1. 1 AN INTRODUCTION TO PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Bratislava, jan. 2011

2. 2 Abstract Title: A systematic approach to plantwide control. Abstract: A chemical plant may have thousands of measurements and control loops. By the term plantwide control it is not meant the tuning and behavior of each of these loops, but rather the control philosophy of the overall plant with emphasis on the structural decisions. In practice, the control system is usually divided into several layers, separated by time scale: scheduling (weeks), site- wide optimization (day), local optimization (hour), supervisory (predictive, advanced) control (minutes) and regulatory control (seconds). Such a hiearchical (cascade) decomposition with layers operating on different time scale is used in the control of all real (complex) systems including biological systems and airplanes, so the issues in this section are not limited to process control. In the talk the most important issues are discussed, especially related to the choice of variables that provide the link the control layers.

3. 3 Trondheim Oslo UK NORWAY DENMARK GERMANY North Sea SWEDEN Arctic circle

4. 4 NTNU, Trondheim

5. 5 Plantwide control intro course: Contents Overview of plantwide control Step1-3. 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 - Many examples Step 4. Where to set the production rate and bottleneck Step 5. Design of the regulatory control layer ("what more should we control") - stabilization - secondary controlled variables (measurements) - pairing with inputs - controllability analysis - cascade control and time scale separation. Step 6. Design of supervisory control layer - Decentralized versus centralized (MPC) - Design of decentralized controllers: Sequential and independent design - Pairing and RGA-analysis Summary and case studies

6. 6 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 Process control The controlled variables (CVs) interconnect the layers

7. 7 Main message 1. Control for economics (Top-down steady-state arguments) –Primary controlled variables c = y 1 : Control active constraints For remaining unconstrained degrees of freedom: Look for “self-optimizing” variables 2. Control for stabilization (Bottom-up; regulatory PID control) –Secondary controlled variables y 2 (“inner cascade loops”) Control variables which otherwise may “drift” Both cases: Control “sensitive” variables (with a large gain)!

8. 8 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down Step 1: Define optimal operation Step 2: Identify degrees of freedom and optimize for expected disturbances Step 3: What to control ? (primary CV’s) (self-optimizing control) Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory control: What more to control (secondary CV’s) ? Step 6: Supervisory control Step 7: Real-time optimization

9. 9 Idealized view of control (“Ph.D. control”)

10. 10 Practice: Tennessee Eastman challenge problem (Downs, 1991) (“PID control”)

11. 11 How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc.

12. 12 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.

13. 13 Plantwide control = 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.). 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

14. 14 Control structure design procedure I Top Down Step 1: Define operational objectives (optimal operation) –Cost function J (to be minimized) –Operational constraints Step 2: Identify degrees of freedom (MVs) and optimize for expected disturbances Step 3: Select primary controlled variables c=y 1 (CVs) Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory / stabilizing control (PID layer) –What more to control (y 2 ; local CVs)? –Pairing of inputs and outputs Step 6: Supervisory control (MPC layer) Step 7: Real-time optimization (Do we need it?) y1y1 y2y2 Process MVs

15. 15 Step 1. 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

16. 16 Step 2: Identify degrees of freedom and optimize for expected disturbances Optimization: Identify regions of active constraints Time consuming! 3 3 unconstrained degrees of freedom -> Find 3 CVs 2 2 1 1 Control 3 active constraints 0

17. 17 Step 3: Implementation of optimal operation Optimal operation for given d * : min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 → u opt (d * ) Problem: Usally cannot keep u opt constant because disturbances d change How should we adjust the degrees of freedom (u)?

18. 18 Implementation (in practice): Local feedback control! “Self-optimizing control:” Constant setpoints for c gives acceptable loss y FeedforwardOptimizing controlLocal feedback: Control c (CV) d

19. 19 Question: What should we control (c)? (primary controlled variables y 1 =c) Introductory example: Runner Issue: What should we control?

20. 20 –Cost to be minimized, J=T –One degree of freedom (u=power) –What should we control? Optimal operation - Runner Optimal operation of runner

21. 21 Sprinter (100m) 1. Optimal operation of Sprinter, J=T –Active constraint control: Maximum speed (”no thinking required”) Optimal operation - Runner

22. 22 2. Optimal operation of Marathon runner, J=T Unconstrained optimum! 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 Optimal operation - Runner Marathon (40 km)

23. 23 Conclusion Marathon runner c = heart rate select one measurement Simple and robust implementation Disturbances are indirectly handled by keeping a constant heart rate May have infrequent adjustment of setpoint (heart rate) Optimal operation - Runner

24. 24 Step 3. What should we control (c)? c = H y y – available measurements (including u’s) H – selection of combination matrix What should we control? Equivalently: What should H be? 1.Control active constraints! 2.Unconstrained variables: Control self-optimizing variables!

