Fundamentals of Measurement Technology Prof Wang Boxiong
Fundamentals of Measurement Technology (7) Prof. Wang Boxiong
3. 4.3 Responses of measuring system to typical excitations u Both the transfer function and the frequency response function describe the response of a measuring instrument or system to sinusoidal excitation u But the frequency response describes only the transfer characteristics of a system with steady-state input and output Ua transient output will reduce gradually to zero, and the system will then reach the steady-state stage. For describing the whole process of the two stages, the transfer function must be employed. and the frequency response is only a special case of the transfer function
❑Both the transfer function and the frequency response function describe the response of a measuring instrument or system to sinusoidal excitation. ❑But the frequency response describes only the transfer characteristics of a system with steady-state input and output. ❑A transient output will reduce gradually to zero, and the system will then reach the steady-state stage. For describing the whole process of the two stages, the transfer function must be employed, and the frequency response is only a special case of the transfer function. 3.4.3 Responses of measuring system to typical excitations
3.4.3 Responses of measuring system to typical excitations UThe dynamic response of a measuring system can be also obtained through applying other excitations to the system UThe most commonly used excitation signals are: unit impulse, unit step, and ramp signals
❑The dynamic response of a measuring system can be also obtained through applying other excitations to the system. ❑The most commonly used excitation signals are: unit impulse, unit step, and ramp signals. 3.4.3 Responses of measuring system to typical excitations
3.4.3 Responses of measuring system to typical excitations 1. Unit impulse response For a unit impulse function d(t,its Fourier transform AGj@)=I and the laplace transform of S(: 4(s=LS(/1. The output of a measuring instrument with d(t) as its excitation: Y(S=H(SX(S=H(S)4(S)=H(S) Making inverse Laplace transform of Y(s) en y()=L[Y(s)]=h(t (3.44) h(t is referred to as the impulse response function or weighting function of a measuring system
1. Unit impulse response For a unit impulse function δ(t), its Fourier transform Δ(jω)=1 and the Laplace transform of δ(t): Δ(s)=L[δ(t)]=1. The output of a measuring instrument with δ(t) as its excitation: Y(s)=H(s)X(s)=H(s)Δ(s)=H(s). Making inverse Laplace transform of Y(s), then h(t) is referred to as the impulse response function or weighting function of a measuring system. 3.4.3 Responses of measuring system to typical excitations y(t) = L Y (s) = h(t) −1 (3.44)
3.4.3 Responses of measuring system to typical excitations The first-order system H( +1 its impulse response h(t) (345) where t△ time constant h (t) Fig 3. 18 Impulse response of first-order system
The first-order system its impulse response h(t) where time constant. 3.4.3 Responses of measuring system to typical excitations ( ) 1 1 + = s H s ( ) t h t e − = 1 (3.45) Fig. 3.18 Impulse response of first-order system