1. Plantwide control: Towards a systematic procedure
Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
March 2002
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2. Outline Introduction Plantwide control procedure
Top-down
Bottom-up
What to control I: Primary controlled variables
Inventory control - where set production rate
What to control II: Secondary controlled variables
Decentralized versus multivariable control
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3. Related work
Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice)
Alan Foss (1973) - control system structure
George Stephanopoulos and Manfred Morari (1980)
Bill Luyben ( ) - “snowball effect”
Ruel Shinnar ( ) - “dominant variables”
Jim Douglas and Alex Zheng (Umass) ( )
Jim Downs (1991) - Tennessee Eastman process
Larsson and Skogestad (2000): Review of plantwide control
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4. Alan Foss (``Critique of chemical process control theory'', AIChE Journal,1973):
The central issue to be resolved ... is the determination of control system structure. Which variables should be measured, which inputs should be manipulated and which links should be made between the two sets? There is more than a suspicion that the work of a genius is needed here, for without it the control configuration problem will likely remain in a primitive, hazily stated and wholly unmanageable form. The gap is present indeed, but contrary to the views of many, it is the theoretician who must close it.
Carl Nett (1989):
Minimize control system complexity subject to the achievement of accuracy specifications in the face of uncertainty.
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5. Idealized view of control (“Ph.D. control”)
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6. Practice I: Tennessee Eastman challenge problem (Downs, 1991)
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7. Practice II: Typical P&ID diagram (PID control)
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8. Practice III: Hierarchical structure
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9. Plantwide control Not the tuning and behavior of each control loop,
But rather the control philosophy of the overall plant with emphasis on the structural decisions:
Selection of controlled variables (“outputs”)
Selection of manipulated variables (“inputs”)
Selection of (extra) measurements
Selection of control configuration (structure of overall controller that interconnects the controlled, manipulated and measured variables)
Selection of controller type (PID, decoupler, MPC etc.).
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10. Stepwise procedure plantwide control
I. TOP-DOWN
Step 1. DEGREE OF FREEDOM ANALYSIS
Step 2. WHAT TO CONTROL? (primary variables)
Step 3. MANIPULATED VARIABLES
Step 4. PRODUCTION RATE
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11. II. BOTTOM-UP (structure control system):
Step 5. REGULATORY CONTROL LAYER
5.1 Stabilization (including level control)
5.2 Local disturbance rejection (inner cascades)
What more to control? (secondary variables)
Step 6. SUPERVISORY CONTROL LAYER Decentralized or multivariable control (MPC)?
Pairing?
Step 7. OPTIMIZATION LAYER (RTO)
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12. I. Top-down Define operational objectives Identify degrees of freedom
Identify primary controlled variables (look for self-optimizing variables)
Determine where to set the production rate
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13. Step 1. Degree of freedom (DOF) analysis
Nm : no. of dynamic (control) DOFs (valves)
Nss = Nm- N0 : steady-state DOFs
N0 : liquid levels with no steady-state effect (N0y)+ purely dynamic control DOFs (N0m)
Cost J depends normally only on steady-state DOFs
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14. Distillation column with given feed
Nm = 5, N0y = 2, Nss = = 3 (2 with given pressure)
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15. Heat-integrated distillation process
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16. Heat exchanger with bypasses
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17. Alternatives structures for optimizing control
What should we control?
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18. Step 2. What should we control? (primary controlled variables)
Intuition: “Dominant variables” (Shinnar)
Systematic: Define cost J and minimize w.r.t. DOFs
Control active constraints (constant setpoint is optimal)
Remaining DOFs: Control variables c for which constant setpoints give small (economic) loss
Loss = J - Jopt(d)
when disturbances d occurs
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19. Self-optimizing control (Skogestad, 2000)
Loss L = J - Jopt (d)
Self-optimizing control is achieved when a
constant setpoint policy results in an acceptable
loss L (without the need to reoptimize when
disturbances occur)
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20. Loss with constant setpoints
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21. Effect of implementation error on cost
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22. Tennessee Eastman plantJ
c = Purge rate
Nominal optimum setpoint is infeasible with disturbance 2
Oopss..
bends backwards
Conclusion: Do not use purge rate as controlled variable
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23. c = Temperature top of column
Example sharp optimum. High-purity distillation :
c = Temperature top of column
Temperature
Ttop
Water (L) - acetic acid (H)
Max 100 ppm acetic acid
100% water: C
99.99 % water: C
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24. Procedure for selecting (primary) controlled variables (Skogestad, 2000)
Step 2.1 Determine DOFs for optimization
Step 2.2 Definition of optimal operation J (cost and constraints)
Step 2.3 Identification of important disturbances
Step 2.4 Optimization (nominally and with disturbances)
Step 2.5 Identification of candidate controlled variables
Step 2.6 Evaluation of loss with constant setpoints for alternative controlled variables
Step 2.7 Final evaluation and selection (including controllability analysis)
Case studies: Tenneessee-Eastman, Propane-propylene splitter, recycle process, heat-integrated distillation
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25. Application: Recycle process J = V (minimize energy)5 4 1
Given feedrate F0 and
column pressure: 2
Nm = 5
N0y = 2
Nss = = 3 3
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26. Recycle process: Selection of controlled variables
Step 2.1 DOFs for optimization: Nss = 3
Step 2.2 J=V (minimize energy with given feed)
Step 2.3 Most important disturbance: Feedrate F0
Step 2.4 Optimization: Constraints on Mr and xB always active
(so Luybens structure is not optimal)
Step DOF left, candidate controlled variables: F, D, L, xD, ...
