Control structure design for complete chemical plants (a systematic procedure to plantwide control) Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Based on: Plenary presentation at ESCAPE’12, May 2002 Updated/expanded April 2004 for 2.5 h tutorial in Vancouver, Canada Further updated: August 2004, December 2004

Outline 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 ? (primary CV’s) (self-optimizing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control (secondary CV’s) ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

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

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

Idealized view II: Optimizing control

Practice II: Hierarchical decomposition with separate layers What should we control?

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.

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 “Ph.D” control

Each plant usually different – modeling expensive 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

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!

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

Regulatory control (seconds) Purpose: “Stabilize” the plant by controlling selected ‘’secondary’’ variables (y2) such that the plant does not drift too far away from its desired operation Use simple single-loop PI(D) controllers Status: Many loops poorly tuned Most common setting: Kc=1, I=1 min (default) Even wrong sign of gain Kc ….

Regulatory control……... Trend: Can do better! Carefully go through plant and retune important loops using standardized tuning procedure Exists many tuning rules, including Skogestad (SIMC) rules: Kc = (1/k) (1/ [c +]) I = min (1, 4[c + ]), Typical: c= “Probably the best simple PID tuning rules in the world” © Carlsberg Outstanding structural issue: What loops to close, that is, which variables (y2) to control?

Supervisory control (minutes) Purpose: Keep primary controlled variables (c=y1) at desired values, using as degrees of freedom the setpoints y2s for the regulatory layer. Status: Many different “advanced” controllers, including feedforward, decouplers, overrides, cascades, selectors, Smith Predictors, etc. Issues: Which variables to control may change due to change of “active constraints” Interactions and “pairing”

Supervisory control…... Trend: Model predictive control (MPC) used as unifying tool. Linear multivariable models with input constraints Tuning (modelling) is time-consuming and expensive Issue: When use MPC and when use simpler single-loop decentralized controllers ? MPC is preferred if active constraints (“bottleneck”) change. Avoids logic for reconfiguration of loops Outstanding structural issue: What primary variables c=y1 to control?

Local optimization (hour) Purpose: Minimize cost function J and: Identify active constraints Recompute optimal setpoints y1s 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

Objectives of layers: MV’s and CV’s RTO Min J; MV=y1s cs = y1s CV=y1; MV=y2s MPC y2s PID CV=y2; MV=u u (valves)

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

Stepwise procedure plantwide control I. TOP-DOWN Step 1. DEGREES OF FREEDOM Step 2. OPERATIONAL OBJECTIVES Step 3. WHAT TO CONTROL? (primary CV’s c=y1) Step 4. PRODUCTION RATE II. BOTTOM-UP (structure control system): Step 5. REGULATORY CONTROL LAYER (PID) “Stabilization” What more to control? (secondary CV’s y2) Step 6. SUPERVISORY CONTROL LAYER (MPC) Decentralization Step 7. OPTIMIZATION LAYER (RTO) Can we do without it?

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

Step 1. Degrees of freedom (DOFs) m – dynamic (control) degrees of freedom = valves u0 – steady-state degrees of freedom Nm : no. of dynamic (control) DOFs (valves) Nu0 = Nm- N0 : no. of steady-state DOFs N0 = N0y + N0m : no. of variables with no steady-state effect N0m : no. purely dynamic control DOFs N0y : no. controlled variables (liquid levels) with no steady-state effect Cost J depends normally only on steady-state DOFs

Distillation column with given feed Nm = 5, N0y = 2, Nu0 = 5 - 2 = 3 (2 with given pressure)

Heat-integrated distillation process

Heat exchanger with bypasses

Typical number of steady-state degrees of freedom (u0) 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) adiabatic flash tank: 1 (0 with fixed pressure) liquid phase reactor: 1 (volume) gas phase reactor: 1 (0 with fixed pressure) heat exchanger: 1 (duty or net area) distillation column excluding heat exchangers: 1 (0 with fixed pressure) + number of sidestreams

Otherwise: Need to add equipment 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

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

Optimal operation (economics) What are we going to use our degrees of freedom for? Define scalar cost function J(u0,x,d) u0: degrees of freedom d: disturbances x: states (internal variables) Typical cost function: Optimal operation for given d: minu0 J(u0,x,d) subject to: Model equations: f(u0,x,d) = 0 Operational constraints: g(u0,x,d) < 0 J = cost feed + cost energy – value products