25. 25 Expected active constraints distillation 1. Valuable product: Purity spec. always active –Reason: Amount of valuable product (D or B) should always be maximized Avoid product “give-away” (“Sell water as methanol”) Also saves energy Control implications valuable product: Control purity at spec. 2. “Cheap” product. May want to over-purify! Trade-off: –Yes, increased recovery of valuable product (less loss) –No, costs energy May give unconstrained optimum valuable product methanol + max. 1% water cheap product (byproduct) water + max. 0.5% methanol + water

26. 26 a)If constraint can be violated dynamically (only average matters) Required Back-off = “bias” (steady-state measurement error for c) b)If constraint cannot be violated dynamically (“hard constraint”) Required Back-off = “bias” + maximum dynamic control error J opt Back-off Loss c ≥ c constraint c J 1. CONTROL ACTIVE CONSTRAINTS! Active input constraints: Just set at MAX or MIN Active output constraints: Need back-off Want tight control of hard output constraints to reduce the back-off “Squeeze and shift”

27. 27 Example. Optimal operation = max. throughput. Want tight bottleneck control to reduce backoff! Time Back-off = Lost production Rule for control of hard output constraints: “Squeeze and shift”! Reduce variance (“Squeeze”) and “shift” setpoint c s to reduce backoff

28. 28 Hard Constraints: «SQUEEZE AND SHIFT» © Richalet SHIFT SQUEEZE

29. 29 SUMMARY ACTIVE CONSTRAINTS –c constraint = value of active constraint –Implementation of active constraints is usually “obvious”, but may need “back-off” (safety limit) for hard output constraints C s = C constraint - backoff –Want tight control of hard output constraints to reduce the back-off “Squeeze and shift”

30. 30 Control “self-optimizing” variables 1. Old idea (Morari et al., 1980): “We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions.” 2. “Self-optimizing control” = acceptable steady-state behavior (loss) with constant CVs. is similar to “Self-regulation” = acceptable dynamic behavior with constant MVs. 3. The ideal self-optimizing variable c is the gradient (c =  J/  u = J u ) –Keep gradient at zero for all disturbances (c = J u =0) –Problem: no measurement of gradient Unconstrained degrees of freedom

31. 31 H

32. 32 H

33. 33 Guidelines for selecting single measurements as CVs Rule 1: The optimal value for CV (c=Hy) should be insensitive to disturbances d (minimizes effect of setpoint error) Rule 2: c should be easy to measure and control (small implementation error n) Rule 3: “Maximum gain rule”: c should be sensitive to changes in u (large gain |G| from u to c) or equivalently the optimum J opt should be flat with respect to c (minimizes effect of implementation error n) Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure”, Journal of Process Control, 10, 487-507 (2000).

34. 34 Optimal measurement combination H Candidate measurements (y): Include also inputs u

35. 35 Nullspace method No measurement noise (n=0)

36. 36 Ref: Halvorsen et al. I&ECR, 2003 Kariwala et al. I&ECR, 2008 Generalization (with measurement noise) Loss with c=Hy=0 due to (i) Disturbances d (ii) Measurement noise n y u J Loss Controlled variables, c s = constant + + + + + - K H y c u d

37. 37 c s = constant + + + + + - K H y c u “Minimize” in Maximum gain rule ( maximize S 1 G J uu -1/2, G=HG y ) “Scaling” S 1 “=0” in nullspace method (no noise) Optimal measurement combination, c = Hy With measurement noise

38. 38 Non-convex optimization problem (Halvorsen et al., 2003) st Improvement 1 (Alstad et al. 2009) st Improvement 2 (Yelchuru et al., 2010) D : any non-singular matrix Have extra degrees of freedom Convex optimization problem Global solution - Do not need J uu - Q can be used as degrees of freedom for faster solution - Analytical solution

39. 39 Example: CO2 refrigeration cycle J = W s (work supplied) DOF = u (valve opening, z) Main disturbances: d 1 = T H d 2 = T Cs (setpoint) d 3 = UA loss What should we control? pHpH

40. 40 CO2 refrigeration cycle Step 1. One (remaining) degree of freedom (u=z) Step 2. Objective function. J = W s (compressor work) Step 3. Optimize operation for disturbances (d 1 =T C, d 2 =T H, d 3 =UA) Optimum always unconstrained Step 4. Implementation of optimal operation No good single measurements (all give large losses): –p h, T h, z, … Nullspace method: Need to combine n u +n d =1+3=4 measurements to have zero disturbance loss Simpler: Try combining two measurements. Exact local method: –c = h 1 p h + h 2 T h = p h + k T h ; k = -8.53 bar/K Nonlinear evaluation of loss: OK!

