Feedback control with integral

% Feedback control with integral
% Input from example 2-4
sympref('FloatingPointOutput',true)
clear
clc
%% Input:

A = [0 1; -7 -9]                % A matrix
B = [0; 1]                      % B matrix
C = [4 1]                       % C matrix
Ts = 0;                         % Time settling
Tp = 2;                         % Time peak
Os = 0.1;                       % Overshoot (100%=1.0)
zero = -4;                      % Open loop zero

%% Process:

syms s k1 k2 k3 ke;
zeta = -(log(Os)/log(exp(1)))/sqrt(pi^2+(log(Os)/log(exp(1)))^2);
if(Tp==0) Wn = 4/(zeta*Ts);
else Wn =  pi/(Tp*sqrt(1-zeta^2));
end

a11 = A-(B*[k1 k2]);
a12 = B*ke;
a21 = -C;
Anew = [a11 a12; a21 0]

Ds = expand((s^2 + 2*zeta*Wn*s + Wn^2)*(s-zero))
Ts = det(s*eye(3)-Anew)

% Solve
Dsm = coeffs(Ds,s);
Tsm = coeffs(Ts,s);
k = vpa(struct2cell((solve(Dsm==Tsm))))