NEW SLIDE IN HERE 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

Step 3. What should we control (c)? Outline Implementation of optimal operation Self-optimizing control Uncertainty (d and n) Example: Marathon runner Methods for finding the “magic” self-optimizing variables: A. Large gain: Minimum singular value rule B. “Brute force” loss evaluation C. Optimal combination of measurements Example: Recycle process Summary

Implementation of optimal operation Optimal operation for given d*: minu0 J(u0,x,d) subject to: Model equations: f(u0,x,d) = 0 Operational constraints: g(u0,x,d) < 0 → u0opt(d*) Problem: Cannot keep u0opt constant because disturbances d change Distillation: Steady-state degrees of freedom u0 could be L/D and V. Cannot keep these constant

Problem: Too complicated Implementation of optimal operation (Cannot keep u0opt constant) ”Obvious” solution: Optimizing control Estimate d from measurements and recompute u0opt(d) Problem: Too complicated (requires detailed model and description of uncertainty)

and control c at constant setpoint cs = copt(d*) Implementation of optimal operation (Cannot keep u0opt constant) Simpler solution: Look for another variable c which is better to keep constant Note: u0 will indirectly change when d changes and control c at constant setpoint cs = copt(d*)

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(u0,d) = 0 CONTROL ACTIVE CONSTRAINTS! cs = value of active constraint Implementation of active constraints is usually simple. WHAT MORE SHOULD WE CONTROL? Find variables c for remaining unconstrained degrees of freedom u. Distillation slides in here

What should we control? (primary controlled variables y1=c) Intuition: “Dominant variables” (Shinnar) Systematic: Minimize cost J(u0,d*) w.r.t. DOFs u0. Control active constraints (constant setpoint is optimal) Remaining unconstrained DOFs: Control “self-optimizing” variables c for which constant setpoints cs = copt(d*) give small (economic) loss Loss = J - Jopt(d) when disturbances d ≠ d* occur c = ? (economics) y2 = ? (stabilization)

Self-optimizing Control Self-optimizing control is when acceptable operation can be achieved using constant set points (cs) for the controlled variables c (without the need to re-optimizing when disturbances occur). c=cs

The difficult unconstrained variables Cost J Jopt c copt Selected controlled variable (remaining unconstrained)

cs = copt(d*) – nominal optimization Implementation of unconstrained variables is not trivial: How do we deal with uncertainty? 1. Disturbances d (copt(d) changes) 2. Implementation error n (actual c ≠ copt) cs = copt(d*) – nominal optimization n c = cs + n d Cost J  Jopt(d)

Problem no. 1: Disturbance d d ≠ d* Cost J d* Jopt Loss with constant value for c copt(d*) Controlled variable ) Want copt independent of d

Example: Tennessee Eastman plant J c = Purge rate Nominal optimum setpoint is infeasible with disturbance 2 Oopss.. bends backwards Conclusion: Do not use purge rate as controlled variable

Problem no. 2: Implementation error n Cost J d* Loss due to implementation error for c Jopt cs=copt(d*) c = cs + n ) Want n small and ”flat” optimum

Effect of implementation error on cost (“problem 2”) Good Good BAD

c = Temperature top of column Example sharp optimum. High-purity distillation : c = Temperature top of column Temperature Ttop Water (L) - acetic acid (H) Max 100 ppm acetic acid 100 C: 100% water 100.01C: 100 ppm 99.99 C: Infeasible

Summary unconstrained variables: Which variable c to control? Self-optimizing control: Constant setpoints cs give ”near-optimal operation” (= acceptable loss L for expected disturbances d and implementation errors n) Acceptable loss ) self-optimizing control

Examples self-optimizing control Marathon runner Central bank Cake baking Business systems (KPIs) Investment portifolio Biology Chemical process plants: Optimal blending of gasoline Define optimal operation (J) and look for ”magic” variable (c) which when kept constant gives acceptable loss (self-optimizing control)

