1. First African Control Conference, Cape Town, 04 December 2003
Control structure design: What should we measure, control and manipulate?
Sigurd Skogestad
Department of Chemical Engineering
NTNU, Trondheim
First African Control Conference, Cape Town, 04 December 2003

2. Outline About myself Control structure design
A procedure for control structure design
Selection of primary controlled variables
Example stabilizing control: Anti slug control
Conclusion

3. Sigurd Skogestad Born in 1955
: Lived in South Africa (Durban & Johannesburg)
1978: Siv.ing. Degree (MS) in Chemical Engineering from NTNU (NTH)
: Process modeling group at the Norsk Hydro Research Center in Porsgrunn
: Ph.D. student in Chemical Engineering at Caltech, Pasadena, USA. Thesis on “Robust distillation control”. Supervisor: Manfred Morari
: Professor in Chemical Engineering at NTNU
Since 1994: Head of process systems engineering center in Trondheim (PROST)
Since 1999: Head of Department of Chemical Engineering
1996: Book “Multivariable feedback control” (Wiley)
2000,2003: Book “Prosessteknikk” (Tapir)
Group of about 10 Ph.D. students in the process control area

4. Research: Develop simple yet rigorous methods to solve problems of engineering significance.
Use of feedback as a tool to
reduce uncertainty (including robust control),
change the system dynamics (including stabilization; anti-slug control),
generally make the system more well-behaved (including self-optimizing control).
limitations on performance in linear systems (“controllability”),
control structure design and plantwide control,
interactions between process design and control,
distillation column design, control and dynamics.
Natural gas processes

5. Outline About myself Control structure design
A procedure for control structure design
Selection of primary controlled variables
Example stabilizing control: Anti slug control
Conclusion

6. Idealized view of control (“Ph.D. control”)

7. Practice: Tennessee Eastman challenge problem (Downs, 1991) (“PID control”)

8. Control structure design
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 (LQG, H-infinity, PID, decoupler, MPC etc.).
That is: Control structure design includes all the decisions we need make to get from ``PID control’’ to “Ph.D” control

9. Process control: Control structure design = plantwide control
Large systems
Each plant usually different – modeling expensive
Slow processes – no problem with computation time
Structural issues important
What to control?
Extra measurements
Pairing of loops

10. Control structure selection issues are identified as important also in other industries.
Professor Gary Balas at ECC’03 about flight control at Boeing:
The most important control issue has always been to select the right controlled variables --- no systematic tools used!

11. Process operation: Hierarchical structure
RTO
Need to define objectives and identify main issues for each layer
MPC
PID

12. Regulatory control (seconds)
Purpose: “Stabilize” the plant by controlling selected ‘’secondary’’ variables (y2) such that the plant does not drift too far away from its desired operation
Use simple single-loop PI(D) controllers
Status: Many loops poorly tuned
Most common setting: Kc=1, I=1 min (default)
Even wrong sign of gain Kc ….

13. Regulatory control……...
Trend: Can do better! Carefully go through plant and retune important loops using standardized tuning procedure
Exists many tuning rules, including Skogestad (SIMC) rules:
Kc = 0.5/k (1/) I = min (1, 8)
“Probably the best simple PID tuning rules in the world”
Outstanding structural issue: What loops to close, that is, which variables (y2) to control?

14. Supervisory control (minutes)
Purpose: Keep primary controlled variables (y1) at desired values, using as degrees of freedom the setpoints y2s for the regulatory layer.
Status: Many different “advanced” controllers, including feedforward, decouplers, overrides, cascades, selectors, Smith Predictors, etc.
Issues:
Which variables to control may change due to change of “active constraints”
Interactions and “pairing”

15. Supervisory control…...
Trend: Model predictive control (MPC) used as unifying tool.
Linear multivariable models with input constraints
Tuning (modelling) is time-consuming and expensive
Issue: When use MPC and when use simpler single-loop decentralized controllers ?
MPC is preferred if active constraints (“bottleneck”) change.
Avoids logic for reconfiguration of loops
Outstanding structural issue:
What primary variables y1 to control?

