1 ECONOMIC PLANTWIDE CONTROL How to design the control system for a complete plant in a systematic manner Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Brazil, July 2011

2 Outline (6 lectures) Control structure design (plantwide control) A procedure for control structure design I Top Down Step S1: Define operational objective (cost) and constraints Step S2: Identify degrees of freedom and optimize operation for disturbances Step S3: Implementation of optimal operation –What to control ? (primary CV’s) (self-optimizing control) Step S4: Where set the production rate? (Inventory control) II Bottom Up Step S5: Regulatory control: What more to control (secondary CV’s) ? –Distillation column control Step S6: Supervisory control Step S7: Real-time optimization PID tuning (+ decentralized control if time) *Each lecture is 2 hours with a 10 min intermediate break after about 55 min (no. of slides) + means that it most likely will continue into the next lecture Lecture 1* (49) Lecture 4 (62)+ Lecture 2 (71)+ Lecture 3 (36) Lecture 5 (19) Lecture 6 (54) Plantwide control lectures. Sigurd Skogestad

3 Plantwide control intro course: Contents Overview of plantwide control Top-down. Selection of primary controlled variables based on economic : The link between the optimization (RTO) and the control (MPC; PID) layers - Degrees of freedom - Optimization - Self-optimizing control - Applications Where to set the production rate and bottleneck Bottom-up. Design of the regulatory control layer ("what more should we control") - stabilization - secondary controlled variables (measurements) - pairing with inputs Design of supervisory control layer - Decentralized versus centralized (MPC) - Pairing and RGA-analysis Summary and case studies

4 Main references 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). The following paper updates the procedure: –S. Skogestad, ``Economic plantwide control’’, Book chapter in V. Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent Developments and Applications”, Wiley (late 2011). / All papers available at:

5 S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, (2000).``Plantwide control: the search for the self-optimizing control structure'', S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'', Comp.Chem.Engng., 24, (2000).``Self-optimizing control: the missing link between steady-state optimization and control'', I.J. Halvorsen, M. Serra and S. Skogestad, ``Evaluation of self-optimising control structures for an integrated Petlyuk distillation column'', Hung. J. of Ind.Chem., 28, (2000).``Evaluation of self-optimising control structures for an integrated Petlyuk distillation column'', T. Larsson, K. Hestetun, E. Hovland, and S. Skogestad, ``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process'', Ind. Eng. Chem. Res., 40 (22), (2001).``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process'', K.L. Wu, C.C. Yu, W.L. Luyben and S. Skogestad, ``Reactor/separator processes with recycles-2. Design for composition control'', Comp. Chem. Engng., 27 (3), (2003).``Reactor/separator processes with recycles-2. Design for composition control'', T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control structure selection for reactor, separator and recycle processes'', Ind. Eng. Chem. Res., 42 (6), (2003).``Control structure selection for reactor, separator and recycle processes'', A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), (2003).``Buffer Tank Design for Acceptable Control Performance'', I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad, ``Optimal selection of controlled variables'', Ind. Eng. Chem. Res., 42 (14), (2003).``Optimal selection of controlled variables'', A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8), (2004).``pH-neutralization: integrated process and control design'', S. Skogestad, ``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'', Computers and Chemical Engineering, 29 (1), (2004).``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'', E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), (2005).``Perfect steady-state indirect control'', M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), (2005).``Selection of controlled variables and robust setpoints'', V. Alstad and S. Skogestad, ``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'', Ind.Eng.Chem.Res, 46 (3), (2007).``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'', S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), (2007).``The dos and don'ts of distillation columns control'', E.S. Hori and S. Skogestad, ``Selection of control structure and temperature location for two-product distillation columns'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A3), (2007).``Selection of control structure and temperature location for two-product distillation columns'', A.C.B. Araujo, M. Govatsmark and S. Skogestad, ``Application of plantwide control to the HDA process. I Steady-state and self- optimizing control'', Control Engineering Practice, 15, (2007).``Application of plantwide control to the HDA process. I Steady-state and self- optimizing control'', A.C.B. Araujo, E.S. Hori and S. Skogestad, ``Application of plantwide control to the HDA process. Part II Regulatory control'', Ind.Eng.Chem.Res, 46 (15), (2007).``Application of plantwide control to the HDA process. Part II Regulatory control'', V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad, ``Control structure design for optimal operation of heat exchanger networks'', AIChE J., 54 (1), (2008). DOI /aic.11366``Control structure design for optimal operation of heat exchanger networks'', (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of Process Control, 18, (2008).``Data reconciliation and optimal operation of a catalytic naphtha reformer'', E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, (2008).``Coordinator MPC for maximizing plant throughput'', A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32 (12), (2008).``Control structure design for the ammonia synthesis process'', E.S. Hori and S. Skogestad, ``Selection of controlled variables: Maximum gain rule and combination of measurements'', Ind.Eng.Chem.Res, 47 (23), (2008).``Selection of controlled variables: Maximum gain rule and combination of measurements'', V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, (2009)``Optimal measurement combinations as controlled variables'', E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), (2009). + MORE``Consistent inventory control'',

