1 ECONOMIC PLANTWIDE CONTROL: Control structure design for complete processing plants Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Mexico, 01 May 2012 2 Abstract and bio ECONOMIC PLANTWIDE CONTROL: Control structure design for complete processing plants. Sigurd Skogestad, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway 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. Bio: Sigurd Skogestad received his Ph.D. degree from the California Institute of Technology, Pasadena, USA in He has been a full professor at Norwegian University of Science and Technology (NTNU), Trondheim, Norway since 1987 and he was Head of the Department of Chemical Engineering from 1999 to He is the principal author, together with Prof. Ian Postlethwaite, of the book "Multivariable feedback control" published by Wiley in 1996 (first edition) and 2005 (second edition). He received the Ted Peterson Award from AIChE in 1989, the George S. Axelby Outstanding Paper Award from IEEE in 1990, the O. Hugo Schuck Best Paper Award from the American Automatic Control Council in 1992, and the Best Paper Award 2004 from Computers and Chemical Engineering. He was an Editor of Automatica during the period His research interests include the use of feedback as a tool to make the system well-behaved (including self- optimizing control), limitations on performance in linear systems, control structure design and plantwide control, interactions between process design and control, and distillation column design, control and dynamics. 3 Trondheim, Norway Mexico 4 Trondheim Oslo UK NORWAY DENMARK GERMANY North Sea SWEDEN Arctic circle 5 NTNU, Trondheim 6 Outline 1. Introduction plantwide control (control structure design) 2. Plantwide control procedure I Top Down Step 1: Define optimal operation Step 2: 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 )? Pairing of inputs and outputs Step 6: Supervisory control (MPC layer) Step 7: Real-time optimization (Do we need it?) y1y1 y2y2 Process MVs 7 Idealized view of control (PhD control) 8 Practice: Tennessee Eastman challenge problem (Downs, 1991) (PID control) TCPCLCACxSRC Where place?? 9 How do we get from PID to PhD control? How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc. 10 How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc. 11 Example: Tennessee Eastman challenge problem (Downs, 1991) TCPCLCACxSRC Where place?? 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. 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 13 Optimal operation of systems Example of systems we want to operate optimally Process plant (minimize J=cost) Runner (minimize J=time) World Economy Maximize welfare (with given environmental impact) Maximize happiness (with given environmental impact) Minimize J=environmental impact (with given minimum welfare) General multiobjective: Min J (scalar cost, $) Subject to satisfying constraints (environment, resources) 14 Theory: Optimal operation ALLMIGHTY GOD? IDEAL COMMUNISM? PROCESS CONTROL? Objectives Present state Model of system Theory: Model of overall system Estimate present state Optimize all degrees of freedom Problems: Model not available Optimization complex Not robust (difficult to handle uncertainty) Slow response time Process control: Excellent candidate for centralized control (Physical) Degrees of freedom CENTRALIZED OPTIMIZER 15 Practice: Engineering systems Most (all?) large-scale engineering systems are controlled using hierarchies of quite simple controllers Large-scale chemical plant (refinery) Commercial aircraft 100s of loops Simple components: on-off + PI-control + nonlinear fixes + some feedforward Same in biological systems 16 Practice: Process control Practice: Hierarchical structure 17 Process control: Hierarchical structure Director Process engineer Operator Logic / selectors / operator PID control u = valves 18 c s = y 1s MPC PID y 2s RTO Follow path (+ look after other variables) Stabilize + avoid drift Min J (economics) u (valves) OBJECTIVE Dealing with complexity Plantwide control: Objectives The controlled variables (CVs) interconnect the layers 19 Translate optimal operation into simple control objectives: What should we control? y 1 = c ? (economics) y 2 = ? (stabilization) 20 y 1 = distance to curb (1 m) y 2 = bike tilt (stabilization) u = muscles Example: Bicycle riding 21 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 22 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 23 Step 2. Optimize Identify degrees of freedom (u) Optimize for expected disturbances (d) Identify regions of active constraints Need model of system Time consuming, but it is offline 24 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)? 25 Implementation (in practice): Local feedback control! Self-optimizing control: Constant setpoints for c gives acceptable loss y FeedforwardOptimizing controlLocal feedback: Control c (CV) d Main issue: What should we control? 