State Space modelling from an ODE
51 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
Teanna Mills
el 15 de Mzo. de 2019
Comentada: Star Strider
el 12 de Dic. de 2019
How would I find the state variable description and transfer function of the 3rd order system of the following on MATLAB?
0 comentarios
Respuesta aceptada
Star Strider
el 15 de Mzo. de 2019
The easiest way is to let the Symbolic Math Toolbox do the heavy lifting:
syms y(t) u(t) t
Dy = diff(y);
D2y = diff(y,2);
D3y = diff(y,3);
DEq = D3y + 6*D2y + 11*Dy + 6*y == 6*u;
[SS,Sbs] = odeToVectorField(DEq)
producing:
SS =
Y[2]
Y[3]
6*u(t) - 6*Y[1] - 11*Y[2] - 6*Y[3]
Sbs =
y
Dy
D2y
The ‘Sbs’ output simply tells you the substitutions the solver made, so for example ‘Y[1]=y’.
I’m sure you can take it from there.
2 comentarios
jokn buntue
el 12 de Dic. de 2019
Can you please explain how to convert the results of odeToVectorField to the A,B,C,D matrices?
Thanks.
Star Strider
el 12 de Dic. de 2019
@jokn buntue — The ‘SS’ matrix is essentially a companion-form matrix, so eliminating the ‘6*u(t)’ term, it is the ‘A’ matrix. The ‘6*u(t)’ term becomes part of the ‘B’ matrix (vector here, since this is a SISO system).
That should get you started.
Más respuestas (1)
djedoui Nassim
el 15 de Mzo. de 2019
Hey
You can follow this mathematical changement using your example,
0 comentarios
Ver también
Categorías
Más información sobre Equation Solving en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!