6 Idealized view of control (“PhD control”)

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

8 How we design a control system for a complete chemical plant? How do we get from PID control to PhD control? Where do we start? What should we control? and why? etc.

9 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.

10 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 “PhD” control

11 Process control: “Plantwide control” = “Control structure design for complete chemical plant” 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 Previous work on plantwide control: Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice) Greg Shinskey (1967) – process control systems Alan Foss (1973) - control system structure Bill Luyben et al. (1975- ) – case studies ; “snowball effect” George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes Ruel Shinnar (1981- ) - “dominant variables” Jim Downs (1991) - Tennessee Eastman challenge problem Larsson and Skogestad (2000): Review of plantwide control

12 Control structure selection issues are identified as important also in other industries. Professor Gary Balas (Minnesota) 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!

13 Main objectives control system 1.Stabilization 2.Implementation of acceptable (near-optimal) operation ARE THESE OBJECTIVES CONFLICTING? Usually NOT –Different time scales Stabilization fast time scale –Stabilization doesn’t “use up” any degrees of freedom Reference value (setpoint) available for layer above But it “uses up” part of the time window (frequency range)

14 Main simplification: Hierarchical structure Need to define objectives and identify main issues for each layer PID RTO MPC Process control

15 c s = y 1s MPC PID y 2s RTO u (valves) Follow path (+ look after other variables) CV=y 1 (+ u) ; MV=y 2s Stabilize + avoid drift CV=y 2 ; MV=u Min J (economics); MV=y 1s OBJECTIVE Dealing with complexity Main simplification: Hierarchical decomposition The controlled variables (CVs) interconnect the layers

16 Example: Bicycle riding Note: design starts from the bottom Regulatory control: –First need to learn to stabilize the bicycle CV = y 2 = tilt of bike MV = body position Supervisory control: –Then need to follow the road. CV = y 1 = distance from right hand side MV=y 2s –Usually a constant setpoint policy is OK, e.g. y 1s =0.5 m Optimization: –Which road should you follow? –Temporary (discrete) changes in y 1s Hierarchical decomposition

17 Plantwide control decisions No matter what procedure we choose to use, the following decisions must be made when designing a plantwide control strategy: Decision 1. Select ”economic” (primary) controlled variables (CV1) for the supervisory control layer (the setpoints CV1s link the optimization layer with the control layers). Decision 2. Select ”stabilizing” (secondary) controlled variables (CV2) for the regulatory control layer (the setpoints CV2s link the two control layers). Decision 3. Locate the throughput manipulator (TPM). Decision 4. Select pairings for the stabilizing layer, that is, pair inputs (valves) and controlled variables (CV2). By “valves” is here meant the original dynamic manipulated variables.

