Find the 0dB crossover frequencies of a single-loop control system with plant given by:

and PI controller given by:

G = zpk([],[-1,-1,-1],1);
C = pid(1.14,0.454);
sys = G*C;
wc = getGainCrossover(sys,1)

wc = 0.5214

The 0 dB crossover frequencies are the frequencies at which the open-loop response sys = G*C has unity gain. Because this system only crosses unity gain once, getGainCrossover returns a single value.

Find the 20 dB stopband of

sys is a notch filter centered at 10 rad/s.

sys = tf([1 0.05 100],[1 5 100]);
gain = db2mag(-20);
wc = getGainCrossover(sys,gain)

wc = 2×1

    9.7531
   10.2531

The db2mag command converts the gain value of -20 dB to absolute units. The getGainCrossover command returns the two frequencies that define the stopband.