H(s) 1.2s +0.18 s(s² + 0.74s + 0.92) Eq. (1) (a) Given H(s) in Eq. (1), set s = jw and put H(s) into Bode form. (b) Using your answer from part (a), identify the class 1, class 2, and class 3 terms that comprise the transfer function H(jw). Determine the parameters Ko and n of the class 1 term. Determine the parameters n, t, wo, and and the break points @BP of the class 2 and class 3 terms. (c) For the class 1 term, find the slope (in dB/decade, where dB = decibels) of the magnitude frequency response (FR), the magnitude (in dB) at @ = 1, and the phase (in deg = degrees). (d) Determine the change in slope (in dB/decade) of the magnitude FR of H(jo) and the change in phase (in deg) of the phase FR of H(jo) at the break points of the class 2 and class 3 terms.
H(s) 1.2s +0.18 s(s² + 0.74s + 0.92) Eq. (1) (a) Given H(s) in Eq. (1), set s = jw and put H(s) into Bode form. (b) Using your answer from part (a), identify the class 1, class 2, and class 3 terms that comprise the transfer function H(jw). Determine the parameters Ko and n of the class 1 term. Determine the parameters n, t, wo, and and the break points @BP of the class 2 and class 3 terms. (c) For the class 1 term, find the slope (in dB/decade, where dB = decibels) of the magnitude frequency response (FR), the magnitude (in dB) at @ = 1, and the phase (in deg = degrees). (d) Determine the change in slope (in dB/decade) of the magnitude FR of H(jo) and the change in phase (in deg) of the phase FR of H(jo) at the break points of the class 2 and class 3 terms.
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Transcribed Image Text:H(s)
1.2s +0.18
s(s² + 0.74s + 0.92)
Eq. (1)
(a) Given H(s) in Eq. (1), set s = jw and put H(s) into Bode form.
(b) Using your answer from part (a), identify the class 1, class 2, and class 3 terms that comprise
the transfer function H(jw). Determine the parameters Ko and n of the class 1 term. Determine the
parameters n, t, wo, and and the break points @BP of the class 2 and class 3 terms.
(c) For the class 1 term, find the slope (in dB/decade, where dB = decibels) of the magnitude
frequency response (FR), the magnitude (in dB) at w = 1, and the phase (in deg = degrees).
(d) Determine the change in slope (in dB/decade) of the magnitude FR of H(jo) and the change
in phase deg) of the phase FR of H(jo) at the break points of the class 2 and class 3 terms.
(e) Sketch the asymptotes of the magnitude and phase FRs of H(jo), with the magnitude in dB
and the phase in degrees, as follows:
For both the magnitude and phase FR plots: Plot @ along the x-axis, ranging from @₁ = 10-²
rad/s to WH = 10² rad/s. Denote the lower break point by @BP,L and the higher break point by @BP,H.
Round up @BP.H to 1. Convert @BP,L and @BP,H into powers of 10 and label them on the x-axis.
For the magnitude FR plot:
• Compute the magnitude of H(jw) in dB, H(jw)|dB, at @=@₁ and @=@BP₁L using your answer
to part (c), which determines the equation for the magnitude FR of the class 1 term. Plot these
magnitudes on the y-axis and draw a line (asymptote) between the points (@L, H(j-WL) dB)
and (@BP,L, Hj @BPL) dB). Label the slope of this asymptote.
Using your answer to part (d), find the slope of the asymptote for a between @BP,L and @BP,H,
the slope of the asymptote for @ > @BP,H, and the magnitudes H(j@BP,H)|dв and H(j-wH) dB.
Plot these magnitudes on the y-axis, draw the two asymptotes, and label their slopes.
For the phase FR plot: Use your answers to parts (c) and (d) to calculate the phase H() of each
asymptote in degrees. Sketch these asymptotes and label their phases on the y-axis.
(f) Use the MATLAB command bode to generate the actual Bode plot of H(s). Submit the plot.
(g) Consider a unity negative feedback loop with the forward-path transfer function KH(s), where
K = 10. Use the margin command in MATLAB to find the crossover frequency wc, the phase
margin PM, and the gain margin GM of KH(s). Use the values of the PM and GM to explain
whether the closed-loop system is stable for this value of K.
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