18 Skogestad plantwide control structure design procedure I Top Down Step S1:Step S1: Define operational objectives (optimal operation) –Cost function J (to be minimized) –Operational constraints Step S2 (optimization): (a) Identify degrees of freedom (MVs). (b) Optimize for expected disturbances and find regions of active constraints Step S3 (implementation): Select primary controlled variables c=y 1 (CVs) (Decision 1). Step S4: Where set the production rate? (Inventory control) (Decision 3) II Bottom Up Step S5: Regulatory / stabilizing control (PID layer) –What more to control (y 2 ; local CVs)? y (Decision 2) –Pairing of inputs and outputs y (Decision 4) –Step S6: Supervisory control (MPC layer) Step S7: Real-time optimization (Do we need it?) Understanding and using this procedure is the most important part of this course!!!! y1y1 y2y2 Process MVs

19 Comment: Luyben procedure Step L1. Establish control objectives Step L2. Determine control degrees of freedom Step L3. Establish energy management system Step L4. Set the production rate (Decision 3) Step L5. Control product quality and handle safety, environmental and operational constraints Step L6. Fix a flow in every recycle loop and control inventories Step L7. Check component balances Step L8. Control individual unit operations Step L9. Optimize economics and improve dynamic controllability Notes: “Establish control objectives” in step L1 does not lead directly to the choice of controlled variables (Decisions 1 and 2). Thus, in Luyben’s procedure, Decisions 1, 2 and 4 are not explicit, but are included implicitly in most of the steps. Even though the procedure is systematic, it is still heuristic and ad hoc in the sense that it is not clear how the authors arrived at the steps or their order. A major weakness is that the procedure does not include economics, except as an afterthought in step L9.

20 Outline Skogestad procedure for control structure design I Top Down Step S1: Define operational objective (cost) and constraints Step S2: Identify degrees of freedom and optimize operation for disturbances Step S3: Implementation of optimal operation –What to control ? (primary CV’s) (self-optimizing control) Step S4: Where set the production rate? (Inventory control) II Bottom Up Step S5: Regulatory control: What more to control (secondary CV’s) ? Step S6: Supervisory control Step S7: Real-time optimization

21 Step S1. Define optimal operation (economics) What are we going to use our degrees of freedom u (MVs) for? Define scalar cost function J(u,x,d) –u: degrees of freedom (usually steady-state) –d: disturbances –x: states (internal variables) Typical cost function*: Optimize operation with respect to u for given d (usually steady-state): min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 J = cost feed + cost energy – value products *No need to include fixed costs (capital costs, operators, maintainance) at ”our” time scale (hours) Note: Operational profit P = -J.

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

23 Outline Skogestad procedure for control structure design I Top Down Step S1: Define operational objective (cost) and constraints Step S2: Identify degrees of freedom and optimize operation for disturbances Step S3: Implementation of optimal operation –What to control ? (primary CV’s) (self-optimizing control) Step S4: Where set the production rate? (Inventory control) II Bottom Up Step S5: Regulatory control: What more to control (secondary CV’s) ? Step S6: Supervisory control Step S7: Real-time optimization

24 Step S2 (Optimize operation): (a) Identify degrees of freedom (b) Optimize for expected disturbances Need good steady-state model Goal: Identify regions of active constraints Time consuming!

25 Plans for next lectures Step 2 (Find optimal operation using offline calculations): –Step 2a : DOF analysis (steady-state) (12 slides) –Step 2b: Optimize for expected disturbances (1 slide) –QUIZ’s Step 3 (Implementation of optimal operation) (Lecture 2, many slides!) Identify primary (“economic”) controlled variables (CVs): 1.Control active constraints. Backoff 2.Remaining unconstrained: Find “self-optimizing” CVs Will use a lot of time on this!

26 Step S2a: Degrees of freedom (DOFs) for operation NOT as simple as one may think! To find all operational (dynamic) degrees of freedom: Count valves! (N valves ) “Valves” also includes adjustable compressor power, etc. Anything we can manipulate! BUT: not all these have a (steady-state) effect on the economics Steady-state DOFs

27 Steady-state degrees of freedom (DOFs) IMPORTANT! DETERMINES THE NUMBER OF VARIABLES TO CONTROL! No. of primary CVs = No. of steady-state DOFs CV = controlled variable (c) Methods to obtain no. of steady-state degrees of freedom (N ss ): 1.Equation-counting N ss = no. of variables – no. of equations/specifications Very difficult in practice 2.Valve-counting (easier!) N ss = N valves – N 0ss – N specs N 0ss = variables with no steady-state effect 3.Potential number for some units (useful for checking!) 4.Correct answer: Will eventually find it when we perform optimization Steady-state DOFs

