ddt

Calculate time derivative as a function of state and input variables of a (nonlinear) dynamic system
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Actualizado 16 Oct 2008

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function ddt(of, n, state,dstate,f,u)

Given:
of: the symbolic function you want the derivative of (e.g. x2)
n: n'th order derivative
state: a column vector denoting the names of the state, e.g. [x1;x2]
dstate: the names of the states plus a d in front of them, e.g. [dx1; dx2]
f: symbolic expression for the derivative of the state, e.g. [x2, sin(u1) ]
u: a list of inputs, e.g. [u1]

Example:
Suppose we have the following (nonlinear) dynamic system:

d/ / x1 \ / 2 * cos(x2) + u1 \
dt \ x2 / = \ - x1^2 + x1*u2 / , y = x2 + x1 + u2

where x1, x2 are time-dependent states and u1/u2 are time-dependent inputs
and we are interested (for some reason) in the second time derivative of
y, expressed in terms of the state [x1;x2] and the inputs and its
derivatives ([u1;u2], [du1;du2], [d2u1; d2u2]). We calculate this as
follows:

clear
syms x1 x2 dx1 dx2 u1 u2;
eqn = [ 2*cos(x2) + u1; -x1^2 + x1*u2];
y = x2 + x1 + u2;
ddy = ddt ( y, 2, [x1;x2], [dx1;dx2], eqn, [u1;u2])

Output:
ddy =
(-2*x1+u2)*(2*cos(x2)+u1)-2*sin(x2)*(-x1^2+x1*u2)+du1+x1*du2+d2u2

Note: This function needs the function 'fulldiff' by Tim Jorris, which
can be downloaded from Matlab's File Exchange.

Citar como

Gijs van Oort (2024). ddt (https://www.mathworks.com/matlabcentral/fileexchange/21764-ddt), MATLAB Central File Exchange. Recuperado .

Compatibilidad con la versión de MATLAB
Se creó con R14SP2
Compatible con cualquier versión
Compatibilidad con las plataformas
Windows macOS Linux
Categorías
Más información sobre Symbolic Math Toolbox en Help Center y MATLAB Answers.
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Inspirado por: fulldiff.m

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Versión Publicado Notas de la versión
1.0.0.0