PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering

PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Sept. 2005

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”)

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

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. ( ) – case studies ; “snowball effect” George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes Ruel Shinnar ( ) - “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)

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 = , N0y = , Nu0 =

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 “given” pressure) liquid phase reactor: 1 (volume) gas phase reactor: 1 (0 with “given” pressure) heat exchanger: 1 (duty or net area) distillation column excluding heat exchangers: 1 (0 with “given” pressure) + number of sidestreams Comment “given” pressure: Either (1) pressure is fixed, or (2) there is no MV (valve) for setting the pressure in the unit, so it is “given” by the surrounding process

HDA process Mixer FEHE Furnace PFR Quench Separator Compressor Cooler
Stabilizer Benzene Column Toluene H2 + CH4 CH4 Diphenyl Purge (H2 + CH4)

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

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

Optimal operation distillation column
Steady-state DOFs (given p and F): 2, for example L/D and V Cost to be minimized (economics) J = - P where P= pD D + pB B – pF F – pV V Constraints Purity D: For example xD, impurity · max Purity B: For example, xB, impurity · max Flow constraints: min · D, B, L etc. · max Column capacity (flooding): V · Vmax, etc. Pressure: 1) p given, 2) p free: pmin · p · pmax Feed: ) F given 2) F free: F · Fmax Optimal operation: Minimize J with respect to steady-state DOFs cost energy (heating+ cooling) value products cost feed

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.

Solution to optimal operation distillation
Cost to be minimized J = - P where P= pD D + pB B – pF F – pV V Optimal operation: Minimize J with respect to DOFs General: Optimal solution with N DOFs: N – Nu DOFs used to satisfy “active” constraints (· is =) Nu remaining unconstrained variables Usually: Nu zero or small Distillation at steady state with given p and F: N=2 DOFs. Three cases: Nu=0: Two active constraints (for example, xD, impurity = max. xB, impurity = max, “TWO-POINT” CONTROL) Nu=1: One constraint active Nu=2: No constraints active very unlikely unless there are no purity specifications (e.g. byproducts or recycle)

Remaining unconstrained variables: What should we control
Remaining unconstrained variables: 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: % water 100.01C: 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)?

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

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: 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

Mathematical: Local analysis
cost J u uopt

Skogestad and Postlethwaite (1996):
Unconstrained degrees of freedom: Looking for “magic” variables to keep at constant setpoints. What properties do they have? Skogestad and Postlethwaite (1996): c-copt should be small: The optimal value of c should be insensitive to disturbances c should be easy to measure and control accurately G-1 should be small, i.e (G) should be large: 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 maximum gain (min. singular value) rule Avoid problem 1 (d) Avoid problem 2 (n)

A. Maximum gain (minimum singular value) rule:
Unconstrained degrees of freedom: Looking for “magic” variables to keep at constant setpoints. How can we find them systematically? A. Maximum gain (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. Maximum gain 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

“Maximum gain rule” (Skogestad and Postlethwaite, 1996):
Unconstrained degrees of freedom: A. Maximum gain (minimum singular value) rule “Maximum gain 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), (2003).

Maximum gain 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

Generally (more than unconstrained variable): Scaling for “maximum gain () rule”
“Control active constraints” and look at the remaining unconstrained problem Candidate outputs: Divide by span = optimal range + implementation error Candidate inputs: A unit deviation in each input should have the same effect on the cost function (i.e. Juu should be constant times identity) Alternatively (often simpler), consider (Juu1/2 G)

B. “Brute-force” procedure for selecting (primary) controlled variables (Skogestad, 2000)
Step 1 Determine DOFs for optimization Step 2 Definition of optimal operation J (cost and constraints) Step 3 Identification of important disturbances Step 4 Optimization (nominally and with disturbances) Step 5 Identification of candidate controlled variables (use active constraint control) Step 6 Evaluation of loss with constant setpoints for alternative controlled variables Step 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