28 Steady-state degrees of freedom (N ss ): 2. Valve-counting N valves = no. of dynamic (control) DOFs (valves) N ss = N valves – N 0ss – N specs : no. of steady-state DOFs N 0ss = N 0y + N 0,valves : no. of variables with no steady-state effect –N 0,valves : no. purely dynamic control DOFs –N 0y : no. controlled variables (liquid levels) with no steady-state effect N specs : No of equality specifications (e.g., given pressure) Steady-state DOFs

29 N valves = 6, N 0y = 2*, N DOF,SS = 6 -2 = 4 (including feed and pressure as DOFs) Typical Distillation column *N 0y : no. controlled variables (liquid levels) with no steady-state effect With given feed and pressure: NEED TO IDENTIFY 2 more CV’s - Typical: Top and btm composition Steady-state DOFs

30 Heat-integrated distillation process QUIZ 3 Steady-state DOFs

31 Heat exchanger with bypasses Steady-state DOFs

32 Steady-state degrees of freedom (N ss ): 3. Potential number for some process units each external feedstream: 1 (feedrate) splitter: n-1 (split fractions) where n is the number of exit streams mixer: 0 compressor, turbine, pump: 1 (work/speed) adiabatic flash tank: 0 * liquid phase reactor: 1 (holdup reactant) gas phase reactor: 0 * heat exchanger: 1 (bypass or flow) column (e.g. distillation) excluding heat exchangers: 0 * + no. of sidestreams pressure * : add 1DOF at each extra place you set pressure (using an extra valve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or absorption column *Pressure is normally assumed to be given by the surrounding process and is then not a degree of freedom Ref: Araujo, Govatsmark and Skogestad (2007) Extension to closed cycles: Jensen and Skogestad (2009) Real number may be less, for example, if there is no bypass valve Steady-state DOFs

33 Heat exchanger with bypasses Steady-state DOFs

34 “Potential number”, N ss = 0 (column distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4 With given feed and pressure: N’ ss = 4 – 2 = 2 Distillation column (with feed and pressure as DOFs) split Steady-state DOFs

35 Heat-integrated distillation process Steady-state DOFs

36 HDA process MixerFEHE FurnacePFR Quench Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) QUIZ 4 Steady-state DOFs

37 HDA process: steady-state degrees of freedom Conclusion: 14 steady-state DOFs Assume given column pressures feed:1.2 hex: 3, 4, 6 splitter 5, 7 compressor: 8 distillation: 2 each column QUIZ 4 solution Hm….. Consider -Feeds -Heat exchangers -Splitters -Compressors -Distillation columns Steady-state DOFs

38 Check that there are enough manipulated variables (DOFs) - both dynamically and at steady-state (step 2) Otherwise: Need to add equipment –extra heat exchanger –bypass –surge tank Steady-state DOFs

39 Step S2b: Optimize with respects to DOFS (u) for expected disturbances (d) …….. and identify regions of active constraints min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 Idea: Prepare operation for expected future disturbances, incl. price changes In principle: simple In practise: very time consuming –Commercial simulators (Aspen, Unisim/Hysys) are set up in “design mode” and often work poorly in “operation (rating) mode”. Example Heat exchanger Easy (Design mode): Given streams (and temperatures), find UA Difficult (Operation mode): Given UA, find outlet temperatures –Optimization methods in commercial simulators often poor We use Matlab or even Excel “on top” Heat exchanger: Let Matlab/Excel vary temperatures to match given UA –Focus on most important disturbances and range. Whole picture is complicated d 1 = feedrate d 2 = energy price Ref. Jacobsen and Skogestad, ESCAPE’21, Greece, 2011

40 Optimal operation Mode 1. Given feedrate Mode 2. Maximum production minimize J = cost feed + cost energy – value products Two main cases (modes) depending on marked conditions:

41 Amount of products is then usually indirectly given and Optimal operation is then usually unconstrained “maximize efficiency (energy)” Control: Operate at optimal trade-off (not obvious what to control to achieve this) Mode 1. Given feedrate J = cost feed– value products + cost energy c J = energy c opt constant

