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System modeling and simulation(ME340)

System modeling and simulation(ME340). Chapter 8 . System Analysis in the Frequency domain 8 .1 Frequency response of First Order System. 邹渊 Yuan Zou Tel: 68915202 Email: zouyuan@bit.edu.cn. Frequency response. How a system responds to a periodic input.

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System modeling and simulation(ME340)

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  1. System modeling and simulation(ME340) Chapter8.System Analysis in the Frequency domain 8.1 Frequency response of First Order System 邹渊 Yuan Zou Tel: 68915202 Email: zouyuan@bit.edu.cn

  2. Frequency response • How a system responds to a periodic input. • Typical input is sinusoid signal with the magnitude (M) and phase angle (). • It is meaningful because all the periodical signal can be divided into sum of Fourier series 2

  3. Frequency response property

  4. Frequency response of first order system

  5. Mass with damping case • m=0.2kg; c=1N.s/m. f(t)=sin(wt). • v(0)=0.Find response when (a) w=15 rad/s; • (b) w=60 rad/s

  6. Magnitude and phase

  7. Bode plot • Decibel unit is applied (dB) • m=10logM2=20logM dB • Phase angle unit is degree. • m(w)=20log(1/sqrt(1+sqr(tw)))

  8. A High-Pass filter

  9. A Model with Numerator Dynamics

  10. System modeling and simulation(ME340) Chapter8.System Analysis in the Frequency domain 8.2 Frequency response of High Order System 邹渊 Yuan Zou Tel: 68915202 Email: zouyuan@bit.edu.cn

  11. For high-order system

  12. Common transfer function factors • Most transfer function parts N(s) or D(s) take the forms in the following table.

  13. The displacement of a mass with a damper but no spring • mx’’+cx’=f(t) • T(s)=X(s)/F(s)=1/[s*(ms+c)

  14. Two real root • T(s)=1/(2sqr(s)+14s+20)

  15. Two complex roots • 6x’’+12x’+174x=15f(t) • f(t)=5sin(7t) • State-state response • Bode plot

  16. Generalized example • T(s)=1/(m*sqr(s)+cs+k)

  17. Frequency response of second order system

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