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1、10.1 Overview of measuring system10.2 Static characteristics of measuring system10.3 Dynamic characteristics of measuring system10.4 Characteristics of typical systemsChapter 10 Characteristics of measuring systemFundamentals of Measurement and Signal Analysis10.3 Dynamic characteristics of measurin
2、g systemWhen the input of the measuring system is a rapid changing quantity,the relationship between the system input and output is called the dynamic characteristics.)(*)()(txthtyh(t)Time domain：Frequency domain:)()()f(fXfHYh(t)：system impulse response functionH(f)：system transfer functionx(t)y(t)1
3、0.3 Dynamic characteristics of measuring systemImpulse response function h(t)Impulse response refers to the output(response)of the system when the input is a unit impulse function.)(t10.3 Dynamic characteristics of measuring systemTransfer function H(f)Let the input function of a system be x(t)and t
4、he output function be y(t),then the quotient of the Fourier transforms of y(t)and x(t),namely Y(f)/X(f),is called the transfer function.)(/)()f(fXfYH)(Im/)(Re)f(fHfHarctg22)(Im)(Re)()f(fHfHfHA10.3 Dynamic characteristics of measuring systemThree types of problems in system analysis:3)If the input x(
5、t)and the system characteristic h(t)/H(f)are known,the system output y(t)can be estimated Prediction 1)When the input x(t)and output y(t)are measurable(known),characteristics of the system h(t)/H(f)can be inferred System Identification2)When the system characteristics h(t)/H(f)are known,and the outp
6、ut y(t)can be measured,then the input x(t)can be calculated Inverse solutionx(t)h(t)y(t)10.3 Dynamic characteristics of measuring systemBasic requirements of measuring systemAn ideal measuring system should have signal-valued mapping between input and output.For each input,there should be only one s
7、ingle output corresponding to it.Knowing one of the quantities can determine the other one.The best relationship between input and output is a linear relationship.YXxyxy10.3 Dynamic characteristics of measuring systemLinear measuring systemIf the relationship between system input x(t)and output y(t)
8、can be described by a constant coefficient linear differential equation,it is called a linear system.01110111.)()()(asasasabsbsbsbsXsYsHnnnnmmmmUsually,the measuring instruments used in engineering can be approximated as a linear system within the measuring range.01110111)(.)()()(.)()(btxbtxbtxbatya
9、tyatyammmmnnnn10.3 Dynamic characteristics of measuring systemCharacteristics of linear system：a)Superposition：the system output of the sum of several inputs is equal to the sum of the outputs of the individual inputsb)Proportionality：the output of the multiplication of an input is equal to the mult
10、iplication of the output of the input10.3 Dynamic characteristics of measuring systemc)Differentiation:the output of the differentiation of an input is equal to the differentiation of the output of the original inputd)Integration：when the initial condition is zero,the output of the integration of an
11、 input is equal to the integration of the output of the original inputIf x(t)y(t)then x(t)y(t)If x(t)y(t)then x(t)dt y(t)dt 10.3 Dynamic characteristics of measuring systeme)Frequency retentivity:if the system input has one frequency,the output will have the same frequency.10.3 Dynamic characteristi
12、cs of measuring systemMethods for measuring dynamic characteristics:According to the relationship between input,output and system characteristics,we can determine the dynamic characteristics of the system by measuring the response of standard signals.10.3 Dynamic characteristics of measuring systema
13、)Impulse functionBecause the Fourier transform of (t)is 1,if the input is a unit pulse (t),then:Y(f)=H(f)，or y(t)=h(t)h(t)F(t)h(t)H(f)Advantage：Simple and intuitiveDisadvantage：Low excitation energy10.3 Dynamic characteristics of measuring systemb)Sine wave/swept sine wave excitation methodx(t)=Acos
14、(t+x)-y(t)=Bcos(t+y)G r a d u a l l y i n c r e a s e t h e sinusoidal excitation signal frequency f from the lowest measurement frequency fmin to the highest fmax,record the amplitude ratio and phase difference corresponding to e a c h f r e q u e n c y t o g e t a m p l i t u d e a n d p h a s e c
15、haracteristics of the system.Advantage:high energy，simple，signal generator,oscilloscope；Disadvantage:low efficiency10.3 Dynamic characteristics of measuring systemSwept frequency input x(t)Response y(t)Example：swept frequency excitation experiment10.3 Dynamic characteristics of measuring systemc)Use
16、 white noise excitation to get H(s)/h(t)；)()(YfHf)()(1fYFthAdvantage:high efficiency；Disadvantage:requires FFT,the equipment is complicated10.3 Dynamic characteristics of measuring systemExample：calibration of the accelerometer10.3 Dynamic characteristics of measuring systemExample：calibration of au
17、dio system)(/)()(YfXfHfPink noise(1 f noise)is a signal with a frequency spectrum such that the power spectral density is inversely proportional to the frequency of the signal.Homework10.3 Dynamic characteristics of measuring system1.What are the dynamic characteristics of the measuring system？2.What is a linear measuring system?3.How to measure the dynamic characteristics of a measuring system?