Why do I get different value for pole placement function?

Folks,

I need to design a state variable feedback regulator for following discrete time closed-loop system with a pair of complex poles at 0.3+i0.4 and 0.3-j0.4 .

For which I am using Ackermann’s formula as below:

Since we know about the location of desired poles, hence:

And to implement above equation in Matlab, I use following:

p1=0.3 + 0.4*1i;
p2=0.3 - 0.4*1i;
P_z=(z-p1)*(z-p2);
P_phi=eval(subs(P_z,z,phi)); 
K1=[0 1]*([gamma,phi*gamma]\P_phi);

Result:

K1 =

           -1463.39992735389          274.509346733496

But, if I use Matlab's place command instead, I get different result:

K2=place(phi,gamma,[p1 p2]);

Result:

K2 =

            321.895478432477          -36.132432596429

Can someone please tell me why I get distinct values for K1 and K2 whereas I am expecting to get the same result for both

Answer 1

[Azzi Abdelmalek]

Your code is not correct

gamma=[0;0.9948*10^(-4)]
phi=[1 0.0001;-0.0503 0.9896]
e=[0 1]*inv([gamma fi*gamma])
p1=0.3 + 0.4*1i;
p2=0.3 - 0.4*1i;
alpha=fliplr(poly([p1,p2]))
k1=alpha(1)*e+alpha(2)*e*phi+e*phi^2
k2=place(phi,gamma,[p1 p2])

[Hasan Ghorbani]

Thank you so much for your answer. fliplr was redundant though. Following code worked beautifully:

P_z = poly([p1,p2]);
P_phi = P_z(1)*(phi^2) + P_z(2)*(phi^1) +  P_z(3)*(phi^0);
K =  [0 1] * inv([gamma,phi*gamma]) * P_phi;

[Walter Roberson]

[0 1] / [gamma,phi*gamma] * P_phi would be more numerically stable