Tank pressure control with vaccum and N2 : two transfer functions ?

Hello all !
I know how to determine a transfer function. I open the valve completely (heaviside step function) and I can take the 63% of the max for tau, the maximum of the output is K, and for an order 1 I have K/(tau*s+1). This is for order 1. Order 2 and more I learnt at the uni a method called Strejc really similar to the one for order 1. I tried them, they work great. (there are people from all around the world here so maybe you have another method)

but for a tank I want to control the pressure of vacuum and N2. So.... there are two different transfer function. Is there a way to merge the two functions so I can control the whole system ? Should I add them ? multiply them ? Any other way ?

Thanks so much !
If you take a giant step backwards you may find what is sometimes called
not seeing wood for the trees.

Before any mathematical modelling is undertaken you need a conceptual model.
If you can describe in simple terms how you can simultaneously control a
vacuum and nitrogen gas in a tank then you are well on the way.
Are you trying to optimize speed , response time? Control accuracy, or just get it to work.

I do a singlePIC pressure control loop -14.7 to + 14.

Dual range output.

With a few tweaks. If error < abs (x). Then opens that valve 100 pct. then

If error is less, the enable pid loop.

When scaling the valves,
0-52 % out = 100-0% open of vac valve
48-100 out =. 0-100 pct pressure valve.

Add the deadband around the set point.
Once you have that going, The. Worry about loop tuning.