1. PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
August/September/December 2006

2. Summary and references
We have developed a systematic procedure for plantwide control. An important part is the selection of controlled variables based on self-optimizing control. These are the controlled variables for the "supervisory" control layer. In addition, we need a regulatory control system to stabilize the plant and avoid drift.
The following paper summarizes the procedure:
S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), (2004).
There are many approaches to plantwide control as discussed in the following review paper:
T. Larsson and S. Skogestad, ``Plantwide control: A review and a new design procedure'' Modeling, Identification and Control, 21, (2000).

3. Main message
1. Control for economics (Top-down steady-state arguments)
Primary controlled variables c = y1 :
Control active constraints
For remaining unconstrained degrees of freedom: Look for “self-optimizing” variables
2. Control for stabilization (Bottom-up; regulatory PID control)
Secondary controlled variables y2 (“inner cascade loops”)
Control variables which otherwise may “drift”
Both cases: Control variables with a large gain!

4. How we design a control system for a complete chemical plant?
Where do we start?
What should we control? and why?
etc.

5. Main simplification: Hierarchical structure
RTO
Need to define objectives and identify main issues for each layer
MPC
PID

6. Objectives of layers: MV’s and CV’s
RTO
Min J (economics); MV=y1s
cs = y1s
CV=y1; MV=y2s
MPC
y2s
PID
CV=y2; MV=u
u (valves)

7. Summary: The three layers
Optimization layer (RTO; steady-state nonlinear model):
Identifies active constraints and computes optimal setpoints for primary controlled variables (y1).
Supervisory control (MPC; linear model with constraints):
Follow setpoints for y1 (usually constant) by adjusting setpoints for secondary variables (MV=y2s)
Regulatory control (PID):
Stabilizes the plant and avoids drift, in addition to following setpoints for y2. MV=valves (u).
Design starts from the bottom. A good example is bicycle riding:
Regulatory control:
First you need to learn how to stabilize the bicycle
Supervisory control:
Then you need to follow the road. Usually a constant setpoint policy is OK, for example, stay y1s=0.5 m from the right hand side of the road (in this case the "magic" self-optimizing variable self-optimizing variable is y1=distance to right hand side of road)
Optimization:
Which road (route) should you follow?

8. Stepwise procedure plantwide control
I. TOP-DOWN
Step 1. DEGREES OF FREEDOM
Step 2. OPERATIONAL OBJECTIVES
Step 3. WHAT TO CONTROL? (primary CV’s c=y1)
Step 4. PRODUCTION RATE
II. BOTTOM-UP (structure control system):
Step 5. REGULATORY CONTROL LAYER (PID)
“Stabilization”
What more to control? (secondary CV’s y2)
Step 6. SUPERVISORY CONTROL LAYER (MPC) Decentralization
Step 7. OPTIMIZATION LAYER (RTO)
Can we do without it?

9. Optimal operation (economics)
What are we going to use our degrees of freedom for?
Define scalar cost function J(u0,x,d)
u0: degrees of freedom
d: disturbances
x: states (internal variables)
Typical cost function:
Optimal operation for given d:
minuss J(uss,x,d)
subject to:
Model equations: f(uss,x,d) = 0
Operational constraints: g(uss,x,d) < 0
J = cost feed + cost energy – value products

10. Optimal operation distillation column
Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V
Cost to be minimized (economics)
J = - P where P= pD D + pB B – pF F – pV V
Constraints
Purity D: For example xD, impurity · max
Purity B: For example, xB, impurity · max
Flow constraints: min · D, B, L etc. · max
Column capacity (flooding): V · Vmax, etc.
Pressure: 1) p given, 2) p free: pmin · p · pmax
Feed: ) F given 2) F free: F · Fmax
Optimal operation: Minimize J with respect to steady-state DOFs
cost energy (heating+ cooling)
value products
cost feed

11. Optimal operation
minimize J = cost feed + cost energy – value products
Two main cases (modes) depending on marked conditions:
Given feed
Amount of products is then usually indirectly given and J = cost energy. Optimal operation is then usually unconstrained:
Feed free
Products usually much more valuable than feed + energy costs small.
Optimal operation is then usually constrained:
“maximize efficiency (energy)”
Control: Operate at optimal trade-off (not obvious how to do and what to control)
“maximize production”
Control: Operate at bottleneck (“obvious”)

12. Step 3: What c’s should we control?
Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u,d) = 0
CONTROL ACTIVE CONSTRAINTS!
cs = value of active constraint
Implementation of active constraints is usually simple.
WHAT MORE SHOULD WE CONTROL?
Find “self-optimizing” variables c for remaining
unconstrained degrees of freedom u.

