# Transfer function derivation

## 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))

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djeitnstine
Gold Member
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 [Broken]

Dont hesitate to ask if you need further assistance.

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