrangement shown, the method of Laplace transformation is employed to replace each indicated differentiation operation so that the linear differential equation describing function of the element is replaced by a number of zero order terms corresponding to the order of the equation the several coefficients of these terms being employed in the algebraic solution of the describing function. The coefficients of the transformed equations are obtained in terms of the time constants of a series of R. C. networks through which the input and output signals of the U. U. T. are processed. The classical Laplace transform is defined by where s is the Laplace operator and F(s) is a function of the operation s on the Laplace transform corresponding to f(t). The operation may be performed for a limited time interval giving a bounded transform defined by Derivatives are theoretically required for the initial conditions but it is argued that in practice such initial conditions can be ignored. The Specification shows that an R. C. low pass filter provides a running left-sided Laplace transform for negative real values of s corresponding to the time constant of the R. C. network for the operator s = -<SP>1</SP>/ RC . In the arrangement shown in Fig. 4 a pair of R.C. filters 25a, 25b, is connected to the input line so as to perform a double operation on the input function and an identical pair of filters 25a, 25b, is connected to the outputs. Between the filters, and between the filters and the inputs and outputs are provided transistor amplifiers which provide impedance isolation. The output of the first set of filters is adjustable by a potentiometer 31 while the input signal and the outputs from both stages of the output networks 25a', 25b#, are fed through potentiometers 32, 33, 34, to provide appropriate coefficients. These four outputs are all fed to differential amplifier 35. The Specification contains a demonstration that a doubly transformed signal I(α #, t) may be equivalent to the sum of output @nal O(t) and a singly transformed output signal O(# t) and a doubly transformed output signal O(α # t) by employing coefficients Z 0 , P 2 , (P 1  + α P 2  + # 2 ) and (1 + α P 1  + α<SP>2</SP> P 2 ) respectively where P1, P2 and Z 0  are the coefficients of the differential equation defining the U. U. T. and where α and # are the time constants of the transform filters. In consequence, the signals from the various stages are attenuated by potentiometers 31-34 at the same time the potentiometers must take account of the attenuations introduced by the filters. Thus, for example, the coefficient introduced by the potentiometer 31 is KZo/# 1 α 1  the various coefficients being shown in the Fig. As explained, with the coefficients correctly adjusted, the combined inputs to the differential amplifier derived from the unit output should equal that derived from the unit input. This is tested by differential amplifier 35 feeding a comparator to produce Go-No-Go output indicator whether the unit is functioning correctly. The invention may be applied to determining the actual coefficients of the describing function. The number of sets of filters shown in Fig. 4 is tripled to generate three equations in three unknowns and the analog. data is then digitized and fed to a computer which provides solutions for Z P 1  and P 2  . The arrangement is described with reference to Fig. 5 (not shown).