13. What should we control? – Sprinter
Optimal operation of Sprinter (100 m), J=T
One input: ”power/speed”
Active constraint control:
Maximum speed (”no thinking required”)

14. What should we control? – Marathon
Optimal operation of Marathon runner, J=T
No active constraints
Any self-optimizing variable c (to control at constant setpoint)?

15. Self-optimizing Control – Marathon
Optimal operation of Marathon runner, J=T
Any self-optimizing variable c (to control at constant setpoint)?
c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles

16. Self-optimizing Control
Self-optimizing control is when acceptable operation can be achieved using constant set points (cs) for the controlled variables c (without the need to re-optimizing when disturbances occur).
c=cs

17. Step 4. Where set production rate?
Very important!
Determines structure of remaining inventory (level) control system
Set production rate at (dynamic) bottleneck
Link between Top-down and Bottom-up parts

18. Production rate set at inlet : Inventory control in direction of flow

19. Production rate set at outlet: Inventory control opposite flow

20. Production rate set inside process

21. Where set the production rate?
Very important decision that determines the structure of the rest of the control system!
May also have important economic implications

22. Often optimal: Set production rate at bottleneck!
“A unit is a bottleneck if maximum throughput is obtained by operating this unit at maximum flow
If feed is cheap and available: Optimal with maximum throughput
If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered.
To reduce “back-off”: Optimal to set throughput (production rate) at bottleneck
Throughput manipulator = Bottleneck flow

23. Outline Control structure design (plantwide control)
A procedure for control structure design
I Top Down
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimizing control)
Step 4: Where set production rate?
II Bottom Up
Step 5: Regulatory control: What more to control ?
Step 6: Supervisory control
Step 7: Real-time optimization
Case studies

24. Step 5. Regulatory control layer
Purpose: “Stabilize” the plant using local SISO PID controllers
Enable manual operation (by operators)
Main structural issues:
What more should we control? (secondary cv’s, y2)
Pairing with manipulated variables (mv’s u2)
y1 = c
y2 = ?

25. Objectives regulatory control layer
Allow for manual operation
Simple decentralized (local) PID controllers that can be tuned on-line
Take care of “fast” control
Track setpoint changes from the layer above
Local disturbance rejection
Stabilization (mathematical sense)
Avoid “drift” (due to disturbances) so system stays in “linear region”
“stabilization” (practical sense)
Allow for “slow” control in layer above (supervisory control)
Make control problem easy as seen from layer above
Implications for selection of y2:
Control of y2 “stabilizes the plant”
y2 is easy to control (favorable dynamics)

26. Cascade control distillation ys y Ts T Ls L z With flow loop +
T-loop in top y XC Ts T TC Ls L FC z XC

27. Step 6. Supervisory control layer
Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs
Degrees of freedom: Setpoints y2s in reg.control layer
Main structural issue: Decentralized or multivariable?

28. Step 7. Optimization layer (RTO)
Purpose: Identify active constraints and compute optimal setpoints (to be implemented by supervisory control layer)
Main structural issue: Do we need RTO? (or is process self-optimizing)
RTO not needed when
Can “easily” identify change in active constraints (operating region)
For each operating region there exists self-optimizing var

29. Summary: Main steps What should we control (y1=c=z)?
Must define optimal operation!
Where should we set the production rate?
At bottleneck
What more should we control (y2)?
Variables that “stabilize” the plant
Control of primary variables
Decentralized?
Multivariable (MPC)?

30. References http://www.nt.ntnu.no/users/skoge/
Halvorsen, I.J, Skogestad, S., Morud, J.C., Alstad, V. (2003), “Optimal selection of controlled variables”, Ind.Eng.Chem.Res., 42,
Larsson, T. and S. Skogestad (2000), “Plantwide control: A review and a new design procedure”, Modeling, Identification and Control, 21,
Larsson, T., K. Hestetun, E. Hovland and S. Skogestad (2001), “Self-optimizing control of a large-scale plant: The Tennessee Eastman process’’, Ind.Eng.Chem.Res., 40,
Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu (2003), “Control of reactor, separator and recycle process’’, Ind.Eng.Chem.Res., 42,
Skogestad, S. and Postlethwaite, I. (1996, 2005), Multivariable feedback control, Wiley
Skogestad, S. (2000). “Plantwide control: The search for the self-optimizing control structure”. J. Proc. Control 10,
Skogestad, S. (2003), ”Simple analytic rules for model reduction and PID controller tuning”, J. Proc. Control, 13,
Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, (Special issue from ESCAPE’12 Symposium, Haag, May 2002).
… + more…..
See home page of S. Skogestad: