Plantwide control: Towards a systematic procedure

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 ESCAPE12, May 2002 Updated/expanded April 2004 for 2.5 h tutorial in Vancouver, Canada 1 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

2 Case studies Trondheim, Norway 3 Trondheim NORWAY Oslo DENMARK GERMANY UK

4 NTNU, Trondheim 5 Process Control professors: Bjarne Foss Morten Hovd EE Jens Balchen Heinz Preisig ChE Sigurd Skogestad Sigurd Skogestad

6 Born in 1955 1978: Siv.ing. Degree (MS) in Chemical Engineering from NTNU (NTH) 1980-83: Process modeling group at the Norsk Hydro Research Center in Porsgrunn 1983-87: Ph.D. student in Chemical Engineering at Caltech, Pasadena, USA. Thesis on Robust distillation control. Supervisor: Manfred Morari

1987 - : Professor in Chemical Engineering at NTNU Since 1994: Head of process systems engineering center in Trondheim (PROST) Since 1999: Head of Department of Chemical Engineering 1996: Book Multivariable feedback control (Wiley) 2000, 2003: Book Prosessteknikk (Tapir) Group of about 10 Ph.D. students in the process control area Research: Develop simple yet rigorous methods to solve problems of engineering significance.

7 Use of feedback as a tool to 1. reduce uncertainty (including robust control), 2. change the system dynamics (including stabilization; anti-slug control), 3. generally make the system more well-behaved (including selfoptimizing control). limitations on performance in linear systems (controllability), control structure design and plantwide control, interactions between process design and control, distillation column design, control and dynamics. Natural gas processes 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 8 Case studies Idealized view of control (Ph.D. control) 9 Practice: Tennessee Eastman challenge problem (Downs, 1991) (PID control) 10

Idealized view II: Optimizing control 11 Practice II: Hierarchical decomposition with separate layers What should we control? 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 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.).

14 That is: Control structure design includes all the decisions we need make to get from ``PID control to Ph.D control 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 15 Previous work on plantwide control

16 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 ECC03 about flight control at Boeing:

The most important control issue has always been to select the right controlled variables --- no systematic tools used! 17 Main simplification: Hierarchical structure RTO MPC PID 18 Need to define objectives and identify main issues for each

layer 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 .

19 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 = 0.5/k (1/) I = min (1, 8) Probably the best simple PID tuning rules in the world Carlsberg

20 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 21 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? 22 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 23 Objectives of layers: MVs and CVs RTO Min J; MV=y1s cs = y1s CV=y1; MV=y2s

MPC y2s PID 24 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-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 25

Case studies Stepwise procedure plantwide control I. TOP-DOWN Step 1. DEGREES OF FREEDOM Step 2. OPERATIONAL OBJECTIVES Step 3. WHAT TO CONTROL? (primary CVs c=y1) Step 4. PRODUCTION RATE II. BOTTOM-UP (structure control system): Step 5. REGULATORY CONTROL LAYER (PID) Stabilization What more to control? (secondary CVs y2) Step 6. SUPERVISORY CONTROL LAYER (MPC) Decentralization Step 7. OPTIMIZATION LAYER (RTO) Can we do without it? 26

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 27 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 28 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) 29 Heat-integrated distillation process Nm = 11 (w/feed), N0y = 4 (levels), Nu0 = 11 4 = 7 30 Heat exchanger with bypasses CW Nm = 3, N0m = 2 (of 3), N0y = 3 2 = 1 31 Typical number of steady-state degrees of

freedom (u0) for some process units 32 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 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 33

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 34 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: J = cost feed + cost energy value products 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 35 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 36 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 37 Example: Recycle process Summary Implementation of optimal operation Optimal operation for given d*: minu0 J(u0,x,d) subject to: Model equations:

Operational constraints: u0opt(d*) f(u0,x,d) = 0 g(u0,x,d) < 0 Problem: Cannot keep u0opt constant because disturbances d change 38 Implementation of optimal operation (Cannot keep u0opt constant) Obvious solution: Optimizing control Estimate d from measurements and recompute u0opt(d) Probem: Too complicated (requires detailed model and description of

uncertainty) 39 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*) 40 What cs should we control?

Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy active constraints, g(u 0,d) = 0 CONTROL ACTIVE CONSTRAINTS! 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. 41 What should we control? (primary controlled variables y1=c) Intuition: Dominant variables (Shinnar)

Systematic: Minimize cost J(u0,d*) w.r.t. DOFs u0. 1. Control active constraints (constant setpoint is optimal) 2. 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 42 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 re-optimizing when disturbances occur). c=cs 43 The difficult unconstrained variables Cost J Jopt c

copt 44 Selected controlled variable (remaining unconstrained) 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) 45

Problem no. 1: Disturbance d d d* Cost J d* Jopt Loss with constant value for c copt(d*) 46 ) Want copt independent of d Controlled variable

Example: Tennessee Eastman plant J Oopss.. bends backwards c = Purge rate Nominal optimum setpoint is infeasible with disturbance 2 Conclusion: Do not use purge rate as controlled variable 47 Problem no. 2: Implementation error n Cost J d* Loss due to implementation error for c

Jopt cs=copt(d*) 48 c = cs + n ) Want n small and flat optimum Effect of implementation error on cost (problem 2) Good 49 Good

BAD Example sharp optimum. High-purity distillation : c = Temperature top of column Ttop Water (L) - acetic acid (H) Max 100 ppm acetic acid 100 C: 100% water 100.01C: 100 ppm 99.99 C: Infeasible Temperature 50 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) 51 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 (selfoptimizing control) 52 Self-optimizing Control Marathon Optimal operation of Marathon runner, J=T Any self-optimizing variable c (to control at constant

setpoint)? 53 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 54 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 : 55 Find the controlled variables used in nature From this possibly identify what overall objective J the biological system has been attempting to optimize 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 Avoid problem 1 (d) c should be easy to measure and control accurately The value of c should be sensitive to changes in the steadystate degrees of freedom (Equivalently, J as a function of c should be flat) For cases with more than one unconstrained degrees of Avoid problem 2 (n) freedom, the selected controlled variables should be independent. Summarized by minimum singular value 56 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): 57 Unconstrained degrees of freedom: A. Minimum singular value rule J Optimizer c

cs Controller that adjusts u to keep cm = cs cm=c+n n n cs=copt u d c Plant

uopt Want the slope (= gain G from u to y) as large as possible 58 u 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 ) 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 optimal variation + noise) Scale inputs u such that they have similar effect on cost J (J uu unitary) 59 (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 optimal variation: due to disturbance

control error = implementation error n 60 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 61 B. Brute-force procedure 62 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

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 63

Want: To achieve this for all values of d: Always possible if Optimal when we disregard implementation error (n) EXAMPLE: Recycle plant (Luyben, Yu, etc.) 5

4 1 Given feedrate F0 and column pressure: 64 Dynamic DOFs: Nm = 5 Column levels: N0y = 2 Steady-state DOFs: N0 = 5 - 2 = 3 2 3 Recycle plant: Optimal operation mT

1 remaining unconstrained degree of freedom 65 Control of recycle plant: Conventional structure (Two-point: xD) LC LC x XC D XC xB LC

Control active constraints (Mr=max and xB=0.015) + xD 66 Luyben rule 67 Luyben rule (to avoid snowballing): Fix a stream in the recycle loop (F or D) Luyben rule: D constant LC LC XC LC

68 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 69 B. Brute force loss evaluation: Disturbance in F0 Luyben rule:

Conventional 70 Loss with nominally optimal setpoints for Mr, xB and c B. Brute force loss evaluation: Implementation error Luyben rule: 71 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 72 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 73 L/F constant: Easier than two-point control Assumption: Minimize energy (V) Active constraint xB = xBmin Recycle systems: Do not recommend Luybens rule of fixing a flow in each recycle loop (even to avoid snowballing) 74 Summary self-optimizing control

Operation of most real system: Constant setpoint policy (c = cs) Central bank Business systems: KPIs Biological systems Chemical processes G) of the appropriately scaled steady-state gain matrix oal: Find controlled variables c such that constant setpoint policy gives acceptable operation in spite of uncertainty ) Self-optimizing control