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

Self-optimizing Control – Marathon Optimal operation of Marathon runner, J=T Any self-optimizing variable c (to control at constant setpoint)? c1 = distance to leader of race c2 = speed c3 = heart rate c4 = level of lactate in muscles

Self-optimizing Control – Marathon Optimal operation of Marathon runner, J=T Any self-optimizing variable c (to control at constant setpoint)? c1 = distance to leader of race (Problem: Feasibility for d) c2 = speed (Problem: Feasibility for d) c3 = heart rate (Problem: Impl. Error n) c4 = level of lactate in muscles (Problem: Large impl.error n)

Self-optimizing Control – Sprinter Optimal operation of Sprinter (100 m), J=T Active constraint control: Maximum speed (”no thinking required”)

Further examples 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 Need to do ”reverse engineering” : Find the controlled variables used in nature From this possibly identify what overall objective J the biological system has been attempting to optimize

Shinnar (1981): Control “Dominant variables” (undefined..) Unconstrained degrees of freedom: Looking for “magic” variables to keep at constant setpoints. What properties do they have? Shinnar (1981): Control “Dominant variables” (undefined..) 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 Avoid problem 1 (d) Avoid problem 2 (n)

A. Minimum singular value rule: Unconstrained degrees of freedom: Looking for “magic” variables to keep at constant setpoints. How can we find them systematically? A. Minimum singular value rule: B. “Brute force”: Consider available measurements y, and evaluate loss when they are kept constant: C. More general: Find optimal linear combination (matrix H):

Unconstrained degrees of freedom: A. Minimum singular value rule J Optimizer c cs n cm=c+n n Controller that adjusts u to keep cm = cs cs=copt u c d Plant uopt u Want the slope (= gain G from u to y) as large as possible

Unconstrained degrees of freedom: A. Minimum singular value rule Minimum singular value rule (Skogestad and Postlethwaite, 1996): Look for variables c that maximize the minimum singular value (G) of the appropriately scaled steady-state gain matrix G from u to c u: unconstrained degrees of freedom Loss Scaling is important: Scale c such that their expected variation is similar (divide by “span”= optimal variation + noise) Scale inputs u such that they have similar effect on cost J (Juu unitary) (G) is called the Morari Resiliency index (MRI) by Luyben Detailed proof: 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).

Minimum singular value rule in words Select controlled variables c for which their controllable range is large compared to their sum of optimal variation and control error controllable range = range c may reach by varying the inputs (=gain) optimal variation: due to disturbance control error = implementation error n span

What should we control? Rule: Maximize the scaled gain Scalar case. Minimum singular value = gain |G| Maximize scaled gain: |Gs| = |G| / span |G|: gain from independent variable (u) to candidate controlled variable (c) span (of c) = optimal variation in c + control error for c

B. “Brute-force” procedure for selecting (primary) controlled variables (Skogestad, 2000) Step 3.1 Determine DOFs for optimization Step 3.2 Definition of optimal operation J (cost and constraints) Step 3.3 Identification of important disturbances Step 3.4 Optimization (nominally and with disturbances) Step 3.5 Identification of candidate controlled variables (use active constraint control) Step 3.6 Evaluation of loss with constant setpoints for alternative controlled variables Step 3.7 Evaluation and selection (including controllability analysis) Case studies: Tenneessee-Eastman, Propane-propylene splitter, recycle process, heat-integrated distillation

B. Brute-force procedure Define optimal operation: Minimize cost function J Each candidate variable c: With constant setpoints cs compute loss L for expected disturbances d and implementation errors n Select variable c with smallest loss Acceptable loss ) self-optimizing control

Basis: Want optimal value of c independent of disturbances ) Unconstrained degrees of freedom: C. Optimal measurement combination (Alstad, 2002) Basis: Want optimal value of c independent of disturbances )  copt = 0 ¢  d Find optimal solution as a function of d: uopt(d), yopt(d) Linearize this relationship: yopt = F d F – sensitivity matrix Want: To achieve this for all values of  d: Always possible if Optimal when we disregard implementation error (n)

Alstad-method continued To handle implementation error: Use “sensitive” measurements, with information about all independent variables (u and d)

