Calculating Critical Frequency and Corresponding Parameters of System Functions Using MATLAB

First, use symbolic variables to write the open-loop transfer function, obtaining the real and imaginary parts of the function. Set the real part equal to -1 and the imaginary part equal to 0, resulting in two equations. Solve these two equations to obtain the critical parameter values and critical frequency.

syms s G1 H1 U1 V1 ;

syms K1 W1 real

j=sqrt(-1);

s=j*W1;

G1=10/(s*(s+4));

H1=1+K1*s;

GH1=G1*H1;

%U1=factor(real(GH1))

U1=real(GH1);

%V1=factor(imag(GH1))

V1=imag(GH1);

s1=sprintf(‘%s=-1’,U1)

s2=sprintf(‘%s=0’,V1)

[K2,W2]=solve(U1==-1,V1==0,K1,W1)