22_freqresp2

22_freqresp2 - u '(t ) = A sin ωt sinusoidal input to...

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Unformatted text preview: u '(t ) = A sin ωt sinusoidal input to 1st-order G ( s ) ω K Y '( s ) = = G ( s )U '( s ) A 2 2 KA τ s + 1 s + ω = y '(t ) ωτ e − t /τ − ωτ cos ωt + sin ωt ) ( freqresp2.mdl = ω 2τ 2 + 1 Frequency Response KA Adjust the Forcing Function y l '(t ) = sin(ωt + φ ), φ =−1 (ωt ) − tan and / or Transfer Function 2 2 ω τ +1 for new situations. Amplitude = 1 K output Frequency omega = 1/time unit Amplitude Ratio = AR = = Clock Period = 2 x pi = 6.2832 time units ω 2τ 2 + 1 input 1 1 = = 0.707 2 1 1 +1 − tan −1 ( − tan −1 (1) Phase Angle = φ = ωτ ) = = Mux tUin t_u_u' Mux2 Mux tYout t_y_y' 1 Mux3 s+1 2 2 Sine Wave Mux Transfer Fcn PC_graph Mux1 −π radians = -1/8 of a cycle = -45 degrees 4 = = / f For ω 1 rad/min, P 1= 2π = 6.2832 min /ω −0.785min then output is "behind" input = − P / 8 = Command Window shortcuts >> xlim([15.7,16.5]) >> ylim([-0.5,0.5]) Time Domain Plot of Frequency Response Time Domain Plot of Frequency Response 0.5 0.4 0.3 y, output = blue solid: u, input = red dash 0.5 0 -0.5 0.2 0.1 0 -0.1 -0.2 -0.3 -1 -0.4 0 5 10 Time tUin variable 15.6900 0.0180 15.7000 0.0080 15.7100 -0.0020 15.7200 -0.0120 15 20 -0.5 15.7 15.8 15.9 16 16.1 Time tYout variable 16.4800 0.0094 16.4900 0.0024 16.5000 -0.0047 16.5100 -0.0118 0.0180 0.0080 -0.0020 -0.0120 Time Domain Plot of Frequency Response linear interpolation of times: 15.708-16.493= = -0.785 minutes -0.69 y, output = blue solid: u, input = red dash y, output = blue solid: u, input = red dash 1 -0.695 -0.7 -0.705 -0.71 17.8 17.9 18 18.1 Time 18.2 18.3 16.2 16.3 0.0094 0.0024 -0.0047 -0.0118 16.4 16.5 ...
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