In the following transfer function models, ???????? is the methane gas feed rate to a gas furnace, measured in cubic feet per minute, and ???????? the percent carbon dioxide in the outlet gas:

(1) ???????? = 10 + 25 1−0.7????

????????−1

(2) ???????? = 10 + 22 − 12.5????
1−0.85????
????????−2 (3) ???????? = 10 + 20 − 8.5????
1−1.2???? + 0.4????2 ????????−3

(a) Verify that the models are stable.

(b) Calculate the steady-state gain ????, expressing it in the appropriate units.