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.Indexed under:
Details:
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This Data Item contains 30 interactive graph(s) as listed below.
Graph | Title |
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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) |