# Append a free integrator to a Transfer Function

1. Nov 27, 2009

### Alw

1. The problem statement, all variables and given/known data
PI Design

The transfer functions represent the dynamics of a typical commercial turbofan engine between fuel flow rate $$\Delta$$WF in pps and fan speed increment $$\Delta$$N1 in rpm and between fuel flow rate and high-pressure turbine outlet temperature increment $$\Delta$$T in degrees Rankine.

"Since zero steady-state error is desired, an integral control approach will be used. To simplify the process, append a free integrator to Eqs. 1 and 2 and regard the resulting transfer functions as design plants. Keep in mind that the integrator has already been included when designing your controllers."

2. Relevant equations

(1) $$\Delta$$N1(s) / ($$\Delta$$WF(s)) = 247.37(s+8.906) / ((s+2.855)(s+5.421))

(2) $$\Delta$$T(s) / ($$\Delta$$WF(s)) = 167.995(s+4.79)(s+2.075) / ((s+2.855)(s+5.421))

3. The attempt at a solution

At this point i really don't even know what a "free integrator" is, and searching my prof's notes and the internet hasn't really given me anything to work with. I'm hoping this is something of a brain fart, because this is only the first part of a very long assignment. Any help would be appreciated.

Last edited: Nov 28, 2009