The Bode plots for the loop transmittance (mathrm{G}(s)) of unity feedback control system are experimentally obtained as
Question:
The Bode plots for the loop transmittance \(\mathrm{G}(s)\) of unity feedback control system are experimentally obtained as shown in Fig. P6.11 (a) and (b) with the loop gain set at nominal value.
(a) Find GM, PM, \(\omega_{g c}\) and \(\omega_{p c}\) as best read from Bode plots.
(b) Repeat part (a) for the loop gain 10 times the nominal value.
(c) Find how much the loop gain must be changed from its nominal value if GM is required to be \(+40 \mathrm{~dB}\).
(d) Find how much the loop gain must be changed from its nominal value if PM is required to be \(+45^{\circ}\).
(e) Find the steady state error of the system if the reference input to it is a unit step function.
( \(f\) ) Find modified values of GM and PM if the system has delay \(t_{d}=0.05\) seconds and loop gain at nominal.
(g) With the gain at nominal, find maximum time delay \(t_{d}\) the system can tolerate without going into instability.
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