I asked a version of this question before and got some unhelpful answers, I think because 1) the minutiae of my question distracted from the core concept, and 2) I didn't adequately describe the operation of my system. Original question can be found here.
In my system, I have a single process variable that I would like to control, concentration (C). The equipment I'm using has two ways to influence C. One way is by changing the amount of stuff (A) or by changing the speed at which stuff is introduced (S). A and S are controlled independently. C is measured by a single sensor. I originally assumed that A was a sort of "coarse" control and S was a "fine" control, but I no longer believe that to be the case.
Currently, I'm choosing A at the start of an experiment and letting a single PI controller change S as needed. This seems like a waste, since the equipment was designed for the tandem use of A and S to control its output. I only have a single sensor to monitor C.
Is there a control scheme that's fitting for this situation? The sole purpose of this system is to control and measure C. I've heard about cascading PI controllers, but I don't have a second sensor or even a second variable to measure, and ultimately I'd like to control both A and S.