16. Local optimization (hour)
Purpose: Identify active constraints and possibly recompute optimal setpoints y1s for controlled variables
Status: Done manually by clever operators and engineers
Trend: Real-time optimization (RTO) based on detailed nonlinear steady-state model
Issues:
Optimization not reliable.
Modelling is time-consuming and expensive

17. Outline About myself Control structure design
A procedure for control structure design
Selection of primary controlled variables
Example stabilizing control: Anti slug control
Conclusion

18. Stepwise procedure plantwide control
I. TOP-DOWN
Step 1. DEFN. OF OPERATIONAL OBJECTIVES
Step 2. MANIPULATED VARIABLES
and DEGREE OF FREEDOM ANALYSIS
Step 3. WHAT TO CONTROL? (primary outputs, c= y1)
Step 4. PRODUCTION RATE

19. II. BOTTOM-UP (structure control system):
Step 5. REGULATORY CONTROL LAYER
Stabilization and Local disturbance rejection
What more to control? (secondary outputs y2)
Step 6. SUPERVISORY CONTROL LAYER Decentralized control or MPC?
Step 7. OPTIMIZATION LAYER (RTO)

20. Outline About myself Control structure design
A procedure for control structure design
Selection of primary controlled variables
Example stabilizing control: Anti slug control
Conclusion

21. What should we control?
y1 = c ? (economics)
y2 = ? (“stabilization”)

22. Optimal operation (economics)
Define scalar cost function J(u0,d)
u0: degrees of freedom
d: disturbances
Optimal operation for given d:
minu0 J(u0,d)
subject to:
f(u0,d) = 0
g(u0,d) < 0

23. Active constraints
Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u0,d) = 0
Implementation of active constraints is usually simple.
We here concentrate on the remaining unconstrained degrees of freedom u.

24. Optimal operation Cost J Jopt uopt Independent variable u
(remaining unconstrained)

25. Implementation: How do we deal with uncertainty?
1. Disturbances d
2. Implementation error n
us = uopt(d*) – nominal optimization n
u = us + n d
Cost J  Jopt(d)

26. Problem no. 1: Disturbance d
Cost J d*
Jopt
Loss with constant value for u
uopt(d0)
Independent variable u

27. Problem no. 2: Implementation error n
Cost J d0
Loss due to implementation error for u
Jopt
us=uopt(d0)
u = us + n
Independent variable u

28. ”Obvious” solution: Optimizing control
Probem: Too complicated

29. Alternative: Look for another variable c to control
Cost J
Jopt
copt
Controlled variable c
and keep at constant setpoint cs = copt(d*)

30. Self-optimizing Control
Define loss:
Self-optimizing Control
Self-optimizing control is when acceptable loss can be achieved using constant set points (cs) for the controlled variables c (without re-optimizing when disturbances occur).

31. Controlled variable: Feedback implementation
Issue:
What should we control?

32. Constant setpoint policy: Effect of disturbances (“problem 1”)

33. Effect of implementation error (“problem 2”)
Good
Good
BAD

34. Self-optimizing Control – Illustrating Example
Optimal operation of Marathon runner, J=T
Any self-optimizing variable c (to control at constant setpoint)?

