Belajar Dasar Convolution Dengan Matlab

Berikut ini yaitu script MATLAB untuk convolution tanpa memakai function conv().

x = input('First signal ');
h = input('Second signal ');
a = length(x);
b = length(h);
n = a + b - 1;
y = zeros(1,n);
l = 1:n;
c = 0:a - 1;
d = 0:b - 1;
for i = 0:n
    for j = 0:n
        if((i - j + 1)>0 && (i - j + 1)<=b && (j + 1)<=a)
            y(i+1) = y(i+1) + x(j+1).*h(i - j +1);
        end
    end
end
disp(y);
subplot(3,1,1)
stem(c,x)
grid on
ylabel('magnitude')
title('\bf First Input')
subplot(3,1,2)
stem(d,h)
grid on
ylabel('magnitude')
title('\bf Second Input')
subplot(3,1,3)
stem(l,y)
grid on
ylabel('magnitude')
xlabel('t')
title('\bf Output')

Sumber http://lang8088.blogspot.com

Matlab Script Fft Sederhana

Berikut ini yakni script MATLAB untuk melaksanakan transformasi Fourier signal discrete tanpa memakai function fft().

x=input('Input signal: ');
len=length(x);

y=zeros(1,len);%create an array
yabs=zeros(1,len);%this line is optional, for determining its absolute value
for k=1:len
    for n=1:len
        w=exp(-1i*2*pi*(k-1)*(n-1)/len);
        a=x(n)*w;
        y(k)=y(k)+a;
    end
    yabs(k)=abs(y(k));%this line is optional
end

yt=fft(x);%this one just for comparation

disp(y)
disp(yabs)%output's absolute value
disp(yt)%fft's output
figure(1)
subplot(3,1,1);
stem(y);
subplot(3,1,2);
stem(yabs);
subplot(3,1,3);
stem(yt);

Berikut ini yakni hasil plot signal.

Sumber http://lang8088.blogspot.com

Matlab: Basic To Control

Berikut ini yakni script MATLAB untuk dasar kendali dengan PID.

clear all, close all, clc;

%% Define the plant

P = tf([1],[1 0 -9]);
% transfer function of the plant
% P =
%      1
%   -------
%   s^2 - 9
pole(P)
% yields s = 3 and s = -3
% thus the plant is not stable

%% The PID controller

Kp = 90;
Ki = 60;
Kd = 30;
% taking into Laplace form
% K = Kd*s + Kp + Ki/s


K = tf([Kd Kp Ki],[1 0]);
% PID controller
% K =
%
%   30 s^2 + 90 s + 60
%   ------------------
%           s
CP = series(K,P);
% the open-loop equals to:
% CP = K*P

CL = feedback(CP,1);
% closed-loop (CL) feedback of the system
pole(CL);
% yields
% s = -27.0919 + 0.0000i
% s =  -1.4540 + 0.3170i
% s =  -1.4540 - 0.3170i

%% Verify the stablility of CL

if isstable(CL,1)
    'Closed-loop is stable'
else
    'Closed-loop is not stable'
end

%% Step response of the system

t = 0:0.1:5;

step(CL,t)

Closed-loop system tersebut stabil. Berikut ini yakni step-response.

Lihat juga tentang.

• Bode plot diagram.
• Transfer function loop shaping.

Kendali state space MATLAB.

• State space controlability and observability.
• State space to transfer function.
• Pole-placement.
• Linear-Quadratic Regulator.
• Bode plot diagram state space.

Sumber http://lang8088.blogspot.com

Matlab: State Space Observability And Controllability

Berikut ini ialah script MATLAB untuk menguji apakah sistem observable juga controllable.

clear all, close all, clc;

%% Define the matrices

A = [1 2;
    7 2]
% A the state matrix

B = [1; 1]
% B the input vector

C = [1 0]
% C the output vector

D = zeros(size(C,1), size(B,2))
% D the feedforward

eig(A)
% eigenvalues of A
% -2.2749
% 5.2749
% it is not stable

%% Verify the controllability and observability

Cm = ctrb(A,B)
% Controllability matrix

Om = obsv(A,C)
% Observability matrix

if rank(Cm) == size(A,1)
    'It is controllable'
else
    'It is not controllable'
end

if rank(Om) == size(A,1)
    'It is observable'
else
    'It is not observable'
end

Lihat juga tentang.

• Basic PID control.
• Bode plot diagram.
• Transfer function loop shaping.

Kendali state space MATLAB.

• State space to transfer function.
• Pole-placement.
• Linear-Quadratic Regulator.
• Bode plot diagram state space.