41. 41 CO2 cycle: Maximum gain rule

42. 42 Refrigeration cycle: Proposed control structure Control c= “temperature-corrected high pressure”

43. 43 Step 4. Where set production rate? Where locale the TPM (throughput manipulator)? Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts

44. 44 TPM (Throughput manipulator) TPM (Throughput manipulator) = ”Unused” degree of freedom that affects the throughput. Definition (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control. Usually set by the operator (manual control), often the main feedrate The TPM is usually a flow (or closely related to a flow) but not always. –One exception is for a reactor where the reactor temperature can be a TPM, because this changes the reactor conversion, which changes the production rate and thus the throughput Usually, only one TPM for a plant, but there can be more if there are –parallel units or splits into alternative processing routes –multiple feeds that do not need to be set in a fixed ratio The feeds usually need to be set in a fixed ratio. For example, for the reaction A+B-> product we need to have the ratio FA/FB close to 1 to have good operation with small loss of reactants, so there is only one TPM even if there are two feeds, FA and FB. If we consider only part of the plant then the TPM may be outside our control. The throughput is then a disturbance which is typically a given feedrate (if our plant is a postprocessing plant) or a given product rate (preprocessing or utility plant) If the TPM becomes unavailable because of saturation as we enter a new region, then a potential new TPM is a variable that is no linger self-optimizing.

45. 45 TPM (Throughput manipulator) TPM (Throughput manipulator) = ”Unused” degree of freedom that affects the throughput. Definition (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control. Usually set by the operator (manual control), often the main feedrate

46. 46 CONSISTENT?

47. 47 Consistency of inventory control Consistency (required property): An inventory control system is said to be consistent if the steady- state mass balances (total, components and phases) are satisfied for any part of the process, including the individual units and the overall plant. Local*-consistency (desired property): A consistent inventory control system is said to be local-consistent if for any part/unit the local inventory control loops by themselves are sufficient to achieve steady-state mass balance consistency for that unit (without relying on other loops being closed). * Previously called self-consistency

48. 48 Local-consistency rule (also called self-consistency) Rule 1. Local-consistency requires that 1. The total inventory (mass) of any part of the process must be locally regulated by its in- or outflows, which implies that at least one flow in or out of any part of the process must depend on the inventory inside that part of the process. 2. For systems with several components, the inventory of each component of any part of the process must be locally regulated by its in- or outflows or by chemical reaction. 3. For systems with several phases, the inventory of each phase of any part of the process must be locally regulated by its in- or outflows or by phase transition. Proof: Mass balances Note: Without the local requirement one gets the more general consistency rule

49. 49 Production rate set at inlet : Inventory control in direction of flow* * Required to get “local-consistent” inventory control TPM

50. 50 Production rate set at outlet: Inventory control opposite flow TPM

51. 51 Production rate set inside process TPM

52. 52 Step 5: Regulatory control layer Step 5. Choose structure of regulatory (stabilizing) layer (a) Identify “stabilizing” CV2s (levels, pressures, reactor temperature,one temperature in each column, etc.). In addition, active constraints (CV1) that require tight control (small backoff) may be assigned to the regulatory layer. (Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat) (b) Identify pairings (MVs to be used to control CV2), taking into account –Want “local consistency” for the inventory control –Want tight control of important active constraints –Avoid MVs that may saturate in the regulatory layer, because this would require either reassigning the regulatory loop (complication penalty), or requiring back-off for the MV variable (economic penalty) Preferably, the same regulatory layer should be used for all operating regions without the need for reassigning inputs or outputs.

53. 53 Rules for pairing of variables and choice of control structure Main rule: “Pair close” 1.The response (from input to output) should be fast, large and in one direction. Avoid dead time and inverse responses! 2.The input (MV) should preferably effect only one output (to avoid interaction between the loops) 3.Try to avoid input saturation (valve fully open or closed) in “basic” control loops for level and pressure 4.The measurement of the output y should be fast and accurate. It should be located close to the input (MV) and to important disturbances. Use extra measurements y’ and cascade control if this is not satisfied 5.The system should be simple Avoid too many feedforward and cascade loops 6.“Obvious” loops (for example, for level and pressure) should be closed first before you spend to much time on deriving process matrices etc.