Toy Example

Toy Example

Toy Example

EXAMPLE: Recycle plant (Luyben, Yu, etc.) 5 4 1 Given feedrate F0 and column pressure: 2 3 Dynamic DOFs: Nm = 5 Column levels: N0y = 2 Steady-state DOFs: N0 = 5 - 2 = 3

Recycle plant: Optimal operation mT 1 remaining unconstrained degree of freedom

Control of recycle plant: Conventional structure (“Two-point”: xD) LC LC xD XC XC xB LC Control active constraints (Mr=max and xB=0.015) + xD

Luyben rule Luyben rule (to avoid snowballing): “Fix a stream in the recycle loop” (F or D)

Luyben rule: D constant LC LC XC LC Luyben rule (to avoid snowballing): “Fix a stream in the recycle loop” (F or D)

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

B. “Brute force” loss evaluation: Disturbance in F0 Luyben rule: Conventional Loss with nominally optimal setpoints for Mr, xB and c

B. “Brute force” loss evaluation: Implementation error Luyben rule: Loss with nominally optimal setpoints for Mr, xB and c

C. Optimal measurement combination 1 unconstrained variable (#c = 1) 1 (important) disturbance: F0 (#d = 1) “Optimal” combination requires 2 “measurements” (#y = #u + #d = 2) For example, c = h1 L + h2 F BUT: Not much to be gained compared to control of single variable (e.g. L/F or xD)

Conclusion: Control of recycle plant Active constraint Mr = Mrmax Self-optimizing L/F constant: Easier than “two-point” control Assumption: Minimize energy (V) Active constraint xB = xBmin

Recycle systems: Do not recommend Luyben’s rule of fixing a flow in each recycle loop (even to avoid “snowballing”)

Summary ”self-optimizing” control Operation of most real system: Constant setpoint policy (c = cs) Central bank Business systems: KPI’s Biological systems Chemical processes Goal: Find controlled variables c such that constant setpoint policy gives acceptable operation in spite of uncertainty ) Self-optimizing control Method A: Maximize (G) Method B: Evaluate loss L = J - Jopt Method C: Optimal linear measurement combination: c = H y where HF=0 More examples later

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

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

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

Production rate set at outlet: Inventory control opposite flow

Production rate set inside process

Definition of bottleneck A unit (or more precisely, an extensive variable E within this unit) is a bottleneck (with respect to the flow F) if - With the flow F as a degree of freedom, the variable E is optimally at its maximum constraint (i.e., E= Emax at the optimum) - The flow F is increased by increasing this constraint (i.e., dF/dEmax > 0 at the optimum). A variable E is a dynamic( control) bottleneck if in addition - The optimal value of E is unconstrained when F is fixed at a sufficiently low value Otherwise E is a steady-state (design) bottleneck.

Reactor-recycle process: Given feedrate with production rate set at inlet

Reactor-recycle process: Reconfiguration required when reach bottleneck (max. vapor rate in column)

Reactor-recycle process: Given feedrate with production rate set at bottleneck (column) F0s

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

II. Bottom-up Determine secondary controlled variables and structure (configuration) of control system (pairing) A good control configuration is insensitive to parameter changes Step 5. REGULATORY CONTROL LAYER 5.1 Stabilization (including level control) 5.2 Local disturbance rejection (inner cascades) What more to control? (secondary variables) Step 6. SUPERVISORY CONTROL LAYER Decentralized or multivariable control (MPC)? Pairing? Step 7. OPTIMIZATION LAYER (RTO)

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 ? Bonus: A little about tuning and “half rule” Step 6: Supervisory control Step 7: Real-time optimization Case studies

Step 5. Regulatory control layer Purpose: “Stabilize” the plant using local SISO PID controllers Enable manual operation (by operators) Main structural issues: What more should we control? (secondary cv’s, y2) Pairing with manipulated variables (mv’s u2) y1 = c y2 = ?

