s=%s;
syms K a
p=s^4+10*s^3+32*s^2+(K+32)*s+(K*a)
cof_a_0=coeffs(p,'s',0);
cof_a_1=coeffs(p,'s',1);
cof_a_2=coeffs(p,'s',2);
cof_a_3=coeffs(p,'s',3);
cof_a_4=coeffs(p,'s',4);
r=[cof_a_0 cof_a_1 cof_a_3 cof_a_4]
n=length(r);
routh=[r([5,3,1]);r([4,2]),0]
routh=[routh;-det(routh(1:2,1:2))/routh(2,1),-det(routh(1:2,2:3))/routh(2,2),0];
routh=[routh;-det(routh(2:3,1:2))/routh(3,1),-det(routh(2:3,2:3))/routh(3,2),0];
routh=[routh;-det(routh(3:4,1:2))/routh(4,1),0,0];
disp(routh,"routh=")
// for the given system to be stable
routh(3,1)>0
K<288;
routh(4,1)>0
(288-K)*(K+32)-100(K*a)>0
// let K=200
K=200;
a=((288-K)*(K+32))/(100*K)
// velocity error 
Kv=(K*a)/(4*2*4);
// % velocity error
Kvs=100/Kv
disp(a,"control parameter=")
disp(K,"Gain=")