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

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SUMMARY

The discussion focuses on deriving a transfer function for a fuel cell air flow system, specifically relating input voltage to output pressure. Key equations include the ideal gas law and mass flow rate equations, such as dm/dt = mdot(in) - mdot(out) and q = k(P(in) - P(out)). The solution involves manipulating these equations to express the relationship between pressure and flow rates, ultimately leading to a state space model that can be converted into a transfer function. A resource for creating a state space model is provided, enhancing understanding of the conversion process.

PREREQUISITES
  • Understanding of transfer functions in control systems
  • Familiarity with the ideal gas law (PV = mRT)
  • Knowledge of mass flow rate equations
  • Basic concepts of state space modeling
NEXT STEPS
  • Study the derivation of transfer functions in control systems
  • Learn about state space modeling techniques
  • Explore the application of the ideal gas law in dynamic systems
  • Investigate the impact of linear restrictions on mass flow rates
USEFUL FOR

Engineers and students in control systems, particularly those focused on fuel cell technology and fluid dynamics, will benefit from this discussion.

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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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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.
 
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