เลือกผลตอบสนองของ DC Motor ตามใจต้องการ ด้วยวิธี Pole Placement

%% State feedback control design 
clear 
close all
clc

%% Problem: Design state feedback control for DC Motor 
% Motor parameters
R=0.5;                  % Armature Resistance (ohm)
L=0.2;                  % Armature inductance (H)
Kt=0.929;               % Torque Constant (Nm/Amp)
Kb=0.929;               % Back emf Constant (V.s/rad)
J=3;                    % Moment of inertia (kg.m^2)
b=0.0408;               % Friction Constant (Nm.s/rad)
V=200;                  % Armature voltage (V)
 
%% State-model of DC motor (Physical variable form)
A=[-R/L -Kb/L;Kt/J -b/J]   % System matrix
B=[1/L;0]                  % Input matrix
C=[0 1]                    % Output matrix
D=0;                        % Direct transmission matrix
 
%% Initial conditions 
x0=[0; -1];                 % Arbitrary initial conditions
 
%% Checking eigenvalues
E=eig(A);                   % Just to check stability and pole locations
 
%% Checking controllability
Qc=ctrb(A,B);               % Needed for feedback control design
R=rank(Qc);
 
%% Desired locations of the poles


M=33;                            % Desired Maximum Overshoot
Ts=17;                           % Desired Settling time

d=Ts;
h=(-log(M/100))^2;
zeta=sqrt(h/(pi^2+h));          % Damping ratio 

wn=4/(Ts*zeta);                 % Natural frequency
 
P=roots([1 2*zeta*wn wn^2])    % Desired Poles result 
 
%% Checking the system response
num=wn^2;
den=[1 2*zeta*wn wn^2];
G=tf(num,den);
 
figure(1)
step(G)
grid on
xlabel('Time')
ylabel('Amplitude')
title('Response of Desire Poles Location')
S=stepinfo(G);                  % Check this is matching with M and Ts or not
 
%% State feedback by pole placement
K=place(A,B,P)                 % Pole placement
 
sys=ss(A-B*K, eye(2), eye(2), eye(2));
                                % Closed-loop system
t=0:0.01:d*2;                  % Time for plotting response
x= initial(sys,x0,t);
x1=[1 0]*x';                    % Current
x2=[0 1]*x';                    % Speed
 
figure(2)
subplot(2,1,1); 
plot(t,x1), grid
xlabel('Time (s)')
ylabel('Current')
title('State Pole Placement Response of current to Initial Condition')
 
subplot(2,1,2); 
plot(t,x2),grid
xlabel('Time (s)')
ylabel('Speed')
title('State Pole Placement Response of speed to Initial Condition')
 
%% Simulink model simulation (It will give same results) 
sim('DC_Model')            % Check simulation results
 
% Results can be plotted here also by writing some more commands
% Check overshoot and settling time of response of speed. It must be same
% as designed.