1 Feedback Applications to self-optimizing control and stabilization of new operating regimes Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Technlogy (NTNU) Trondheim South China University of Technology, Guangzhou, 05 January 2004

2 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables A procedure for control structure design (plantwide control) Example stabilizing control: Anti-slug control Conclusion

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4 Sigurd Skogestad Born in : 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” (Norwegian) Group of about 10 Ph.D. students in the process control area

5 Trondheim!! Oslo UK NORWAY DENMARK GERMANY North Sea SWEDEN Arctic circle

6 NTNU, Trondheim - view from south-west

7 NTNU, Trondheim - view from south-east

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9 Research: Develop simple yet rigorous methods to solve problems of engineering significance. Use of feedback as a tool to 1. reduce uncertainty (including robust control), 2.change the system dynamics (including stabilization; anti-slug control), 3.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

10 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables A procedure for control structure design (plantwide control) Example stabilizing control: Anti-slug control Conclusion

11 Example 1 G GdGd u d y Plant (uncontrolled system) 1 k=10 time 25

12 G GdGd u d y

13 Model-based control = Feedforward (FF) control G GdGd u d y ”Perfect” feedforward control: u = - G -1 G d d Our case: G=G d → Use u = -d

14 G GdGd u d y FF control: Nominal case (perfect model)

15 G GdGd u d y FF control: change in gain in G

16 G GdGd u d y FF control: change in time constant

17 G GdGd u d y FF control: change in delay (in G or G d )

18 Measurement-based correction = Feedback (FB) control d G GdGd u y C ysys e

19 Feedback PI-control: Nominal case d G GdGd u y C ysys e Input u Output y Feedback generates inverse! Resulting output

20 G GdGd u d y C ysys e Feedback PI control: change in gain in G

21 FB control: change in time constant in G G GdGd u d y C ysys e

22 FB control: change in time delay in G G GdGd u d y C ysys e

23 FB control: all cases G GdGd u d y C ysys e

24 G GdGd u d y FF control: all cases

25 Comment Time delay error in disturbance model (G d ): No effect (!) with feedback (except time shift) Feedforward: Similar effect as time delay error in G

26 Why feedback? (and not feedforward control) Counteract unmeasured disturbances Reduce effect of changes / uncertainty (robustness) Change system dynamics (including stabilization) No explicit model required MAIN PROBLEM Potential instability (may occur suddenly)

27 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables A procedure for control structure design (plantwide control) Example stabilizing control: Anti-slug control Conclusion

28 Example 2: Plant with delay G1G1 u d y C ysys e G2G2 PI-control y s =1 d=6

29 Fundamental limitation feedback: Delay θ Effective delay PI-control = ”original delay” + ”inverse response” + ”half of second time constant” + ”all smaller time constants”

30 Improve control? Feedback: Some improvement possible with more complex controller –For example, add derivative action (PID-controller) –May reduce θ eff from 5 s to 2 s –Problem: Sensitive to measurement noise –Does not remove the fundamental limitation Feedforward: Good for time delay systems, but need model + measurement of disturbance. Sensitive to uncertainty. Feedback cascade: Add extra measurement and introduce local control –May remove the fundamental limitation from high-order dynamics

31 Cascade control w/ extra secondary measurement (2 PI’s) d Without cascade With cascade G1G1 u y C1C1 ysys G2G2 C2C2 y2y2 y 2s

32 Cascade control Inner fast (secondary) loop that control secondary variable: –P or PI-control –Local disturbance rejection –Much smaller effective delay (0.2 s) Outer slower primary loop: –Reduced effective delay (2 s) No loss in degrees of freedom –Setpoint in inner loop new degree of freedom Time scale separation –Inner loop can be modelled as gain=1 + effective delay Very effective for control of large-scale systems

33 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables A procedure for control structure design (plantwide control) Example stabilizing control: Anti-slug control Conclusion

34 Process operation: Hierarchical structure PID RTO MPC Includes stabilizing control. As just shown: Can itself be hiearchical (cascaded)

35 Engineering systems Most (all?) large-scale engineering systems are controlled using hierarchies of quite simple single-loop controllers –Commercial aircraft –Large-scale chemical plant (refinery) 1000’s of loops Simple components: on-off + P-control + PI-control + nonlinear fixes + some feedforward Same in biological systems

36 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?

