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s=poly(0,'s');
F=syslin('c',[1/((2+s)*s*(s+10))]) //without k
fmin=0.1; //Min freq in Hz
fmax=20; //Max freq in Hz
scf(1);clf;
bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
disp(GainMargin,"GM=")
disp(freqGM*2*3.14,"omegaPC=")
[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
disp(PhaseMargin,"PM=")
disp(freqPM*2*3.14,"omegaGC")
show_margins(F) //display gain and phase margin and associated crossover frequencies
// TO FIND VALUE OF K
//we have to make omegaPC=omegaGC. the required upward shift is 22dB
k1=10^(22/20) // 20*log(k1)=22
disp(20*k1,"k marginal = ")
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