ESDU 69005:2009

INTRODUCTION

This Item presents sets of normalised response curves for simple
first- and second-order systems.

The data are restricted to certain basic forms of input, which
are presented in Figure 1, and to systems that can be described by
a linear differential equation with constant coefficients. The
characteristic equation, and also the denominator of the
corresponding transfer function, is therefore a first or second
degree polynomial.

The response curves for first- and second-order systems are
presented in Figures 2 (2a, 2b, 2c, 2d, 2e, 2f, 2g and 2h) and
Figures 3 (3a, 3b, 3c, 3d, 3e, 3f, 3g and 3h) respectively, and
maxima in response to some of the input functions are given in
Figure 4 and Figures 5 (5a, 5b, 5c, 5d and 5e).

A step input, its time integral (ramp input) and its derivative
(impulsive or "Delta function" input), are considered independently
although the responses to any two of these inputs can be deduced
from the response to the third. Similarly the responses to related
inputs of ramp-step and triangular form are given, although these
could be deduced by superposition of the responses to suitably
chosen ramp inputs. Brief mention is made of the convolution
integral (Duhamel integral) method for determining the response to
an arbitrary input when the response to an impulse is known.

Data for the simple frequency response, i.e. the
ultimate steady state of a stable system subjected to a sinusoidal
input, are presented in Figures 6 (6a and 6b) and Figures 7 (7a and
7b). In this case the diagrams give the ratio of the amplitudes and
the difference in phase of the response variable and the input.

Finally Appendix A considers the response of a system having a
modified form of transfer function for one of the inputs used, the
ramp-step input.