42 Assume feedrate is degree of freedom Assume products much more valuable than feed Optimal operation is then to maximize product rate –But must remain feasible –constrained by bottleneck Mode 2. Maximum production Control: Focus on tight control of bottleneck (“obvious what to control”) c J c opt Infeasible region J = cost feed + cost energy – value products

43 Example with Quiz: Optimal operation of two distillation columns in series

44 Operation of Distillation columns in series With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column) DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011) Energy price: p V =0-0.2 $/mol (varies) Cost (J) = - Profit = p F F + p V (V 1 +V 2 ) – p D1 D 1 – p D2 D 2 – p B2 B 2 > 95% B p D2 =2 $/mol F ~ 1.2mol/s p F =1 $/mol < 4 mol/s < 2.4 mol/s > 95% C p B2 =1 $/mol N=41 α AB =1.33 N=41 α BC =1. 5 > 95% A p D1 =1 $/mol QUIZ: What are the expected active constraints? 1. Always. 2. For low energy prices. QUIZ 1

45 DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011) Energy price: p V =0-0.2 $/mol (varies) Cost (J) = - Profit = p F F + p V (V 1 +V 2 ) – p D1 D 1 – p D2 D 2 – p B2 B 2 > 95% B p D2 =2 $/mol F ~ 1.2mol/s p F =1 $/mol < 4 mol/s < 2.4 mol/s > 95% C p B2 =1 $/mol 1. x B = 95% B Spec. valuable product (B): Always active! Why? “Avoid product give-away” N=41 α AB =1.33 N=41 α BC =1. 5 > 95% A p D1 =1 $/mol 2. Cheap energy: V 1 =4 mol/s, V 2 =2.4 mol/s Max. column capacity constraints active! Why? Overpurify A & C to recover more B QUIZ: What are the expected active constraints? 1. Always. 2. For low energy prices. Hm….? Operation of Distillation columns in series With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column) SOLUTION QUIZ 1

46 Active constraint regions for two distillation columns in series [mol/s] [$/mol] CV = Controlled Variable Energy price SOLUTION QUIZ 1 (more details) BOTTLENECK Higher F infeasible because all 5 constraints reached

47 Active constraint regions for two distillation columns in series [mol/s] [$/mol] CV = Controlled Variable QUIZ. Assume low energy prices (pV=0.01 $/mol). How should we control the columns? Energy price QUIZ 2

48 Control of Distillation columns in series Given LC PC QUIZ. Assume low energy prices (pV=0.01 $/mol). How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTS Red: Basic regulatory loops QUIZ 2

49 Control of Distillation columns in series Given LC PC Red: Basic regulatory loops CC xBxB x BS =95% MAX V1 MAX V2 1 unconstrained DOF (L1): Use for what?? CV=? Not: CV= x A in D1! (why? x A should vary with F!) Maybe: constant L1? (CV=L1) Better: CV= x A in B1? Self-optimizing? General for remaining unconstrained DOFs: LOOK FOR “SELF-OPTIMIZING” CVs = Variables we can keep constant WILL GET BACK TO THIS! SOLUTION QUIZ 2 Hm……. HINT: CONTROL ACTIVE CONSTRAINTS! QUIZ. Assume low energy prices (pV=0.01 $/mol). How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTS

50 In practise New figure, that is, update the one fom next slide Column with T-loops, column 1 with T btm V1 and V2 max repøaced by dp-contrpø

51 Control of Distillation columns in series Given LC PC Comment: Should normally stabilize column profiles with temperature control, Should use reflux (L) in this case because boilup (V) may saturate. T1 S and T2 S would then replace L1 and L2 as DOFs…… but leave this out for now.. Red: Basic regulatory loops TC T1 s T2 s T1 T2 Comment

52 Active constraint regions for two distillation columns in series CV = Controlled Variable [mol/s] [$/mol] 1 Cheap energy: 1 remaining unconstrained DOF (L1) -> Need to find 1 additional CVs (“self-optimizing”) More expensive energy: 3 remaining unconstrained DOFs -> Need to find 3 additional CVs (“self-optimizing”) Energy price SOLUTION QUIZ 2 (more details)