# Plant-Wide Control Approach

## Herding Cats: Successfully Manage All Those Process Variables With a Systematic Approach to Plant-Wide Control

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Decision 4—Select pairings for the stabilizing layer, that is, pair inputs (valves) and controlled variables (CV2). By "valves," I mean original dynamic manipulated variables.

The key idea is to start top-down with the economics and identify the various operating regions (Figure 1). In each of these regions, we need to identify the controlled variables that link optimization and control. After an intermediate step where we consider the location of the throughput manipulator, we proceed with the bottom-updesign of the stabilizing layer. The goal is to find a simple control structure that combines all the possibly conflicting objectives with minimal need for switching and other kinds of supervisory control.

#### Overview of Plant-Wide Control Procedure—Top Down

Top-down analysis (focus on steady-state economics) begins with Step 1—Define operational objectives (economic cost J to be minimized) and constraints. A systematic approach to plant-wide control requires that we first quantify the operational objectives with a scalar cost function J (or equivalently, a scalar profit function, P = -J). This is usually not very difficult, and typically we have J = cost feed + cost utilities (energy) – value products.

The goal of operation (and of control) is to minimize the cost J (or equivalently, to maximize the profit P = - J). The cost J should be minimized subject to satisfying the operational constraints, including safety and environmental constraints.
Typical operational constraints are minimum and maximum values on flows, pressures, temperatures and compositions. For example, we always have that all flows, pressures and compositions must be non-negative.

Step 2—Identify degrees of  freedom (MVs) and optimize the operation for important disturbances (offline analysis) to identify regions of active constraints. Identifying the economic (usually steady-state) degrees of freedom is not usually as simple as one would expect. One approach is to first identify all the (dynamic and steady-state) control degrees of freedom (inputs, "valves"), and then subtract the ones with no steady-state effect. The optimization of the plant for expected operation is usually the most time- consuming step. Note that there are two main modes of operation Mode I. Given throughput. Maximize efficiency.

Mode II. Throughput is a degree of freedom. Find optimal throughput (often this equals maximum throughput). Maximize throughput (with production rate as a degree of freedom).

Although the plant and its control system are most often designed for Mode 1, usually the most profit is made when product processes are high and optimal operation is the same as maximum throughput (Mode II). Plant-wide control should generally be focused much more on Mode II.

Step 3—Selection of primary controlled variables (CV1) (Decision 1). "What should we control?" This question has been the main topic for my research in the plant-wide control area over the last 25 years, and I think I finally have found the solution:

• Control active constraints
• Control "self-optimizing" CV1s for the remaining unconstrained degrees of freedom.

In particular, the research has been focused towards the latter unconstrained CV1s. "Self-optimizing" means that when the selected variables are kept constant at their setpoints, then the operation remains close to its economic optimal in spite of the presence of disturbances.

In general, the controlled variables (CV1) will be individual measurements or combinations of measurements. Thus we can write, CV1 = H y. Here, y contains all the available measurements (including MVs) and H is the selection or combination matrix to be found. [See V. Alstad, S. Skogestad and E.S. Hori, "Optimal Measurement Combinations as Controlled Variables," J. Proc. Control, 19, 138-148, 2009.]

Step 4—Select location of throughput manipulator (TPM) (Decision 3).

The main purpose of a process plant is to transform feedstocks into more valuable products, and this involves moving mass through the plant. The amount of mass moved through the plant, as expressed by the feed rate or product rate, is determined by specifying one degree of freedom, which we call the TPM.

In addition, most plants have one TPM, but complex plants with six parallel units and multiple or alternative products may have more. From a steady-state point of view, the location of the TPM does not matter, but it is important dynamically.
There are two main concerns when placing the TPM:

1. Economics—This is relevant when the plant is operated at maximum capacity. The TPM should then be located close to the bottleneck to reduce the back-off from the active constraint that has the largest effect on the production rate.
2. Structure of the regulatory control system—Because of the radiation rule, the location of the throughput manipulator has a profound influence on the regulatory control structure of the entire plant (Figure 2).

An underlying assumption for the radiation rule is that we want "local consistency" of the inventory control system. [See E.M.B. Aske and S. Skogestad, "Consistent Inventory

Control," Ind. Eng. Chem. Res, 48 (44), 10892-10902, 2009.] This means that the inventory in each unit is controlled

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