Please tell me how to use ode45 code
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sang un jung
am 4 Jun. 2020
Kommentiert: Rena Berman
am 12 Okt. 2020
num=134;
den=[1 16 134];
x=tf(num,den)
subplot(1,2,1)
step(x)
title('(a)')
I want to express this code as ode45, how do I do it?
2 Kommentare
Ameer Hamza
am 4 Jun. 2020
Original Question:
Please tell me how to use ode45 code.
num=134;
den=[1 16 134];
x=tf(num,den)
subplot(1,2,1)
step(x)
title('(a)')
I want to express this code as ode45, how do I do it?
Akzeptierte Antwort
Ameer Hamza
am 4 Jun. 2020
Bearbeitet: Ameer Hamza
am 4 Jun. 2020
Following is one way of using ode45 to solve this
[t, y] = ode45(@odeFun, [0 1], [0; 0]);
plot(t, y(:,1), 'o-')
function dydt = odeFun(t, y)
% transfer function is equivalent to following ODE
% y'' = -16y'-124y+134u
u = 1; % step input
dydt = zeros(2, 1);
dydt(1) = y(2);
dydt(2) = -16*y(2)-124*y(1)+134*u;
end
3 Kommentare
Ameer Hamza
am 4 Jun. 2020
Bearbeitet: Ameer Hamza
am 4 Jun. 2020
Check my answer on your other question. I paste the code here for reference
[t, y] = ode45(@odeFun, [0 1], [0; 0]);
plot(t, y(:,1), 'o-')
function dxdt = odeFun(t, x)
% transfer function is equivalent to following ODE
% x'' = 4/9(-16x'+ea(t))
ea = (1-x(1))*303;
if ea > 100
ea = 100;
elseif ea < -100
ea = -100;
end
dxdt = zeros(2, 1);
dxdt(1) = x(2);
dxdt(2) = 4/9*(-16*x(2)+ea);
end
Weitere Antworten (1)
Stephan
am 4 Jun. 2020
You need to perform a inverse laplace transformation:
num=134;
den=[1 16 134];
x=tf(num,den)
subplot(1,2,1)
step(x)
title('(a)')
syms s
ode = matlabFunction(ilaplace(134/(s^2 + 16*s + 134)),'Vars',{'t','y'})
[t, y] = ode45(ode,[0 1],0);
subplot(1,2,2)
plot(t,y)
title('(b) - with ode45')
xlabel('Time (seconds)')
ylabel('Amplitude')
3 Kommentare
Ameer Hamza
am 4 Jun. 2020
Bearbeitet: Ameer Hamza
am 4 Jun. 2020
ode45 is not needed here. It worked in this specific case because of the step input, but for any other input (impulse, ramp), this method will not work. Following is the general method for inverse Laplace
syms s
u = 1/s; % laplace of step signal
ode = matlabFunction(ilaplace(134/(s^2 + 16*s + 134)*u),'Vars','t');
subplot(1,2,2)
fplot(ode, [0 1])
title('(b) - with ode45')
xlabel('Time (seconds)')
ylabel('Amplitude')
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