37 What should we control? y 1 = c ? (economics) y 2 = ? (cascade control)

38 Optimal operation (economics) Define scalar cost function J(u 0,d) –u 0 : degrees of freedom –d: disturbances Optimal operation for given d: min u0 J(u 0,d) subject to: f(u 0,d) = 0 g(u 0,d) < 0

39 Active constraints Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u 0,d) = 0 CONTROL ACTIVE CONSTRAINTS! –Implementation of active constraints is usually simple. WHAT MORE SHOULD WE CONTROL? –We here concentrate on the remaining unconstrained degrees of freedom u.

40 Optimal operation Cost J Independent variable u (remaining unconstrained) u opt J opt

41 Implementation: How do we deal with uncertainty? 1. Disturbances d 2. Implementation error n u s = u opt (d 0 ) – nominal optimization n u = u s + n d Cost J  J opt (d)

42 Problem no. 1: Disturbance d Cost J Independent variable u u opt (d 0 ) J opt d0d0d0d0 d ≠ d 0 Loss with constant value for u

43 Problem no. 2: Implementation error n Cost J Independent variable u u s =u opt (d 0 ) J opt d0d0d0d0 Loss due to implementation error for u u = u s + n

44 Probem: Too complicated ”Obvious” solution: Optimizing control

45 Alternative: Feedback implementation Issue: What should we control?

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

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

48 Effect of implementation error (“problem 2”) BADGood

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

50 Self-optimizing Control – Marathon Optimal operation of Marathon runner, J=T –Any self-optimizing variable c (to control at constant setpoint)? c 1 = distance to leader of race c 2 = speed c 3 = heart rate c 4 = level of lactate in muscles

51 Self-optimizing control: Recycle process J = V (minimize energy) N m = 5 3 economic (steady- state) DOFs Given feedrate F 0 and column pressure: Constraints: Mr < Mrmax, xB > xBmin = 0.98 DOF = degree of freedom

52 Recycle process: Control active constraints Active constraint M r = M rmax Active constraint x B = x Bmin One unconstrained DOF left for optimization: What more should we control? Remaining DOF:L

53 Recycle process: Loss with constant setpoint, c s Large loss with c = F (Luyben rule) Negligible loss with c =L/F or c = temperature

54 Recycle process: Proposed control structure for case with J = V (minimize energy) Active constraint M r = M rmax Active constraint x B = x Bmin Self-optimizing loop: Adjust L such that L/F is constant

55 Further examples Central bank. J = welfare. c=inflation rate (3%) Cake baking. J = nice taste, c = Temperature (200C) Business, J = profit. c = ”Key performance indicator (KPI) (e.g. response time to order) Investment (portofolio management). J = profit. c = Fraction of investment in shares (50%) Biological systems: –”Self-optimizing” controlled variables c have been found by natural selection –Need to do ”reverse engineering” : Find the controlled variables used in nature From this identify what overall objective J the biological system has been attempting to optimize

56 Looking for “magic” variables to keep at constant setpoints. How can we find them? Consider available measurements y, and evaluate loss when they are kept constant (“brute force”): More general: Find optimal linear combination (matrix H):

57 Good candidate controlled variables c (for self-optimizing control) Requirements: The optimal value of c should be insensitive to disturbances (avoid problem 1) c should be easy to measure and control (rest: avoid problem 2) The value of c should be sensitive to changes in the 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

58 Optimal measurement combination Recall first requirement: Its optimal value c opt (d) is insensitive to disturbances (to avoid problem 1) Can we always find a variable combination c = H y which satisfies YES!! Provided