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 = = 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. Maximum gain 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: Procedure selection controlled variables
Define economics and operational constraints Identify degrees of freedom and important disturbances Optimize for various disturbances Identify (and control) active constraints (off-line calculations) May vary depending on operating region. For each operating region do step 5: Identify “self-optimizing” controlled variables for remaining degrees of freedom (A) Identify promising (single) measurements from “maximize gain rule” (gain = minimum singular value) (C) Possibly consider measurement combinations if no promising (B) “Brute force” evaluation of loss for promising alternatives Necessary because “maximum gain rule” is local. In particular: Look out for feasibility problems. Controllability evaluation for promising alternatives

Selection of controlled variables More examples and exercises
HDA process Cooling cycle Distillation (C3-splitter) Blending

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

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

Where set the production rate?
Very important decision that determines the structure of the rest of the control system! May also have important economic implications

Often optimal: Set production rate at bottleneck!
"A bottleneck is an extensive variable that prevents an increase in the overall feed rate to the plant" If feed is cheap and available: Optimal to set production rate at bottleneck If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered.

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

Bottleneck: max. vapor rate in column
Reactor-recycle process: Given feedrate with production rate set at inlet Bottleneck: max. vapor rate in column

Bottleneck: max. vapor rate in column
Reactor-recycle process with production rate set at inlet Want to maximize feedrate: reach bottleneck in column Alt.1: Loss Bottleneck: max. vapor rate in column Vs FC Vmax V Vmax-Vs=Back-off = Loss

Reactor-recycle process with increased feedrate: Optimal: Set production rate at bottleneck
Alt.2 “long loop” MAX

Reactor-recycle process with increased feedrate: Optimal: Set production rate at bottleneck
Alt.3: reconfigure MAX

Alt.3: reconfigure (permanently) F0s
Reactor-recycle process: Given feedrate with production rate set at bottleneck Alt.3: reconfigure (permanently) F0s

Alt.4: Multivariable control (MPC)
Can reduce loss BUT: Is generally placed on top of the regulatory control system (including level loops), so it still important where the production rate is set!

Conclusion production rate manipulator
Think carefully about where to place it! Difficult to undo later

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

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)

Example: Distillation
Primary controlled variable: y1 = c = xD, xB (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) Unstable (Integrating) + No steady-state effect Disturbs (“destabilizes”) other loops Almost unstable (integrating)

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 = ?

Cascade control distillation 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

Hierarchical control: Time scale separation
With a “reasonable” time scale separation between the layers (typically by a factor 5 or more in terms of closed-loop response time) we have the following advantages: The stability and performance of the lower (faster) layer (involving y2) is not much influenced by the presence of the upper (slow) layers (involving y1) Reason: The frequency of the “disturbance” from the upper layer is well inside the bandwidth of the lower layers With the lower (faster) layer in place, the stability and performance of the upper (slower) layers do not depend much on the specific controller settings used in the lower layers Reason: The lower layers only effect frequencies outside the bandwidth of the upper layers

Objectives regulatory control layer
Allow for manual operation Simple decentralized (local) PID controllers that can be tuned on-line Take care of “fast” control Track setpoint changes from the layer above Local disturbance rejection Stabilization (mathematical sense) Avoid “drift” (due to disturbances) so system stays in “linear region” “stabilization” (practical sense) Allow for “slow” control in layer above (supervisory control) Make control problem easy as seen from layer above 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”
A. “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 B. “Practical 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 (y2)? 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 Note optimal variation: This is generally NOT the same as the optimal variation used for selecting primary controlled variables (c) because we at the “fast” regulatory time scale have that the “slower” (unused) inputs (u1) are constant. For each disturbance find optimal input change (u2) that keeps primary variables c=y1 closest to setpoint (with u1 constant), and from this obtain optimal variation (copt)

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 NOTE: The first (largest) time constant is NOT important for controllability!

