Acker_controller

clc
clear

numg = 0.072*conv([1 23],[1 0.05 0.04]); % Define numerator of G(s)
deng = conv([1 0.08 0.04],poly([0.7 -1.7])); % Define denominator of G(s)
G = tf(numg,deng) % Generate transfer function G(s)

%% STEP 1:

pos = 10;
Ts = 0.5;
z = (-log(pos/100))/(sqrt(pi^2+log(pos/100)^2));
wn = 4/(z*Ts);

% Produce a second-order system that meets transient response requirements
[num,den] = ord2(wn,z);
r = roots(den);
zeros = roots(numg);
poles = [r(1) r(2) zeros(2) zeros(3)];
Ds = poly(poles)

%% STEP 2:

% Find controller canonical form of state-space representation
[Ac Bc Cc Dc] = tf2ss(numg,deng);

% Find controller canonical form of state-space representation
P = flip(eye(order(G)));

% Transform Ac, Bc, Cc and Dc to phase-variable form
Ap = inv(P)*Ac*P
Bp = inv(P)*Bc
Cp = Cc*P
Dp = Dc

% Calculate controller gains in phase-variable form.
Kp = acker(Ap,Bp,poles)

% Form compensated state-space model
Apnew = Ap-Bp*Kp;
Bpnew = Bp;
Cpnew = Cp;
Dpnew = Dp;

% Form transfer function of state-feedback controller
[numt,dent] = ss2tf(Apnew,Bpnew,Cpnew,Dpnew);
Tsc = tf(numt,dent)

% Plot
step(Tsc);
title('State Feedback Controller');
xlim([0 0.6]);