Example: Distillation Primary controlled variable: y1 = c = y,x (compositions top, bottom) BUT: Delay in measurement of x + unreliable Regulatory control: For “stabilization” need control of: Liquid level condenser (MD) Liquid level reboiler (MB) Pressure (p) Holdup of light component in column (temperature profile) No steady-state effect

ys y XC Ts T TC Ls L FC z XC

Degrees of freedom unchanged No degrees of freedom lost by control of secondary (local) variables as setpoints become y2s replace inputs u2 as new degrees of freedom Cascade control: G K y2s u2 y2 y1 Original DOF New DOF

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 control) Make control problem easy as seen from layer above Stabilization (mathematical sense) Local disturbance rejection Local linearization (avoid “drift” due to disturbances) “stabilization” (practical sense) Implications for selection of y2: Control of y2 “stabilizes the plant” y2 is easy to control (favorable dynamics)

1. “Control of y2 stabilizes the plant” “Mathematical stabilization” (e.g. reactor): Unstable mode is “quickly” detected (state observability) in the measurement (y2) and is easily affected (state controllability) by the input (u2). Tool for selecting input/output: Pole vectors y2: Want large element in output pole vector: Instability easily detected relative to noise u2: Want large element in input pole vector: Small input usage required for stabilization “Extended stabilization” (avoid “drift” due to disturbance sensitivity): Intuitive: y2 located close to important disturbance Or rather: Controllable range for y2 is large compared to sum of optimal variation and control error More exact tool: Partial control analysis

Recall rule for selecting primary controlled variables c: Controlled variables c for which their controllable range is large compared to their sum of optimal variation and control error Restated for secondary controlled variables y2: Control variables y2 for which their controllable range is large compared to their sum of optimal variation and control error controllable range = range y2 may reach by varying the inputs optimal variation: due to disturbances control error = implementation error n Want large Want small

What should we control? Rule: Maximize the scaled gain Scalar case. Minimum singular value = gain |G| Maximize scaled gain: |Gs| = |G| / span |G|: gain from independent variable (u) to candidate controlled variable (y) span (of y) = optimal variation in c + control error for y

Implication for selecting temperature control stage (y2) in distillation Consider controlling temperature (y=T) with reflux (u=L) G= “Controllable range”: Given by gain  T/L (“sensitivity”). This will be largest where temperature changes are the largest, that is, toward the feed stage for a binary separation Topt = “Optimal variation” for disturbances (in F, zF, etc.): We want to control compositions. The optimal variation in T will be small towards the end of the column and largest toward the feed stage Terr = “Control error” (=implementation error = static measurement error) – This will typically be 0.5 C and the same on stages Rule: Select location corresponding to max. value of G / (Topt + Terr) Binary separation: This will have a max. in the middle of the top section and middle of bottom section Multicomponent separation: Will have a max. towards column ends

Distillation example columnn A. Which temperature should we control? >> res=[x0' gain' yoptz' yoptq' yoptxb' ] res = 0.0100 1.1461 -0.0000 -0.0000 0.0100 0.0143 1.6249 0.0001 0.0000 0.0141 0.0197 2.2289 0.0005 0.0001 0.0190 0.0267 2.9826 0.0011 0.0002 0.0250 0.0355 3.9105 0.0023 0.0003 0.0321 0.0467 5.0332 0.0040 0.0006 0.0402 0.0605 6.3613 0.0067 0.0010 0.0494 0.0776 7.8877 0.0105 0.0015 0.0591 0.0982 9.5783 0.0157 0.0023 0.0690 0.1229 11.3629 0.0224 0.0032 0.0783 0.1515 13.1315 0.0306 0.0044 0.0862 0.1841 14.7391 0.0403 0.0058 0.0917 0.2202 16.0237 0.0508 0.0073 0.0942 0.2587 16.8365 0.0616 0.0088 0.0932 0.2986 17.0759 0.0718 0.0104 0.0887 0.3385 16.7139 0.0806 0.0117 0.0813 0.3770 15.8040 0.0875 0.0129 0.0716 0.4130 14.4656 0.0923 0.0137 0.0607 0.4455 12.8536 0.0951 0.0143 0.0494 0.4742 11.1248 0.0962 0.0146 0.0385 0.4987 9.4123 0.0959 0.0147 0.0284 0.5265 10.6946 0.0930 0.0144 0.0278 0.5578 11.8664 0.0886 0.0139 0.0267 0.5922 12.8279 0.0827 0.0131 0.0251 0.6290 13.4841 0.0754 0.0120 0.0231 0.6675 13.7626 0.0669 0.0108 0.0206 0.7065 13.6297 0.0578 0.0093 0.0179 0.7449 13.0978 0.0485 0.0079 0.0150 0.7816 12.2229 0.0394 0.0064 0.0122 0.8158 11.0922 0.0310 0.0050 0.0096 0.8469 9.8065 0.0235 0.0038 0.0073 0.8744 8.4631 0.0172 0.0028 0.0053 0.8983 7.1431 0.0121 0.0019 0.0037 0.9187 5.9059 0.0081 0.0013 0.0025 0.9358 4.7883 0.0052 0.0008 0.0016 0.9501 3.8078 0.0030 0.0005 0.0009 0.9617 2.9674 0.0016 0.0002 0.0005 0.9712 2.2603 0.0007 0.0001 0.0002 0.9789 1.6739 0.0002 0.0000 0.0001 0.9851 1.1934 0.0000 0.0000 0.0000 0.9900 0.8033 0.0000 0.0000 0.0000 Distillation example columnn A. Which temperature should we control? Nominal simulation (gives x0) One simulation: Gain with constant inputs (u) Make small change in input (L) with the other inputs (V) constant Find gain =  xi/ V One simulation for each disturbance: “Optimal” change for candidate measurements to disturbances (with inputs adjusted to keep primary variables at setpoint, i.e. xD=0.99, xB=0.01). Find xi,opt (yopt) for the following disturbances F (but this is zero) yoptf=0 zF from 0.5 to 0.6 yoptz qF from 1 to 1.2 yoptq xB from 0.01 to 0.02 yoptxb Control (implementation) error. Assume=0.05 on all stages Find scaled-gain = gain/variation where variation= yoptf+yoptz+yoptq+yoptzb+0.05 “Maximize gain rule”: Prefer stage where scaled-gain is large 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

