Crossover frequencies for specified gain
wc = getGainCrossover(sys,gain) returns the vector wc of frequencies at which the frequency response of the dynamic system model, sys, has principal gain of gain. For SISO systems, the principal gain is the frequency response. For MIMO models, the principal gain is the largest singular value of sys.
Find the 0dB crossover of a single-loop control system with plant
and PI controller
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 crossovers 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 = 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.
Input dynamic system, specified as any SISO or MIMO dynamic system model.