Linear / NonLinear Dynamic Modelling

[uetian98]

Hi All,

I am given a task to generate a linear as well as a nonlinear dynamic model of a process.

All that I am given is a differential equation.

Now Situation is that, I dont know the procedure and/or steps to generate thus models.

Can anyone help me please ?

Thanks

[Klaynos]

Hi, if it was me, I'd find some programming language that can solve differntial equations... I think Maple can...

 

I'd also write down exactly what I want to find out and what values I input and what I want to get out.

[uetian98]

Klaynos,

thanks for you much considerate reply. Let me state my problem once again.

I will generate linear / nonlinear dynamic model of that system them will simulate them into MATLAB.

I dont need a readymade solution.

thanks. ANY one who can guide:-( ?

[Klaynos]

Well I think from what I remember you can solve differential equations using a matrix method? Or does matlab have a solve method that I don't know about?

[uetian98]

What I require here is a set of procedure / steps to have it solve

[timo]

There is a large number of methods for solving differential equations. Usually, the best choice is the easiest solution that already gives acceptable results in an acceptable time. Also, the method employed might depend on the type of additional conditions you are given (boundary conditions or initial conditions). An example for a very simple integration of a diff. eq. (an equation of motion) is http://www.wisci.org/wiki/Geodesic_equation . It is not a guide for numerical integration but it is a complete example of starting from a diff. eq. and obtaining a numeric solution. Not sure if that helps you, but perhaps you can extract some information from it.

It would probably help if you´d post what kind of process we are talking about and what the diff. eqs. are.

[uetian98]

Thanks Atheist / Klynos...

Let me paste the equations here. V(dC0/dt) = FW (C1-C0) – NAV

Here only V & C0 are the only constant -

 

V.....................Volume of tank

C0.....................Outlet conc. of Oxygen in Water

C1.....................Inlet conc. of Oxygen in Water

FW.....................Volumetric Flow rate of Water

NA.....................Mass Transfer rate (NA = KLA(C0-C*)

KL.....................Liquid Film Mass Transfer Coefficient

A.....................Surface Area of Bubbles / Unit Volume

C*.....................Equilibrium Conc. of Oxygen in Water

Actually I am working on a pilot scale rig. This pilot rig consists of a water filled glass walled Jar with an impeller (vertically mounted) in there. Water enters the Jar near the bottom and leaves (overflows) from a point near the top.

 

Nitrogen is bubbled via a sparger sitting on the botom of the jar to disturbed the already dissolved oxygen (resulting in desorbing the Oxygen out of water body). We have analysers installed that measure the oxygen contents in the water body

I have the equation as above. now considering all the parameters like Water flowrate, extra extra.... I need a dynamic model taking care of all the changes and disturbances.

Where to start form

 

 

[Klaynos]

Quick question, if C0 is a constant then surely dC0/dt = 0 as that is the rate of change of dC0?

[uetian98]

lol ... C1 is constant ... Inlet concentration of Oxygen is constant where as outlet concentration of Oxygen varies with Nitrogen bubling rate, water flowrate, agitation speed etc.

sorry