1 C(s) P(S) у P(s) 800 (s + 5)(s + 20) Bode plot for P(s) = 800 (s+5)(s+20) 20 10 0 - 10 -20 Magnitude (dB) -30 -40

[answerhappygod]

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Raphael has provided the Bode plots for these plants.
(a) Compute the steady-state tracking error for a unit
step input when 𝐶(𝑠) = 1.
(b) Determine the phase margin when 𝐶(𝑠) = 1.
(c) Design a lag compensator that accomplishes two
objectives: (i) decreases by 50% the steady-state error for a step
input, and (ii) increases the phase margin by 10° from the value
computed in part (b). Be sure to clearly explain which numbers you
have read off the Bode plot at each step.

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1 C(s) P(S) у
P(s) 800 (s + 5)(s + 20)
Bode plot for P(s) = 800 (s+5)(s+20) 20 10 0 - 10 -20 Magnitude (dB) -30 -40 -50 -60 - 70 0.1 1 10 100 1000
0 -20 -40 -60 -80 Phase (deg) - 100 -120 - 140 - 160 - 180 0.1 1 100 1000 10 Frequency (rad/s)