Method A: Maximize (G) of the appropriately scaled steady-state gain matrix ) Method B: Evaluate loss L = J - Jopt Method C: Optimal linear measurement combination: c = H y where HF=0 More examples later 75 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

76 Case studies Step 4. Where set production rate? 77 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 78 Production rate set at outlet: Inventory control opposite flow 79 Production rate set inside process 80 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. 81 Reactor-recycle process: Given feedrate with production rate set at inlet 82 Reactor-recycle process: Reconfiguration required when reach bottleneck (max. vapor rate in column)

MAX 83 Reactor-recycle process: Given feedrate with production rate set at bottleneck (column) F0s 84 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

85 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 5.2 Stabilization (including level control) Local disturbance rejection (inner cascades) What more to control? (secondary variables) Step 6. SUPERVISORY CONTROL LAYER

Decentralized or multivariable control (MPC)? Pairing? 86 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 87 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 cvs, y2) Pairing with manipulated variables (mvs u2) y1 = c y2 = ? 88 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: y2s New DOF 89 K u2 G y1 Original DOF

y2 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

stabilization Local linearization (avoid drift due to disturbances) (practical sense) Implications for selection of y2: 1. Control of y2 stabilizes the plant 90 2. 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 91 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 92 Want small Want large 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 y1 = P1 u1 + Pr1 (y2s-n2) + Pd1 d P1 = G11 G12 G22-1 G21 Pd1 = Gd1 G12 G22-1 Gd2 - WANT SMALL Pr1 = G12 G22-1 93 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) 94

Aside: Effective delay and tunings PI-tunings from SIMC rule Use half rule to obtain first-order model Effective delay = True delay + inverse response time constant + half of second time constant + all smaller time constants Time constant 1 = original time constant + half of second time constant 95 Example cascade control (PI) d=6 ys

96 K1 y2s K2 u2 G2 y2 G1 y1

Example cascade control (PI) d=6 ys K1 y2s K2 Without cascade With cascade 97 u

G2 y2 G1 y1 Example cascade control Inner fast (secondary) loop: P or PI-control Local disturbance rejection Much smaller effective delay (0.2 s)

Outer slower primary loop: Reduced effective delay (2 s instead of 6 s) Time scale separation 98 Inner loop can be modelled as gain=1 + 2*effective delay (0.4s) Very effective for control of large-scale systems 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 99 Case studies Step 6. Supervisory control layer 10 0 Purpose: Keep primary controlled outputs c=y 1 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 10

1 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 - 10 2 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 10 3 Case studies Step 7. Optimization layer (RTO)

10 4 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 selfoptimizing) 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 10 5

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). 10 6 References

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 ESCAPE12 Symposium, Haag, May 2002). + more.. See home page of S. Skogestad: 10 7

http://www.chembio.ntnu.no/users/skoge/

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    UK EE DE FR AT BE EU28 SK ES LT CZ LV SI MT HU IE PT CY IT PL EL HR BG RO 0.15027699999999999 0.14004800000000001 0.124709 0.12820200000000001 0.14577899999999999 ... (EURES). To help people make informed career and learning choices,...
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    CTC / MTC 222 Strength of Materials Chapter 6 Centroids and Moments of Inertia of Areas Chapter Objectives Define centroid and locate the centroid of a shape by inspection or calculation Define moment of inertia and compute its values with...
  • Health Safety and Environmental Management The Compliance Consultancy

    Health Safety and Environmental Management The Compliance Consultancy

    An innovative approach to Bridge Building - Build the unit on flat ground, once finished dig the "Roadway" under it We choose collective control measures whenever possible because it protects the greater number of people, it only requires that nobody...
  • Crosby/Krieger - Idaho State University

    Crosby/Krieger - Idaho State University

    Constitutive Equations: expressions that describe the relationships between stress and strain, or stress and rates of distortion. Goal: to relate stress tensor to strain tensor. Not derived from general laws of mechanics but rather from empirical (laboratory or field) observations!...
  • Introduction to English and Metric Measurement

    Introduction to English and Metric Measurement

    Count the number of whole centimeters (cm). These are the larger lines with numbers. 2. Count the number of lines after the whole number. The smaller lines are millimeters (mm). 3. Put in correct terms. Since mm are 1/10th of...