59 Derivation of optimal combination (Alstad) Starting point: Find optimal operation as a function of d: –u opt (d), y opt (d) Linearize this relationship:  y opt = F  d F – sensitivity matrix Look for a linear combination c = Hy which satisfies:  c opt = 0 To achieve Always possible if Application: See Adchem-paper by Alstad and Skogestad (Hong Kong, Jan. 2004)

60 Conclusion so far Negative Feedback is an extremely powerful tool Complex systems can be controlled by hierarchies (cascades) of single- input-single-output (SISO) control loops Control extra local variables (secondary outputs) to avoid fundamental feedback control limitations Control the right variables (primary outputs) to achieve ”self- optimizing control” Optimal linear combination

61 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables Example stabilizing control: Anti-slug control A procedure for control structure design (plantwide control) Conclusion

62 Hierarchical structure PID RTO MPC Includes stabilizing control.

63 Application stabilizing feedback control: Anti-slug control Slug (liquid) buildup Two-phase pipe flow (liquid and vapor)

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

65 Experimental mini-loop

66 p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 100%

67 p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 25%

68 p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 15%

69 p1p1 p2p2 z Experimental mini-loop: Bifurcation diagram Valve opening z % No slug Slugging

70 p1p1 p2p2 z Avoid slugging: 1. Close valve (but increases pressure) Valve opening z % No slugging when valve is closed

71 Avoid slugging: 2. Build large slug-catcher Most common strategy in practice p1p1 p2p2 z

72 Avoid slugging: 3. Other design changes to avoid slugging p1p1 p2p2 z

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

74 Avoid slugging: 4. ”Active” feedback control PT PC ref Simple PI-controller p1p1 z

75 Anti slug control: Mini-loop experiments Controller ONController OFF p 1 [bar] z [%]

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

77 Analysis: Poles and zeros y z P 1 [Bar]DP[Bar]ρ T [kg/m 3 ]F Q [m 3 /s]F W [kg/s] Operation points: Zeros: z P1P1 DPPoles ±0.0067i ±0.0092i P1P1 ρTρT DP FT Topside Topside measurements: Ooops.... RHP-zeros or zeros close to origin

78 Stabilization with topside measurements: Avoid “RHP-zeros by using 2 measurements Model based control (LQG) with 2 top measurements: DP and density ρ T

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

80 Outline About myself Example 1: Why feedback (and not feedforward) ? What should we control? Secondary variables (Example 2) What should we control? Primary controlled variables Example stabilizing control: Anti-slug control A procedure for control structure design (plantwide control) Conclusion

81 Stepwise procedure for design of control system in chemical plant I. TOP-DOWN Step 1. DEFINE OVERALL CONTROL OBJECTIVE Step 2. DEGREE OF FREEDOM ANALYSIS Step 3. WHAT TO CONTROL? (primary outputs) control active constraints unconstrained: “self-optimizing variables” Mainly economic considerations: Little control knowledge required! Stepwise procedure chemical plant

82 II. BOTTOM-UP (structure control system): Step 4. REGULATORY CONTROL LAYER 5.1Stabilization 5.2Local disturbance rejection (inner cascades) ISSUE: What more to control? (secondary variables) Step 5. SUPERVISORY CONTROL LAYER Decentralized or multivariable control (MPC)? Pairing? Step 6. OPTIMIZATION LAYER (RTO) Stepwise procedure chemical plant

83 Summary 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). Stepwise procedure chemical plant Skogestad, S. (2000), “Plantwide control -towards a systematic procedure”, Proc. ESCAPE’12 Symposium, Haag, Netherlands, May S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), (2004). Larsson, T. and S. Skogestad, 2000, “Plantwide control: A review and a new design procedure”, Modeling, Identification and Control, 21, Skogestad, S. (2000). “Plantwide control: The search for the self-optimizing control structure”. J. Proc. Control 10, See also the home page of Sigurd Skogestad:

84 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 intelligense - people are better at this Set high standards for acceptable control Do not forget the simple and effective idea of feedback More information: Home page of Sigurd Skogestad - Or even simpler: Search for Skogestad on google

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