% Define the transfer function model

tau = 0.5; % time delay parameter
s = tf('s');
Gp = exp(-tau*s)/s^2; % transfer function G

% Calculate the crucial gain Kc
%phi_des = 63.4; % desired phase margin in degrees
%wgc = 1/tau; % gain crossover frequency
%alpha = (1+sin(deg2rad(phi_des)))/(1-sin(deg2rad(phi_des)));
% Kc = alpha*wgc^2;
Kc = 0.707;

% Design the controller using the DDCD method

Kp = 0.6*Kc; % proportional gain
Td = 0.5*(tau+0.1*tau); % derivative time constant
Kd = (Td*Kp)/0.1; % derivative gain
C = pid(Kp,0,Kd); % PD controller
setpoint = 2; % define a setpoint for the controller.

% Compute the closed-loop transfer function

Gcl = feedback(C*Gp,1);
Gcl_sp = setpoint*Gcl;

% Plot the step response of the closed-loop system with setpoint
step(Gcl_sp);