derivatives of state variables

Dear,

I want to find the derivative of this

α*x_1+b*x_2+q*abs(x_2)*x_2+r*x_3. Where x_1,x_2,x_3 are state variables from aircraft

How can I do in Matlab?

Answer 1

[Ameer Hamza]

Use symbolic toolbox. First define the equation

syms alpha b q r x_1 x_2 x_3
eq = alpha*x_1 + b*x_2 + q*abs(x_2)*x_2 + r*x_3;

and take derivative w.r.t to different variables

>> diff(eq, x_1) % derivative w.r.t x_1
ans =
alpha

>> diff(eq, x_2) % derivative w.r.t x_2
ans =
b + q*abs(x_2) + q*x_2*sign(x_2)

>> diff(eq, x_3) % derivative w.r.t x_3
ans =
r

[RoBoTBoY]

Thanks! But I don't want something like that.

Μy result I want to be something like that in order to confirm it with matlab.

[Ameer Hamza]

You can also do this

syms alpha b q r x_1(t) x_2(t) x_3(t)
eq = alpha*x_1 + b*x_2 + q*abs(x_2)*x_2 + r*x_3;
deq = diff(eq)

If you run it in live script, it will show you output rendered in mathematical form.

[RoBoTBoY]

I think that's what I wanted. thank you very much

[Ameer Hamza]

I am glad to be of help.