26 Cost to be minimized, J=T One degree of freedom (u=power) What should we control? Optimal operation - Runner Example: Optimal operation of runner 27 Sprinter (100m) 1. Optimal operation of Sprinter, J=T Active constraint control: Maximum speed (no thinking required) Optimal operation - Runner 28 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) 29 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 30 Further examples Central bank. J = welfare. c=inflation rate (2.5%) Cake baking. J = nice taste, 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 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 31 Step 3. What should we control (c)? (primary controlled variables y 1 =c) Selection of controlled variables c 1.Control active constraints! 2.Unconstrained variables: Control self-optimizing variables! 32 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 AB =1.33 N=41 BC =1. 5 > 95% A p D1 =1 $/mol QUIZ: What are the expected active constraints? 1. Always. 2. For low energy prices. Example /QUIZ 1 = == 33 Control of Distillation columns in series Given LC PC QUIZ. Assume low energy prices (pV=0.01 $/mol). How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTS Red: Basic regulatory loops QUIZ 2 34 Control of Distillation columns in series Given LC PC Red: Basic regulatory loops CC xBxB x BS =95% MAX V1 MAX V2 SOLUTION QUIZ 2 UNCONSTRAINED CV=? 35 Active constraint regions for two distillation columns in series [mol/s] [$/mol] CV = Controlled Variable Energy price SOLUTION QUIZ 1 (more details) BOTTLENECK Higher F infeasible because all 5 constraints reached 36 Control self-optimizing variables 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. 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 u cost J J u =0 JuJu 37 H Ideal: c = J u In practise: c = H y. Task: Determine H! 38 Systematic approach: What to control? Define optimal operation: Minimize cost function J Each candidate c = Hy: Brute force approach: With constant setpoints c s compute loss L for expected disturbances d and implementation errors n Select variable c with smallest loss Acceptable loss self-optimizing control 39 Control of Distillation columns in series Given LC PC Red: Basic regulatory loops CC xBxB x BS =95% MAX V1 MAX V2 CC xBxB x AS =2.1% Cost (J) = - Profit = p F F + p V (V 1 +V 2 ) p D1 D 1 p D2 D 2 p B2 B 2 40 Example recycle plant. 3 steady-state degrees of freedom (u) Minimize J=V (energy) Active constraint M r = M rmax Active constraint x B = x Bmin L/F constant: Easier than two-point control Self-optimizing 41 Optimal operation Cost J Controlled variable c c opt J opt Unconstrained optimum 42 Optimal operation Cost J Controlled variable c c opt J opt Two problems: 1. Optimum moves because of disturbances d: c opt (d) 2. Implementation error, c = c opt + n d n Unconstrained optimum 43 Good candidate controlled variables c (for self-optimizing control) 1.The optimal value of c should be insensitive to disturbances Small F c = dc opt /dd 2.c should be easy to measure and control 3.Want flat optimum -> The value of c should be sensitive to changes in the degrees of freedom (large gain) Large G = dc/du = HG y BADGood 44 Optimizer Controller that adjusts u to keep c m = c s Plant cscs c m = c + n u y nyny d u c J c s =c opt u opt n Want c sensitive to u (large gain) Flat optimum is same as large gain H 45 Optimal measurement combinations Optimal policy independent of disturbances Need model or data for optimal response to disturbances Marathon runner case c = h 1 hr + h 2 v Extension to polynomial systems Preheat train for energy recovery (Jschke) Patent pending 46 Optimal measurement combination H Candidate measurements (y): Include also inputs u 47 Optimal measurement combination: Nullspace method Want optimal value of c independent of disturbances c opt = 0 d Find optimal solution as a function of d: u opt (d), y opt (d) Linearize this relationship: y opt = F d F optimal sensitivity matrix Want: To achieve this for all values of d (Nullspace method): Always possible if Comment: Nullspace method is equivalent to J u =0 48 Example. Nullspace Method for Marathon runner u = power, d = slope [degrees] y 1 = hr [beat/min], y 2 = v [m/s] F = dy opt /dd = [ ] H = [h 1 h 2 ]] HF = 0 -> h 1 f 1 + h 2 f 2 = 0.25 h 1 0.2 h 2 = 0 Choose h 1 = 1 -> h 2 = 0.25/0.2 = 1.25 Conclusion: c = hr v Control c = constant -> hr increases when v decreases (OK uphill!) 49 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 50 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 51 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 = bar/K Nonlinear evaluation of loss: OK! 52 CO2 cycle: Maximum gain rule 53 Refrigeration cycle: Proposed control structure Control c= temperature-corrected high pressure. k = -8.5 bar/K 54 Control structure design using self-optimizing control for economically optimal CO 2 recovery * Step S1. Objective function= J = energy cost + cost (tax) of released CO 2 to air Step S3 (Identify CVs). 1. Control the 4 equality constraints 2. Identify 2 self-optimizing CVs. Use Exact Local method and select CV set with minimum loss. 4 equality and 2 inequality constraints: 1.stripper top pressure 2.condenser temperature 3.pump pressure of recycle amine 4.cooler temperature 5.CO 2 recovery 80% 6.Reboiler duty < 1393 kW (nominal +20%) 4 levels without steady state effect: absorber 1,stripper 2,make up tank 1 *M. Panahi and S. Skogestad, ``Economically efficient operation of CO2 capturing process, part I: Self-optimizing procedure for selecting the best controlled variables'', Chemical Engineering and Processing, 50, (2011).