Some important comments:
1. Each plant generally has one TPM and its location is very imortant from a dynamic point of view
(from a steady-state point of view its location does not matter).
Usually the TPM-varable is NOT included as a degree of freedom when we choose CVs
(because we want to be able to adjust the throughput, so it is in essence already a CV).
2. In this paper, we talk about moving the TPM away from the feed, partly for
economic reasons (bottleneck control) and partly for dynami reasons (avoid
snowballing). However, there may be good reasons to keep the TPM at the feed
(not really discussed in this paper).
3. In terms of selecting CVs, this paper requires one to define a cost function (J), which should be minimized
with respect to the degrees of freedom, subject to satisfying the constraints.
Next, we need to find a CV for each degree of freedom (MV).
These will be the active constraints + "self-optimizing" unconstrained variables for the remaining.
4. The "bottle neck" for the process is reached when we reach a constraint where no further increase in the throughput is feasible (feasible means that we satisfy the all constraints).
The TPM is then used to control this bottleneck constraint (in order to have optimal operation, which at this
point is at maximize throyghput).
Note: If this bottleneck constraint is the cost function (which is quite common), then we still need to keep controlling an
unconstrained variable (to keep the bottleneck variable minimized), so it is NOT necessarily true that all MVs are
are to control active constraints at the bottleneck.
Some less important comments
1. If we fix the compressor speed, then the compressor work is no longer a degree of freedom
(instead it becomes something we want to minimize).