I have successful developed a continuous mathematical model for my physical system. The model comprises of sets of 7 nonlinear ODE. My objective is to transform the continuous-time ODE into a set of discrete-time difference equations and implement a digital controller for the system.
I will like to know the method/ technique for converting sets of ODE to discrete-time equations.
Example of the ODE is shown below.
$\frac{dT_1}{dt} = \frac{\frac{A(T_2 - T_1)}{M_1.C_v} + \frac{T_1}{M_1}.\frac{dM_1}{dt} }{1 + \frac{T_1.M_1}{vol.P}}$
$\frac{dT_2}{dt} = A(T_2 - T_1) + T_2^4$
$\frac{dM_1}{dt} = -A_v.\rho_{gas}.u$
$\frac{dV}{dt} = g.\rho_{air}.vol - M_1 - Drag$
$ \frac{dh}{dt} = V$
Thank you for your help.