54. 54 Example: Distillation Primary controlled variable: y 1 = c = x D, x B (compositions top, bottom) BUT: Delay in measurement of x + unreliable Regulatory control: For “stabilization” need control of (y 2 ): –Liquid level condenser (M D ) –Liquid level reboiler (M B ) –Pressure (p) –Holdup of light component in column (temperature profile) Unstable (Integrating) + No steady-state effect Variations in p disturb other loops Almost unstable (integrating) TC TsTs T-loop in bottom

55. 55 Why simplified configurations? Why control layers? Why not one “big” multivariable controller? Fundamental: Save on modelling effort Other: –easy to understand –easy to tune and retune –insensitive to model uncertainty –possible to design for failure tolerance –fewer links –reduced computation load

56. 56 Degrees of freedom unchanged No degrees of freedom lost by control of secondary (local) variables as setpoints become y 2s replace inputs u 2 as new degrees of freedom GK y 2s u2u2 y2y2 y1y1 Original DOF New DOF Cascade control:

57. 57 ”Advanced control” STEP 6. SUPERVISORY LAYER Objectives of supervisory layer: 1. Switch control structures (CV1) depending on operating region Active constraints self-optimizing variables 2. Perform “advanced” economic/coordination control tasks. –Control primary variables CV1 at setpoint using as degrees of freedom (MV): Setpoints to the regulatory layer (CV2s) ”unused” degrees of freedom (valves) –Keep an eye on stabilizing layer Avoid saturation in stabilizing layer –Feedforward from disturbances If helpful –Make use of extra inputs –Make use of extra measurements Implementation: Alternative 1: Advanced control based on ”simple elements” Alternative 2: MPC

58. 58 Control configuration elements Control configuration. The restrictions imposed on the overall controller by decomposing it into a set of local controllers (subcontrollers, units, elements, blocks) with predetermined links and with a possibly predetermined design sequence where subcontrollers are designed locally. Some control configuration elements: Cascade controllers Decentralized controllers Feedforward elements Decoupling elements Selectors Split-range control

59. 59 Summary. Systematic procedure for plantwide control 1.Start “top-down” with economics: –Step 1: Identify degrees of freeedom –Step 2: Define operational objectives and optimize steady-state operation. –Step 3A: Identify active constraints = primary CVs c. Should be controlled to maximize profit) –Step 3B: For remaining unconstrained degrees of freedom: Select CV1s c based on self-optimizing control. –Step 4: Where to set the throughput (usually: feed) 2.Regulatory control I: Decide on how to move mass through the plant: Step 5A: Propose “local-consistent” inventory (level) control structure. 3.Regulatory control II: “Bottom-up” stabilization of the plant Step 5B: Control variables CV2 to stop “drift” (sensitive temperatures, pressures,....) –Pair variables to avoid interaction and saturation 4.Finally: make link between “top-down” and “bottom up”. Step 6: “Advanced control” system (MPC): CVs: Active constraints and self-optimizing economic variables + look after variables in layer below (e.g., avoid saturation) MVs: Setpoints to regulatory control layer. Coordinates within units and possibly between units cscs CV2 CV1

60. 60 Summary and references The following paper summarizes the procedure: –S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), 219-234 (2004).``Control structure design for complete chemical plants'', 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, 209-240 (2000).``Plantwide control: A review and a new design procedure''

61. 61 S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, 487-507 (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, 569- 575 (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, 11-15 (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), 4889-4901 (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), 401-421 (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), 1225-1234 (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), 2198-2208 (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), 3273-3284 (2003).``Optimal selection of controlled variables'', A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8), 1475-1487 (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), 127-137 (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), 863-867 (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), 2207-2217 (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), 846-853 (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), 13-23 (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), 293-306 (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, 1222-1237 (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), 5159-5174 (2007).``Application of plantwide control to the HDA process. Part II Regulatory control'', V. Kariwala, S. Skogestad and J.F. Forbes, ``Reply to ``Further Theoretical results on Relative Gain Array for Norn-Bounded Uncertain systems'''' Ind.Eng.Chem.Res, 46 (24), 8290 (2007).``Reply to ``Further Theoretical results on Relative Gain Array for Norn-Bounded Uncertain systems'''' V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad, ``Control structure design for optimal operation of heat exchanger networks'', AIChE J., 54 (1), 150-162 (2008). DOI 10.1002/aic.11366``Control structure design for optimal operation of heat exchanger networks'', T. Lid and S. Skogestad, ``Scaled steady state models for effective on-line applications'', Computers and Chemical Engineering, 32, 990-999 (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of Process Control, 18, 320-331 (2008).``Scaled steady state models for effective on-line applications'', ``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, 195-204 (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), 2920-2932 (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), 9465-9471 (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, 138-148 (2009)``Optimal measurement combinations as controlled variables'', E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009).``Consistent inventory control'',