35. Self-optimizing Control – Illustrating Example
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

36. Further examples Central bank. J = welfare. c=inflation rate
Cake baking. J = nice taste, c = Temperature
Biology. J = ?, c = regulatory mechanism
Business, J = profit. c = KPI = response time to order

37. Good controlled Variables c: Guidelines
Requirements for good candidate controlled variables (Skogestad & Postlethwaite, 1996):
Its optimal value copt(d) is insensitive to disturbances d (to avoid problem 1)
It should be easy to measure and control accurately (n small to avoid problem 1)
The variables c should be sensitive to change in inputs (to avoid problem 2)
The selected variables c should be independent (to avoid problem 2)
Rule: Maximize minimum singular value of scaled G
c = G u

38. Candidate controlled variables
Selected among available measurements y,
More generally: Find the optimal linear combination (matrix H):

39. Candidate Controlled Variables: Guidelines
Recall first requirement:
Its optimal value copt(d) is insensitive to disturbances (to avoid problem 1)
Can we always find a variable combination c = H y
which satisfies
YES!! Provided

40. Derivation of optimal combination (Alstad)
Starting point: Find optimal operation as a function of d:
uopt(d), yopt(d)
Linearize this relationship: yopt = F d
Look for a linear combination c = Hy which satisfies: copt = 0
To achieve
Always possible if

41. Applications of self-optimizing control
Distillation
Tennessee Eastman Challenge problem
Power plant
+++

42. Outline About myself Control structure design
A procedure for control structure design
Selection of primary controlled variables
Example stabilizing control: Anti-slug control
Conclusion

43. Application: Anti-slug control
Two-phase pipe flow
(liquid and vapor)
Slug (liquid) buildup

44. Slug cycle (stable limit cycle)
Experiments performed by the Multiphase Laboratory, NTNU

45. Experimental mini-loop

46. Experimental mini-loop Valve opening (z) = 100%

47. Experimental mini-loop Valve opening (z) = 25%

48. Experimental mini-loop Valve opening (z) = 15%

49. Experimental mini-loop: Bifurcation diagramz
Experimental mini-loop: Bifurcation diagram
No slug
Valve opening z %
Slugging

50. Avoid slugging: 1. Close valve (but increases pressure)z
Avoid slugging: 1. Close valve (but increases pressure)
No slugging when valve is closed
Valve opening z %

51. Avoid slugging: 2. Build large slug-catcher
Most common strategy in practice p1 p2 z

52. Avoid slugging: 3. Other design changes to avoid sluggingp1 p2 z

53. Avoid slugging: 4. Control?
Comparison with simple 3-state model:
Valve opening z %
Predicted smooth flow: Desirable but open-loop unstable

54. Avoid slugging: 4. ”Active” feedback controlPT PC
ref z p1
Simple PI-controller

55. Anti slug control: Mini-loop experiments
p1 [bar] z
[%]
Controller ON
Controller OFF

56. Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

57. Topside measurements: Ooops.... RHP-zeros or zeros close to origin
Poles and zeros
Topside FT
Operation points: ρT DP z P1 DP
Poles
0.175
70.05
1.94
-6.11
0.0008±0.0067i
0.25 69
0.96
-6.21
0.0027±0.0092i P1
Zeros: y z
P1 [Bar]
DP[Bar]
ρT [kg/m3]
FQ [m3/s]
FW [kg/s]
0.175
3.2473
0.0142
0.0048
0.25
3.4828
0.0131
Topside measurements: Ooops.... RHP-zeros or zeros close to origin

58. Stabilization with topside measurements: Avoid “RHP-zeros by using 2 measurements
Model based control (LQG) with 2 top measurements: DP and density ρT

59. Summary anti slug control
Stabilization of smooth flow regime = $$$$! (or Rand!)
Stabilization using downhole pressure simple
Stabilization using topside measurements possible
Control can make a difference!
Thanks to: Espen Storkaas + Heidi Sivertsen and Ingvald Bårdsen

60. Conclusion
What would I do if I was manager in a large chemical company?
Define objective of control: Better operation (objective is not just to collect data)
Define control as a function in my organization
Define operational objectives for each plant ($ + other..)
Unified approach (”company policy”):
Stabilizing control. PID rules
MPC
Avoid rule-based systems / Artificial intelligens /operator support systems - people are better at this
Set high standards for acceptable control
My view
More information: Home page of Sigurd Skogestad -