How to Derive a Transfer Function for a Fuel Cell Air Flow System?

[ookt2c]

Homework Statement

Derive a transfer function relating the input(volts) to the out put (pressure) of a fuel celll air fllow system.

Homework Equations

P(gage)=P(abs)-P(atm)

Ideal gas law(PV=mRT)

$dm/dt=mdot(in)-mdot(out)$

q=k(P(in)-P(out)) mass flowrate for a linear restriiction

The Attempt at a Solution

$dm/dt=mdot(in)-mdot(out)$

m=(RT)/(PV)

$(dRT/PV)/dt=mdot (in)-K(p(in)-P(out))$
take out constants
$RT/V*(d*1/p)/dt=Mdont(in)-K(p(in)-P(out))$ units for pressure is in seconds ( Pascal = 1 kg/(m*s^2))

 

[djeitnstine]

Here is a nice guide for creating a state space model of your system, which can be easily converted into a transfer function:

http://www.me.cmu.edu/ctms/modeling/tutorial/statespace/mainframes.htm

Dont hesitate to ask if you need further assistance.