stage 31 TOP variation=yoptz+yoptq+yoptxb+0.05 plot(gain./variation)

Partial control analysis Primary controlled variable y1 = c (supervisory control layer) Local control of y2 using u2 (regulatory control layer) Setpoint y2s : new DOF for supervisory control

2. “y2 is easy to control” Main rule: y2 is easy to measure and located close to manipulated variable u2 Statics: Want large gain (from u2 to y2) Dynamics: Want small effective delay (from u2 to y2)

Aside: Effective delay and tunings PI-tunings from “SIMC rule” Use half rule to obtain first-order model Effective delay θ = “True” delay + inverse response time constant + half of second time constant + all smaller time constants Time constant τ1 = original time constant + half of second time constant

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 ? (primary CV’s) (self-optimizing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control (secondary CV’s) ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

Step 6. Supervisory control layer Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs Degrees of freedom: Setpoints y2s in reg.control layer Main structural issue: Decentralized or multivariable?

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 active constraints move

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 no need for logic smooth transition - Requires multivariable dynamic model - Tuning may be difficult - Less transparent - “Everything goes down at the same time”

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

Step 7. Optimization layer (RTO) Purpose: Identify active constraints and compute optimal setpoints (to be implemented by supervisory control layer) Main structural issue: Do we need RTO? (or is process self-optimizing)

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 Conclusion / References Case studies

Conclusion Procedure plantwide control: I. Top-down analysis to identify degrees of freedom and primary controlled variables (look for self-optimizing variables) II. Bottom-up analysis to determine secondary controlled variables and structure of control system (pairing).

References http://www.chembio.ntnu.no/users/skoge/ Halvorsen, I.J, Skogestad, S., Morud, J.C., Alstad, V. (2003), “Optimal selection of controlled variables”, Ind.Eng.Chem.Res., 42, 3273-3284. Larsson, T. and S. Skogestad (2000), “Plantwide control: A review and a new design procedure”, Modeling, Identification and Control, 21, 209-240. 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, 4889-4901. Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu (2003), “Control of reactor, separator and recycle process’’, Ind.Eng.Chem.Res., 42, 1225-1234 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, 487-507. Skogestad, S. (2003), ”Simple analytic rules for model reduction and PID controller tuning”, J. Proc. Control, 13, 291-309. Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, 219-234. (Special issue from ESCAPE’12 Symposium, Haag, May 2002). … + more….. See home page of S. Skogestad: http://www.chembio.ntnu.no/users/skoge/