Sumber http://lang8088.blogspot.com

Matlab: Transform State Space Transfer Function

Berikut ini ialah script MATLAB untuk mengubah dari state space menjadi transfer function.

clear all, close all, clc;

%% State space representation
A = [-11 -18;
    1 0]
% the state matrix

B = [1; 0]
% the input vector

C = [0 1]
% the output vector

D = zeros(size(C,1),size(B,2))
% the feedforward

%% Verify the controllability and observability

Cm = ctrb(A,B)
% Controllability matrix

Om = obsv(A,C)
% Observability matrix

if rank(Cm) == size(A,1)
    'It is controllable'
else
    'It is not controllable'
end

if rank(Om) == size(A,1)
    'It is observable'
else
    'It is not observable'
end

%% Transform into transfer function

[num,den] = ss2tf(A,B,C,D)
sys = tf(num,den)
pole(sys)
% yields
% s = -9
% s = -2

step(sys)
% plot the step response

Berikut ini ialah step response dari sistem tersebut.

Lihat juga tentang.

• Basic PID control.
• Bode plot diagram.
• Transfer function loop shaping.

Kendali state space MATLAB.

• State space controlability and observability.
• Pole-placement.
• Linear-Quadratic Regulator.
• Bode plot diagram state space.

Sumber http://lang8088.blogspot.com

Matlab: Pole-Placement State Space

Berikut ini yakni script MATLAB untuk state feedback controller.

clear all, close all, clc;

%% Define the system

A = [1 0 2;
    2 3 0;
    1 2 3]
% the state matrix

B = [1; 0; 0]
% the input vector

eig(A)
% the eigenvalues are
% 4.7511 + 0.0000i
% 1.1244 + 1.0251i
% 1.1244 - 1.0251i
% it is not stable

%% The pole-placement

desiredPoles = -0.5*ones(3,1)
% desired poles = [-0.5; -0.5; -0.5]

K = acker(A,B,desiredPoles)
% determine the gain K
% based on the Ackermann's formula
% yields
% K = [8.5000 13.0156 12.7188]

%% State feedback controller

sys = ss(A-B*K, eye(size(A)), eye(size(A)), eye(size(A)))

eig(sys.a)
% the eigenvalues are
% -0.5000 + 0.0000i
% -0.5000 + 0.0000i
% -0.5000 - 0.0000i

x0 = [0.1; 0.1; 0.1]
% initial state

t = 0:0.01:25;
% the time duration

x = initial(sys,x0,t);
% response of the state-space
% with initial condition x0
% and time duration t

x1 = [1 0 0]*x';
x2 = [0 1 0]*x';
x3 = [0 0 1]*x';
% the state variables


%% Plot the state variables

subplot(3,1,1); plot(t,x1), grid
title('Response to initial condition')
ylabel('x1')

subplot(3,1,2); plot(t,x2), grid
ylabel('x2')

subplot(3,1,3); plot(t,x3), grid
ylabel('x3')
xlabel('t (seconds)')

Berikut ini ialah plot response dari state variable.

Lihat juga tentang.

• Basic PID control.
• Bode plot diagram.
• Transfer function loop shaping.

Kendali state space MATLAB.

• State space controlability and observability.
• State space to transfer function.
• Linear-Quadratic Regulator.
• Bode plot diagram state space.

Sumber http://lang8088.blogspot.com

Matlab: Linear-Quadratic Regulator Design For State Space Systems

Berikut ini yaitu script MATLAB untuk LQR (Linear-Quadratic Regulator) controller.

clear all, close all, clc;

%% Define the system

A = [1 0 2;
    2 3 0;
    1 2 3]
% the state matrix

B = [1; 0; 0]
% the input vector

eig(A)
% the eigenvalues are
% 4.7511 + 0.0000i
% 1.1244 + 1.0251i
% 1.1244 - 1.0251i
% it is not stable

%% LQR design

Q = eye(size(A))

R = 1

K = lqr(A,B,Q,R)
% K =
%    14.5461   24.4004   41.9475

%% State feedback controller

sys = ss(A-B*K, eye(size(A)), eye(size(A)), eye(size(A)))

eig(sys.a)
% the eigenvalues are
% -4.7742 + 0.0000i
% -1.3860 + 1.1477i
% -1.3860 - 1.1477i
% it is stable

x0 = [5; 5; 5]
% initial state

t = 0:0.01:5;
% the time duration

x = initial(sys,x0,t);
% response of the state-space
% with initial condition x0
% and time duration t

x1 = [1 0 0]*x';
x2 = [0 1 0]*x';
x3 = [0 0 1]*x';
% the state variables

%% Plot the state variables

subplot(3,1,1); plot(t,x1), grid
title('Response to initial condition')
ylabel('x1')

subplot(3,1,2); plot(t,x2), grid
ylabel('x2')

subplot(3,1,3); plot(t,x3), grid
ylabel('x3')
xlabel('t (seconds)')

Berikut ini ialah plot response dari state variable.

Lihat juga tentang.

• Basic PID control.
• Bode plot diagram.
• Transfer function loop shaping.

Kendali state space MATLAB.

• State space controlability and observability.
• State space to transfer function.
• Pole-placement.
• Bode plot diagram state space.

Sumber http://lang8088.blogspot.com