Step 2.6 Loss with constant setpoints. Good: xD, L/F. Poor: F, D, L
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27. Recycle process: Loss with constant setpoint, cs
Large loss with c = F (Luyben rule)
Negligible loss with c = L/F
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28. “Snowball effect” Forget Luyben’s rule about fixing a flow in each recycle loop
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29. Recycle process: Proposed control structure J = V (minimize energy)
Active constraint
Mr = Mrmax
Active constraint
xB = xBmin
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30. Good candidate controlled variables c (for self-optimizing control)
Requirements:
The optimal value of c should be insensitive to disturbances
c should be easy to measure and control
The value of c should be sensitive to changes in the steady-state degrees of freedom
(Equivalently, J as a function of c should be flat)
For cases with more than one unconstrained degrees of freedom, the selected controlled variables should be independent.
Singular value rule (Skogestad and Postlethwaite, 1996):
Look for variables that maximize the minimum singular value of the
appropriately scaled steady-state gain matrix G from u to c
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31. Step 3. Manipulated variables
Check that there are enough manipulated variables (DOFs) - both dynamically and at steady-state
Otherwise: Need to add equipment
extra heat exchanger
bypass
surge tank
…….
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32. 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
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33. Production rate set at inlet : Inventory control in direction of flow
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34. Production rate set at outlet: Inventory control opposite flow
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35. Production rate set inside process
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36. Definition of bottleneck
A unit (or more precisely, an extensive variable E within this unit)
is a bottleneck (with respect to the flow F) if
- With the flow F as a degree of freedom, the variable E is optimally
at its maximum constraint (i.e., E= Emax at the optimum)
- The flow F is increased by increasing this constraint
(i.e., dF/dEmax > 0 at the optimum).
A variable E is a dynamic( control) bottleneck if in addition
- The optimal value of E is unconstrained when F is fixed at a
sufficiently low value
Otherwise E is a steady-state (design) bottleneck.
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37. Heat integrated distillation process: Given feedrate with production rate set at inlet
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38. Heat integrated distillation process: Reconfiguration required when reach bottleneck (max. cooling in column 2)
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39. Heat integrated distillation process: Given feedrate with production rate adjusted at bottleneck (column 2)
SET
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40. Recycle process: Given feedrate
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41. Bottleneck in column
MAX
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42. II. Bottom-up
Determine secondary controlled variables and structure (configuration) of control system (pairing)
A good control configuration is insensitive to parameter changes
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43. Step 5. Regulatory control layer
Purpose: “Stabilize” the plant using local SISO PID controllers to enable manual operation (by operators)
Main structural issues:
What more should we control? (secondary cv’s, y2)
Pairing with manipulated variables (mv’s)
y1 = c
y2 = ?
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44. Selection of secondary controlled variables (y2)
The variable is easy to measure and control
For stabilization: Unstable mode is “quickly” detected in the measurement (Tool: pole vector analysis)
For local disturbance rejection: The variable is located “close” to an important disturbance (Tool: partial control analysis).
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45. Partial control Primary controlled variable y1 = c Local control of y2
(supervisory control layer)
Local control of y2
using u2
(regulatory control layer)
Setpoint y2s : new DOF
for supervisory control
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46. 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?
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47. Decentralized control (single-loop controllers)
Use for: Noninteracting process and no change in active constraints
+ Tuning may be done on-line
+ No or minimal model requirements
+ Easy to fix and change
- Need to determine pairing
- Performance loss compared to multivariable control
- Complicated logic required for reconfiguration when active constraints move
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48. Multivariable control (with explicit constraint handling - MPC)
Use for: Interacting process and changes in active constraints
+ Easy handling of feedforward control
+ Easy handling of changing constraints
no need for logic
smooth transition
- Requires multivariable dynamic model
- Tuning may be difficult
- Less transparent
- “Everything goes down at the same time”
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49. 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)
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50. Conclusion Procedure plantwide control:
I. Top-down analysis to identify degrees of freedom and primary controlled variables (look for self-optimizing variables)
II. Bottom-up analysis to determine secondary controlled variables and structure of control system (pairing).
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51. References http://www.chembio.ntnu.no/users/skoge/
Larsson, T., Studies on plantwide control, Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim.
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, 2002, “Control of reactor, separator and recycle process’’, Submitted to Ind.Eng.Chem.Res.
Skogestad, S. (2000). “Plantwide control: The search for the self- optimizing control structure”. J. Proc. Control 10,
See also the home page of S. Skogestad:
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