1 Structure of the process control system Benefits from MPC (Model Predictive Control) and RTO (Real Time Optimization) Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Gassco Summit, 10 June 2004

2 Outline About Trondheim and myself 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-optimzing 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

3 Trondheim Oslo UK NORWAY DENMARK GERMANY

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” (Tapir) Group of about 10 Ph.D. students in the process control area

5 Outline About Trondheim and myself 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-optimzing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control ? Step 6: Supervisory control (MPC) Step 7: Real-time optimization (RTO) Case studies

6 Plantwide control Need to define objectives and identify main issues for each layer PID RTO MPC

7 Outline About Trondheim and myself 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

8 Outline About Trondheim and myself 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-optimzing 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

9 Dynamic DOFs = valves = 5, Steady-state (economic) DOFs = = 3 (incl. pressure) Example: Distillation column with given feed

10 Outline About Trondheim and myself 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-optimzing 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

11 Optimal operation (economics) What are we going to use our degrees of freedom for? Define scalar cost function J(u 0,x,d) –u 0 : degrees of freedom –d: disturbances –x: states (internal variables) Typical cost function: Optimal operation for given d: min u0 J(u 0,x,d) subject to: Model equations: f(u 0,x,d) = 0 Operational constraints: g(u 0,x,d) < 0 Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u 0,x,d) = 0 J = cost feed + cost energy – value products

12 Outline About Trondheim and myself 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

13 Implementation of optimal operation: Self-optimizing Control Self-optimizing control is when acceptable operation can be achieved using constant set points (c s ) for the controlled variables c (without re-optimizing when disturbances occur). c=c s Acceptable loss ) self-optimizing control

14 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 0,d) = 0 CONTROL ACTIVE CONSTRAINTS! –c s = value of active constraint –Usually large economic benefit –Requires good control system (PID/MPC) WHAT MORE SHOULD WE CONTROL? –Look for “self-optimizing” variables c for remaining unconstrained degrees of freedom u.

15 Example Active constraints control Optimal operation of 100m- runner, J=T –Active constraint: Maximum speed (energy)

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

17 Example 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

18 Further examples self-optimizing control Central bank. J = welfare. u = interest rate. c=inflation rate (2.5%) Cake baking. J = nice taste, u = heat input. c = Temperature (200C) Business, J = profit. c = ”Key performance indicator (KPI), e.g. –Response time to order –Energy consumption pr. kg or unit –Number of employees –Research spending Optimal values obtained by ”benchmarking” 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

19 EXAMPLE: Recycle plant (Luyben, Yu, etc.) Given feedrate F 0 and column pressure: Dynamic DOFs: N m = 5 Column levels: N 0y = 2 Steady-state DOFs:N 0 = = 3

20 Recycle plant: Optimal operation mTmT 1 remaining unconstrained degree of freedom

21 Singular value rule: Steady-state gain Luyben rule: Not promising economically Conventional: Looks good

22 Control of recycle plant 1: Given feedrate LC XC LC XC LC xBxB xDxD Control active constraints (M r =max and x B =0.015) + x D Self-optimizing variable Active constraint

23 Control of recycle plant 2: Max. feedrate LC XC LC XC LC xBxB xDxD Rearrange loops (or use MPC) Self-optimizing variable Active constraint New active constraint: Max. vapor flow

24 Outline About Trondheim and myself 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-optimzing 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

25 Outline About Trondheim and myself 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

26 Step 5. Regulatory control layer Purpose: “Stabilize” the plant by controlling selected ‘’secondary’’ variables (y 2 ) such that the plant does not drift too far away from its desired operation Use simple single-loop PI(D) controllers Exists many tuning rules, including Skogestad (SIMC) rules: –K c = 0.5/k (  1 /  )  I = min (  1, 8  ) Structural issue: What loops to close. That is, which variables (y 2 ) to control, and how to pair with “inputs” (u 2 ) ? u2u2 process y2y2 y 2s

27 Objectives regulatory control layer Take care of “fast” control Simple decentralized (local) PID controllers that can be tuned on-line Allow for “slow” control in layer above (supervisory MPC control) Make control problem easy as seen from layer above Stabilization (mathematical sense, e.g. liquid level or reactor) Local disturbance rejection Local linearization (avoid “drift” due to disturbances) “stabilization” (practical sense) Implications for selection of y 2 : 1.Control of y 2 “stabilizes the plant” 2.y 2 is easy to control (favorable dynamics)

28 Outline About Trondheim and myself 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

29 Step 6. Supervisory control layer (MPC) Purpose: Keep primary controlled variables (c=y 1 ) at desired values, using as degrees of freedom the setpoints y 2s for the regulatory layer. Status: Many different “advanced” controllers, including feedforward, decouplers, overrides, cascades, selectors, Smith Predictors, etc. Trend: Model predictive control (MPC) used as unifying tool. Structural issues: 1.What primary variables c=y 1 to control? 2.When use MPC and when use simpler single-loop decentralized controllers ? process y2y2 y 2s c=y 1 cscs

30 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 steady-state active constraints move -Logic needed to handle dynamic constraints

31 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 (both dynamic and steady-state) no need for logic smooth transition -Requires multivariable dynamic model -Tuning may be difficult -Less transparent -“Everything goes down at the same time”

32 Outline About Trondheim and myself 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-optimzing 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

33 Step 7. Optimization layer (RTO) Purpose: Minimize cost function J and: –Identify active constraints –Recompute optimal setpoints c s for the 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. –Need nonlinear steady-state model –Modelling is time-consuming and expensive –Do we need RTO? (or is optimal policy “obvious” – e.g. max. load – or min. energy) process y2y2 y 2s c=y 1 cscs

34 Summary: Objectives of layers c s = y 1s MPC PID y 2s RTO u (valves) “Maintain setpoints” CV=y 1 ; MV=y 2s “Stabilize” CV=y 2 ; MV=u “Optimize setpoints” Min J; MV=y 1s

35 Benefits of MPC and RTO “10% more capacity and 20% less energy” EVEN MORE IMPORTANT: ORGANIZATIONAL CHANGES More focus on operation and control More professional operation Better control: Less variation

36 Gassco 3PM project (Plant Production Performance model) Benefits: RTO: Optimized setpoints (including identification of optimal active constraints) that will improve plant performance and increase plant utilization. Optimized production planning, including the optimization of unscheduled maintenance sequences of equipment related to production forecasts Reliable and business oriented capacity figures for the booking Identification of de-bottlenecking measures Reliable capacity figures for alternative feed gas compositions More accurate basis for tariffing More efficient use of resources, including energy savings Improved basis for future expansion projects ACHIEVING BENEFITS: REQUIRES FUTURE COMMITMENT

37 References 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), 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:

38 Looking for “magic” self-optimizing variables to keep at constant setpoints. What properties do they have? Skogestad and Postlethwaite (1996): The optimal value of c should be insensitive to disturbances c should be easy to measure and control accurately 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. Summarized by minimum singular value rule

39 Optimizer Controller that adjusts u to keep c m = c s Plant cscs c m =c+n u c n d u c J c s =c opt u opt n Minimum singular value rule  (G) Want the slope (= gain G from u to c) as large as possible

40 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

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

42 Production rate set at outlet: Inventory control opposite flow

43 Production rate set inside process