Chapter 4

% Chapter 4 example 3
clear
clc
sympref('FloatingPointOutput',true)
syms s k1 k2 k3 k4 ke;

%% Input:

numg = [20 100];
deng = poly([0 1 4]);
Ts = 0.74;
Os = 9.5;
zeros = s+5;

%% Process

G = tf(numg,deng)   % Generate transfer function G(s)
[Ac Bc Cc Dc] = tf2ss(numg,deng);
P = flip(eye(order(G)));
A = inv(P)*Ac*P
B = inv(P)*Bc
C = Cc*P
D = Dc

zeta = (-log(Os/100))/(sqrt(pi^2+log(Os/100)^2));
Wn = 4/(zeta*Ts);

%% state-feedback control

pole1 = s^2 + 2*zeta*Wn*s + Wn^2;
pole2 = zeros

Anew = A-(B*[k1 k2 k3])

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

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