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1、1,Chapter 5 Frequency-response analysis,Applying Frequency-response to study linear system.,Reason :1.the difficulty to get the transfer function; 2.The property of the input .,2,（1）The frequency response has clear and definite physical meaning, it can be determined by experiment method. To the syst
2、em difficult to write the differential equation, it has actual meaning of importance. (2) because the frequency response analyzes system by open -loop frequency characteristic, it is direct,simple, has little calculation. (3) the frequency response not only is applicable to the linear time-invariant
3、 system, but also the system with pure delay and part non-linear system.,characteristics,3,5.1Frequency-response and description 5.1.1 Frequency-response basic concept,Frequency characteristic,also called Frequency response，is the response characteristic to sine signal of a system or component.,The
4、output amplitude and phase generally differ from input, and vary with different input signal frequency .,4,t/s,5,Assume system TF,Given input,its Laplace transformation,A is a constant，output:,(5-1),G(s),poles,(5-2),To a stable system,6,(5-2),0,when,Coefficient to be determined,Owing to,is a complex
5、 vector，can be expressed,(5-7),(5-5),(5-6),(5-4),7,(5-11),Steady-state output of a linear system is a sine signal and its frequency is the same as input sine signal frequency. the amplitude ratio of output to input is,Phase deviation of output to input,phase-frequency characteristic,Amplitude-freque
6、ncy characteristic,note,8,As a case,see R-C circuit。Fig.5-3. TF is,Set input,(5-15),where,9,10,-frequency characteristic of RC circuit 。,and,Are the function of input signal frequency,They are called respectively amplitude-frequency characteristic and phase-frequency characteristic。,Physical meaning
7、:the output/input ratio,Or output/input amplitude ratio and output/input phase deviation . The relation between input and output when a sine signal with a frequency is exerted,to a circuit.,connected with construction and parameters of RC circuit, independent of the input signal。, output/input ampli
8、tude ratio when steady state, output/input phase deviation when steady state,because,11,Circuit output/input amplitude ratio,(a) amplitude-frequency characteristic,12,(b) phase-frequency characteristic。,Circuit output/input phase deviation,13,phase-frequency characteristic and TF is of very similar
9、form.。,compare,14,5.1.2 expressed forms,(1) Bode diagram or logarithmic plot (2) Polar plot (3) Log-magnitude versus phase plot,logarithmic frequency characteristic,Logarithmic amplitude-frequency characteristic,Logarithmic phase-frequency characteristic,(),The longitudinal coordinate is marked acco
10、rding to linearity,Horizontal coordinate is,marked according to,15,BODE diag.,16,Polar plot,also amplitude-phase frequency characteristic .,Can be expressed by a vector with amplitude and phase,， Amplitude and phase of,the vector G(jw) vary,the curve which its end point traces in complex plane is ca
11、lled polar diagram- Nyquist curve- Nyquist diag.,When input signal frequency,Nyquist analysed feedback control system stability in 1932.,17,Nyquist DIAG.,18,5.2typical component bode diag.,5.2.1 proportion K,Please look at the following page,19,Number- decibel conversion,20,Diag.5-7 Number- decibel
12、conversion straight line,21,5.2.2 integer and differential,These amplitudes-frequency curve pass the point,Inference,Difference :sign,22,Diag.5-8 logfrequency characteristic of the integral,23,Diag. 5-9 The logfrequency characteristic of the differential,24,-20dB/dec,-40dB/dec,-60dB/dec,logfrequency
13、 characteristic,Diag. 5-10,25,5.2.3 first-order,first-order,Low frequency,Low frequency,log-amplitude frequency characteristic is a 0 decibel line,Diag.5-10 gives the asymptote and the accurate curve of first order system.,high frequency,high frequency,log-amplitude frequency is a line whose slope i
14、s -20db/dec,Please look at following page,phasefrequency characteristic,26,Asymptote,Asymptote,Corner frequency,Exact curve,Exact curve,Diag.5-11 logfrequency characteristic of the 1 order system,27,Diag.5-12 log amplitude error between Asymptote and Exact curve,28,Diag. 5-13 logfrequency characteri
15、stic of the 1 order factor,29,5.2.4 2th order factor,30,Low frequency,Low frequency asymptote,-20log1=0dB,High frequency,A line whose slope is -40db/dec,because,cross point low frequency and High frequency appears at,31,Relation between amplitude frequency characteristic and,32,Relation between ampl
16、itude frequency characteristic and,33,Relation between amplitude frequency characteristic and,34,Relation between amplitude frequency characteristic and,35,Relation between amplitude frequency characteristic and,36,Fig.5-13 amplitude frequency characteristic of 2th factor,37,Relation between phase f
17、requency characteristic and,38,Relation between amplitude frequency characteristic and,39,Relation between amplitude frequency characteristic and,40,Relation between amplitude frequency characteristic and,41,Relation between amplitude frequency characteristic and,42,Relation between amplitude freque
18、ncy characteristic and,43,Relation between amplitude error and,44,Relation between amplitude error and,45,Relation between amplitude error and,46,Relation between amplitude error and,47,Relation between amplitude error and,48,Fig.5-14 log amplitude error of 2th order factor,49,set,(5-22),(5-23),(5-2
19、5),Resonant frequency,Resonant frequency and Resonant peak,Resonant peak,when,，no peak ,no resonance.,and,Is as following page.,relation between,50,Fig.5-15 relation between,and,/dB,51,Low frequency,Low frequency asymptote,20log1=0dB,High frequency,A line whose slope is 40db/dec,because,cross point
20、low frequency and High frequency appears at,52,53,5.2.5 delay,54,5.3.1integer and differential factor,So,polar plot of,is negative imaginary axis.,fig5-26 integer factor polar plot,polar plot of,is positive imaginary axis.,5.3typical component nyquist diag.,55,fig5-27 differential factor polar plot,
21、56,5.3.2first order factor,Fig.5-28 first order factor,Polar plot,57,Fig.5-29 first order factor,Polar plot,58,5.3.3 2-th order factor,high frequency part is tangent to negative real axis.its accurate shape of the polar plot has relation with damped ratio, but for under-damped and over-damped,they a
22、re basically similar.,Fig.5-30 2-th order factor polar plot,59,for under-damped,phase is 90.the crossing point frequency at,Trajectory,The point Farthest From origin corresponds to resonant frequency,corresponds resonant peak Mr.,when,and imaginary axis is,60,For over damped,Increases to1，,The traje
23、ctory of trends a semicircle。This is because to a big damped system, characteristic roots are real number,and one root is much less than another。The bigger affects system much less than the smaller. thus,the system is similar to a first order system.,when,61,62,63,64,65,66,low frequency part ：,high frequency part ：,Fig 5-31 2-th factor,Polar plot,67,5.3.4 pure delay,when,，,when,Both exists hypostatic difference,Low frequency part is similar to first order system,68,thanks！,end,