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?

[Ameer Hamza]

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?

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Ameer Hamza]

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

[Ameer Hamza]

Sang, what is ea(t)? What does this equation

ea(t) = 9/4dx^2/dt^2+16dx/dt

represent?

[Ameer Hamza]

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

[sang un jung]

thanks!!

Answer 2

[Stephan]

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')

[Stephan]

see my comment to your answer - the laplace transformation is one way to solve ode's - if we transform the transfer function back to time domain, we get an ode again - this is why ode45 is needed.

[Ameer Hamza]

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')

[sang un jung]

thank you