Control system observer

% Control observer
% Input from example 2-5
sympref('FloatingPointOutput',true)
clear
clc
%% Input:

A = [-24 1 0; -191 0 1; -504 0 0]           % A matrix
B = [0; 1; 6]                               % B matrix
C = [1 0 0]                                 % C matrix
Ts = 2;                                     % Time settling
Tp = 0;                                     % Time peak
Os = 0.2;                                   % Overshoot (100%=1.0)
zeta = 0;                                   % Zeta
Wn = 0;                                     % Natural frequency
speed = 10;                                 % speed to be faster

%% Process:

syms s L1 L2 L3 ke;
if(zeta==0)
    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
end

pole1 = s+zeta*Wn*speed + (Wn*sqrt(1-zeta^2)*1i)*speed;
pole2 = s+zeta*Wn*speed - (Wn*sqrt(1-zeta^2)*1i)*speed;
pole3 = s+zeta*Wn*speed*10;
Anew = A-[L1; L2; L3]*C

Ds = expand(pole1*pole2*pole3)
Ts = det(s*eye(3)-Anew)

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