Summary: Rules for selecting y2
y2 should be easy to measure Control of y2 stabilizes the plant y2 should have good controllability, that is, favorable dynamics for control y2 should be located “close” to a manipulated input (u2) (follows from rule 3) The (scaled) gain from u2 to y2 should be large Additional rule for selecting u2: Avoid using inputs u2 that may saturate (should generally avoid saturation in lower layers)

Exercise level control (10.1 in Seborg)
Consider control of liquid condenser level (M1) in a distillation column. Should we use L or D to control M1? What is your answer if L/D=5? What is your answer if it is important to avoid disturbing downstream process?

LV-configuration preferred in practice for most columns
(even when L and V are large) ys y XC Ts T TC Ls L FC z XC

Exercise distillation (10.3 in Seborg)
Consider a column design to separate methanol and water. The desired distillate composition (xD) is methanol with only 5 ppm of water. Because a composition analyzer is not available, it is proposed to control XD indirectly by measuring and controlling a temperature at one of the following locations the reflux stream the top tray (stage) of the column an intermediate tray in the top section (where?) Discuss the relative advantages and disadvantages of each choice based on both steady-state and dynamic considerations

More exact: Selecting stage for temperature control (y2) in distillation
Consider controlling temperature (y=T) with reflux (u=L) Avoid V because it may saturate (i.e. reach maximum) 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.): This is generally NOT the same as the optimal variation used for selecting primary controlled variables (c) because we have to assume that the “slower” variables (e.g. u1=V) are constant. Here: We want to control product 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. u=L. Which temperature (c) to 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/ L From process gains: Obtain “optimal” change for candidate measurements to disturbances, (with input L adjusted to keep both xD and xB close to setpoint, i.e. min ||xD-0.99; xb-0.01|| , with V=constant). w=[xB,xD]. Then (- Gy pinv(Gw) Gwd + Gyd) d (Note: Gy=gain, d=F: Gyd=gainf etc.) Find xi,opt (yopt) for the following disturbances F (from 1 to 1.2; has effect!) yoptf zF from 0.5 to 0.6 yoptz qF from 1 to 1.2 yoptq xB from 0.01 to 0.02 yoptxb=0 (no effect) Control (implementation) error. Assume=0.05 on all stages Find scaled-gain = gain/span where span = abs(yoptf)+abs(yoptz)+abs(yoptq)+0.05 “Maximize gain rule”: Prefer stage where scaled-gain is large >> res=[x0' gain' gainf' gainz' gainq'] res =

u=L Gwf = 0.5862 0.3938 >> Gw Gw = 1.0853 0.8747
>> [yoptf yoptq yoptz span] ans = >> Gw Gw = 1.0853 0.8747 Gwf = 0.5862 0.3938 >> yoptf = (-gain'*pinv(Gw)*Gwf + gainf')*0.2 >> yoptq = (-gain'*pinv(Gw)*Gwq + gainq')*0.2 >> yoptz = (-gain'*pinv(Gw)*Gwz + gainz')*0.1 have checked with nonlinear simulation. OK!

u=L: max. on stage 15 (below feed stage)
In practice (because of dynamics): Will use tray in top (peak at 25) >> span = abs(yoptf)+abs(yoptz)+abs(yoptq)+0.05; >> plot(gain’./span)

Using scalings from selection of primary variables
NOT QUITE CORRECT: Using scalings from selection of primary variables stage 31 TOP variation=yoptz+yoptq+yoptxb+0.05 plot(gain./variation)

Another tool for stabilization: Pole vectors
Maximum gain rule is good for integrating (drifting) modes For “fast” unstable modes (e.g. reactor): Pole vectors useful for determining which input (valve) and output (measurement) to use for stabilizing unstable modes Assumes input usage (avoiding saturation) may be a problem

