ESDU 69005

The response of first- and second-order systems.

Abstract:

ESDU 69005 presents sets of normalised response curves for simple first- and second-order systems. The data are restricted to certain basic forms of input 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 and maxima in response to some of the input functions are given. 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 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 that case the diagrams give the ratio of the amplitudes and the difference in phase of the response and the input. The response to a ramp-step input of a system having a modified form of transfer function is also considered.

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Details:

Data Item ESDU 69005
Format:	PDF with interactive graphs
Status:	Amendment (A), 01 Nov 2009 Published in Release 2009-04
Previous Releases:	ESDU 69005
ISBN:	978 1 86246 094 2

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This Data Item contains 30 interactive graph(s) as listed below.

Graph	Title
Figure 3d - Part 1	Response of a second-order system to a unit rectangular input
Figure 3d - Part 2	Response of a second-order system to a unit rectangular input
Figure 3d - Part 3	Response of a second-order system to a unit rectangular input
Figure 3d - Part 4	Response of a second-order system to a unit rectangular input
Figure 3e - Part 1	Response of a second-order system to a unit ramp-step input
Figure 3e - Part 2	Response of a second-order system to a unit ramp-step input
Figure 3e - Part 3	Response of a second-order system to a unit ramp-step input
Figure 3e - Part 4	Response of a second-order system to a unit ramp-step input
Figure 3f - Part 1	Response of a second-order system to a unit exponential-step input
Figure 3f - Part 2	Response of a second-order system to a unit exponential-step input
Figure 3f - Part 3	Response of a second-order system to a unit exponential-step input
Figure 3f - Part 4	Response of a second-order system to a unit exponential-step input
Figure 3g - Part 1	Response of a second-order system to a unit cosine-step input
Figure 3g - Part 2	Response of a second-order system to a unit cosine-step input
Figure 3g - Part 3	Response of a second-order system to a unit cosine-step input
Figure 3g - Part 4	Response of a second-order system to a unit cosine-step input
Figure 3h - Part 1	Response of a second-order system to a unit triangular input
Figure 3h - Part 2	Response of a second-order system to a unit triangular input
Figure 3h - Part 3	Response of a second-order system to a unit triangular input
Figure 3h - Part 4	Response of a second-order system to a unit triangular input
Figure 4	Maxima in response of a first-order system to a unit triangular input
Figure 5a	Maxima in response of a second-order system to a unit rectangular input
Figure 5b	Maxima in response of a second-order system to a unit ramp-step input
Figure 5c	Maxima in response of a second-order system to a unit exponential-step input
Figure 5d	Maxima in response of a second-order system to a unit cosine-step input
Figure 5e	Maxima in response of a second-order system to a unit triangular input
Figure 6a	Steady-state response of a first-order system to a sinusoidal input (amplitude ratio)
Figure 6b	Steady-state response of a first-order system to a sinusoidal input (phase angle)
Figure 7a	Steady-state response of a second-order system to a sinusoidal input (amplitude ratio)
Figure 7b	Steady-state response of a second-order system to a sinusoidal input (phase angle)