|Oct22-12, 10:27 AM||#1|
Higher order DE to State space
I've been trying to run a few simulations in Matlab using ODE45. This algorithm requires a function which gives the first order differential as an output i.e a state space format (Correct me if I'm wrong here).
If its a normal N order differential such as d2x/dt2 + dx/dt -1 =0 . dx/dt can be substituted as y and hence the differential equation becomes:
y(dot) = 1-y i.e. the required state space format.
Now comes the question , what do I do if the DE is something like
d2z/dt2 + d2x/dt2 +dx/dt -1=0 ? How Do I convert this to state space format ?
And more specifically , how do I code this as a function to use in ODE45 in Matlab ?
Thanks in advance!
|Nov1-12, 05:57 PM||#2|
There are second order derivatives so you you will have two state variables. You then use one of following methods:
- Phase Canonical Forms of State Space Equation
- State Space Equation Generation via 'Nested Integrals'
There are other methods as well.
|differential eqn, matlab, state space|
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