23_Freq_Resp_t_domain

# 23_Freq_Resp_t_domain - freq_resp 1/2 Frequency Responses...

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freq_resp 1/2 Frequency Responses: t "domain" CHE 361 9 Constant2 yout + + Sum2 Mux Mux Sine Wave1 1 1/(2*3.14159)s+1 Transfer Fcn1 + + Sum1 7 Constant1 1 Constant3 + + Sum3 1 1/(2*3.14159)s+1 Transfer Fcn2 Sine Wave2 + + Sum4 3 Constant4 -5 Constant5 + + Sum5 1 1/(2*3.14159)s+1 Transfer Fcn3 Sine Wave3 + + Sum6 -3 Constant6 For G 1st order ( s ) = K 1 τ 1 s 1 from Eqns (5 26), (5 27) and (13 3a) we have AR 1 = K 1 ω 2 τ 2 1 1 and φ 1 = tan 1 ( ω τ 1 ) For G 2nd order ( s ) = K 2 τ 2 2 s 2 2 τ 2 ζ s 1 from Eqns (5 61), (5 62) and (13 41a,b) we have AR 2 = K 2 1 ( ωτ 2 ) 2 2 2 ζωτ 2 2 and φ 2 = tan 1 2 ζωτ 2 1 ( ωτ 2 ) 2 For ζ < 2 2 from Eqns (5 65,66) or (13 44,45) we have AR 2,max = K 2 2 ζ 1 ζ 2 > K 2 occurs at ω resonant = 1 2 ζ 2 τ 2 See page 2 for Simulink plots of 3 frequencies into G 1 and Bode plot

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freq_resp 2/2 0 1 2 3 4 5 6 7 8 -6 -4 -2 0 2 4 6 8 10 Time y', output = lower curve : u', input = upper curve Low, Medium, or High Frequency: Input u'(t) on Top, Output y'(t) on Bottom τ process = 1 2 π = 0.16 min , t i
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