routhhurwitz.m

this the matlab tuning of pid with root locus

%-det([si() si();sj() sj()])/sj()
syms e
 s5=[1 3 5 0 0];
 s4=[2 6 3 0 0];

if -det([s5(1) s5(2);s4(1) s4(2)])/s4(1) == 0
       s3=[e...
      -det([s5(1) s5(3);s4(1) s4(3)])/s4(1) 0 0];
   else
       s3=[-det([s5(1) s5(2);s4(1) s4(2)])/s4(1)   -det([s5(1) s5(3);s4(1) s4(3)])/s4(1) 0 0];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 if -det([s4(1) s4(2);s3(1) s3(2)])/s3(1) == 0
       s2=[e ...
        -det([s4(1) s4(3);s3(1) s3(3)])/s3(1) 0 0];
    else
         s2=[-det([s4(1) s4(2);s3(1) s3(2)])/s3(1)   -det([s4(1) s4(3);s3(1) s3(3)])/s3(1) 0 0];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if -det([s3(1) s3(2);s2(1) s2(2)])/s2(1) == 0
       s1=[e ...
        -det([s3(1) s3(3);s2(1) s2(3)])/s2(1) 0 0];
    else
         s1=[-det([s3(1) s3(2);s2(1) s2(2)])/s2(1) -det([s3(1) s2(3);s2(1) s2(3)])/s2(1) 0 0];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

s0=[-det([s2(1) s2(2);s1(1) s1(2)])/s1(1)   -det([s2(1) s2(3);s1(1) s2(3)])/s1(1) 0 0];

's5'
s5=sym(s5);
s5=simplify(s5)
s4=sym(s4);
s4=simplify(s4)
s3=sym(s3);
s3=simplify(s3)
s2=sym(s2);
s2=simplify(s2)
s1=sym(s1);
s1=simplify(s1)
s0=sym(s0);
s0=simplify(s0)