solving 5 non linear equations equaton

Neelanjan Pal

2019 11 19

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how do you solve 5 non linear equations in in matlab? I am working on fractional order PIDs .

can it be done by solve, fsolve?

I have tried by 'solve' operator, vpasolve but its giving 'empty sym' ,plz help? Or you can give some alternate methods.

Also note that 'y' is the differentiation of y2 wrt 'w'.

syms kp ki w l c alp T kd m
A0=1+0.4*(10^(0.5))*cos(0.5*pi/2);
B0=0.4*(10^(0.5))*sin(0.5*pi/2);
p=((A0)^2 +(B0)^2)^-0.5;
A=-ki*kp*w^(-l)*sin(l*pi/2)+kd*w^(m)*sin(m*pi/2);
B=kp+ki*kp*w^(-l)*cos(l*pi/2)+kd*w^(m)*cos(m*pi/2);
c=((A)^2 +(B)^2)^0.5;
g=p*c;
y1=subs(g,w,10);
ang=atan(A/B)+atan(B0/A0);
y2=subs(ang,w,10);
y=diff(ang,w);
y3=subs(y,w,10);
y4=subs(g,w,100);
y5=subs(g,w,0.1);
[l,ki,kp,kd,m]=vpasolve(y3==0,y2==-1.92,y1==1,y4==0.1,y5==0.1,[l,ki,kp,kd,m],[1;1;1;1;1]);