Example: Tennessee Eastman challenge problem

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

Partial control Cascade control: y2 not important in itself, and setpoint (r2) is available for control of y1 Decentralized control (using sequential design): y2 important in itself

Limitations of partial control?
Cascade control: Closing of secondary loops does not by itself impose new problems Theorem The partially controlled system [P1 Pr1] from [u1 r2] to y1 has no new RHP-zeros that are not present in the open-loop system [G11 G12] from [u1 u2] to y1 provided r2 is available for control of y1 K2 has no RHP-zeros Decentralized control (sequential design): Can introduce limitations. Avoid pairing on negative RGA for u2/y2 – otherwise Pu likely has a RHP-zero

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

Cascade control arises when the output from one controller is the input to another. This is broader than the conventional definition of cascade control which is that the output from one controller is the reference command (setpoint) to another. In addition, in cascade control, it is usually assumed that the inner loop K2 is much faster than the outer loop K1. Feedforward elements link measured disturbances to manipulated inputs. Decoupling elements link one set of manipulated inputs (“measurements”) with another set of manipulated inputs. They are used to improve the performance of decentralized control systems, and are often viewed as feedforward elements (although this is not correct when we view the control system as a whole) where the “measured disturbance” is the manipulated input computed by another decentralized controller.

Why simplified configurations?
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

Cascade control (conventional; with extra measurement)
The reference r2 is an output from another controller General case (“parallel cascade”) Special common case (“series cascade”)

Series cascade Disturbances arising within the secondary loop (before y2) are corrected by the secondary controller before they can influence the primary variable y1 Phase lag existing in the secondary part of the process (G2) is reduced by the secondary loop. This improves the speed of response of the primary loop. Gain variations in G2 are overcome within its own loop. Thus, use cascade control (with an extra secondary measurement y2) when: The disturbance d2 is significant and G1 has an effective delay The plant G2 is uncertain (varies) or n onlinear Design: First design K2 (“fast loop”) to deal with d2 Then design K1 to deal with d1

Tuning cascade y2 = T2 r2 + S2d2 Use SIMC tuning rules
K2 is designed based on G2 (which has effective delay 2) then y2 = T2 r2 + S2 d2 where S2 ¼ 0 and T2 ¼ 1 ¢ e-(2+c2)s T2: gain = 1 and effective delay = 2+c2 SIMC-rule: c2 ¸ 2 Time scale separation: c2 · c1/5 (approximately) K1 is designed based on G1T2 same as G1 but with an additional delay 2+c2

Exercise: Tuning cascade
(without cascade, i.e. no feedback from y2). Design a controller based on G1G (with cascade) Design K2 and then K1

Exercise: Tuning cascade

Extra inputs Exercise: Explain how “valve position control” fits into this framework. As en example consider a heat exchanger with bypass

Exercise Exercise: In what order would you tune the controllers?
Give a practical example of a process that fits into this block diagram

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”

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 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) RTO not needed when Can “easily” identify change in active constraints (operating region) For each operating region there exists self-optimizing var

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 Conclusion / References

Summary: Main steps What should we control (y1=c=z)?
Must define optimal operation! Where should we set the production rate? At bottleneck What more should we control (y2)? Variables that “stabilize” the plant Control of primary variables Decentralized? Multivariable (MPC)?

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, Larsson, T. and S. Skogestad (2000), “Plantwide control: A review and a new design procedure”, Modeling, Identification and Control, 21, 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, Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu (2003), “Control of reactor, separator and recycle process’’, Ind.Eng.Chem.Res., 42, 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, Skogestad, S. (2003), ”Simple analytic rules for model reduction and PID controller tuning”, J. Proc. Control, 13, Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, (Special issue from ESCAPE’12 Symposium, Haag, May 2002). … + more….. See home page of S. Skogestad:

PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering

Similar presentations

Presentation on theme: "PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering

Similar presentations

Presentation on theme: "PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering"— Presentation transcript:

Similar presentations

About project

Feedback