``Economically efficient operation of CO2 capturing process, part I: Self-optimizing procedure for selecting the best controlled variables'', Step S2. (a) 10 degrees of freedom: 8 valves + 2 pumps Disturbances: flue gas flowrate, CO 2 composition in flue gas + active constraints (b) Optimization using Unisim steady-state simulator. Region I (nominal feedrate): No inequality constraints active 2 unconstrained degrees of freedom = Case study 55 Proposed control structure with given feed 56 Step 4. Where set production rate? Where locale the TPM (throughput manipulator)? The gas pedal of the process Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts 57 Production rate set at inlet : Inventory control in direction of flow* * Required to get local-consistent inventory controlC TPM 58 Production rate set at outlet: Inventory control opposite flow TPM 59 Production rate set inside process TPM Radiating inventory control around TPM (Georgakis et al.) 60 Sellers marked = high product prices: Optimal operation = max. throughput (active constraint) 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 Want tight bottleneck control to reduce backoff! 61 LOCATE TPM? Conventional choice: Feedrate Consider moving if there is an important active constraint that could otherwise not be well controlled Good choice: Locate at bottleneck 62 Step 5. Regulatory control layer Purpose: Stabilize the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades) Enable manual operation (by operators) Main structural decisions: What more should we control? (secondary CVs, y 2, use of extra measurements) Pairing with manipulated variables (MVs u 2 ) y 1 = c y 2 = ? 63 Control CV2s that stabilizes the plant (stops drifting) In practice, control: 1.Levels (inventory liquid) 2.Pressures (inventory gas/vapor) (note: some pressures may be left floating) 3.Inventories of components that may accumulate/deplete inside plant E.g., amount of amine/water (deplete) in recycle loop in CO2 capture plant E.g., amount of butanol (accumulates) in methanol-water distillation column E.g., amount of inert N2 (accumulates) in ammonia reactor recycle 4.Reactor temperature 5.Distillation column profile (one temperature inside column) Stripper/absorber profile does not generally need to be stabilized 64 Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s Degrees of freedom for supervisory control, MV1=CV2s + unused valves Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs) Optimizer (RTO) PROCESS Supervisory controller (MPC) Regulatory controller (PID) H2H2 H CV 1 CV 2s y nyny d Stabilized process CV 1s CV 2 Physical inputs (valves) Optimally constant valves Always active constraints 65 Main objectives control system 1.Implementation of acceptable (near-optimal) operation 2.Stabilization ARE THESE OBJECTIVES CONFLICTING? Usually NOT Different time scales Stabilization fast time scale Stabilization doesnt use up any degrees of freedom Reference value (setpoint) available for layer above But it uses up part of the time window (frequency range) 66 Example: Exothermic reactor (unstable) u = cooling flow (q) y 1 = composition (c) y 2 = temperature (T) u TC y 2 =T y 2s CC y 1 =c y 1s feed product cooling LC L s =max Active constraints (economics): Product composition c + level (max) 67 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. 68 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 ): 1.Liquid level condenser (M D ) 2.Liquid level reboiler (M B ) 3.Pressure (p) 4.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 69 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 70 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 71 Summary. Systematic procedure for plantwide control Start top-down with economics: Step 1: Define operational objectives and identify degrees of freeedom Step 2: Optimize steady-state operation. Step 3A: Identify active constraints = primary CVs c. Step 3B: Remaining unconstrained DOFs: Self-optimizing CVs c. Step 4: Where to set the throughput (usually: feed) Regulatory control I: Decide on how to move mass through the plant: Step 5A: Propose local-consistent inventory (level) control structure. Regulatory control II: Bottom-up stabilization of the plant Step 5B: Control variables to stop drift (sensitive temperatures, pressures,....) Pair variables to avoid interaction and saturation Finally: make link between top-down and bottom up. Step 6: Advanced/supervisory 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 72 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), (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 (2012). More information: 73 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. 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), (2008). DOI /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, (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of Process Control, 18, (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, (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).``Consistent inventory control'',