Assignment2

clear
clc

%% Input:

numg = 5; % Define numerator of G(s)
deng = poly([0.4 0.8 5]); % Define denominator of G(s)
Ts = 600;   % Time settling
Os = 5;    % Overshoot (%)

%% Process
syms s k1 k2 k3 ke;

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

Cm = det(ctrb(A,B))      % Controlbility

zeta = (-log(Os/100))/(sqrt(pi^2+log(Os/100)^2));
Wn = 4/(zeta*Ts); % pi/(Tp*sqrt(1-zeta^2))

%% state-feedback control

pole1 = s^2 + 2*zeta*Wn*s + Wn^2;
pole2 = s+50

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))))

%% Plot

% Subs k into transfer function
Ts = subs(Ts,k1,k(1));
Ts = subs(Ts,k2,k(2));
Ts = subs(Ts,k3,k(3));

% Form transfer function
dent = double(flip(coeffs(Ts,s)));
Tsc = tf(numg,dent)

% Plot
step(Tsc);
title('State Feedback Controller');