ESDU 69005
The response of first and secondorder systems.
Abstract:
ESDU 69005 presents sets of normalised response curves for simple first and secondorder 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 seconddegree polynomial. The response curves for first and secondorder 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 rampstep 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 rampstep input of a system having a modified form of transfer function is also considered.Indexed under:
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Data Item ESDU 69005  

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Figure 3d  Part 1  Response of a secondorder system to a unit rectangular input 
Figure 3d  Part 2  Response of a secondorder system to a unit rectangular input 
Figure 3d  Part 3  Response of a secondorder system to a unit rectangular input 
Figure 3d  Part 4  Response of a secondorder system to a unit rectangular input 
Figure 3e  Part 1  Response of a secondorder system to a unit rampstep input 
Figure 3e  Part 2  Response of a secondorder system to a unit rampstep input 
Figure 3e  Part 3  Response of a secondorder system to a unit rampstep input 
Figure 3e  Part 4  Response of a secondorder system to a unit rampstep input 
Figure 3f  Part 1  Response of a secondorder system to a unit exponentialstep input 
Figure 3f  Part 2  Response of a secondorder system to a unit exponentialstep input 
Figure 3f  Part 3  Response of a secondorder system to a unit exponentialstep input 
Figure 3f  Part 4  Response of a secondorder system to a unit exponentialstep input 
Figure 3g  Part 1  Response of a secondorder system to a unit cosinestep input 
Figure 3g  Part 2  Response of a secondorder system to a unit cosinestep input 
Figure 3g  Part 3  Response of a secondorder system to a unit cosinestep input 
Figure 3g  Part 4  Response of a secondorder system to a unit cosinestep input 
Figure 3h  Part 1  Response of a secondorder system to a unit triangular input 
Figure 3h  Part 2  Response of a secondorder system to a unit triangular input 
Figure 3h  Part 3  Response of a secondorder system to a unit triangular input 
Figure 3h  Part 4  Response of a secondorder system to a unit triangular input 
Figure 4  Maxima in response of a firstorder system to a unit triangular input 
Figure 5a  Maxima in response of a secondorder system to a unit rectangular input 
Figure 5b  Maxima in response of a secondorder system to a unit rampstep input 
Figure 5c  Maxima in response of a secondorder system to a unit exponentialstep input 
Figure 5d  Maxima in response of a secondorder system to a unit cosinestep input 
Figure 5e  Maxima in response of a secondorder system to a unit triangular input 
Figure 6a  Steadystate response of a firstorder system to a sinusoidal input (amplitude ratio) 
Figure 6b  Steadystate response of a firstorder system to a sinusoidal input (phase angle) 
Figure 7a  Steadystate response of a secondorder system to a sinusoidal input (amplitude ratio) 
Figure 7b  Steadystate response of a secondorder system to a sinusoidal input (phase angle) 