Please tell me how to use ode45 code

1 次查看(过去 30 天)
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 个评论
Ameer Hamza
Ameer Hamza 2020-6-4
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?

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采纳的回答

Ameer Hamza
Ameer Hamza 2020-6-4
编辑:Ameer Hamza 2020-6-4
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 个评论
Ameer Hamza
Ameer Hamza 2020-6-4
编辑:Ameer Hamza 2020-6-4
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

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更多回答(1 个)

Stephan
Stephan 2020-6-4
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 个评论
Ameer Hamza
Ameer Hamza 2020-6-4
编辑:Ameer Hamza 2020-6-4
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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