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Practical plantwide process controlPart 1

Sigurd Skogestad, NTNU

Thailand, April 2014

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Part 1 (3h): Plantwide control

Introduction to plantwide control (what should we really control?) Part 1.1 Introduction.

– Objective: Put controllers on flow sheet (make P&ID)– Two main objectives for control: Longer-term economics (CV1) and shorter-term stability (CV2)– Regulatory (basic) and supervisory (advanced) control layer

Part 1.2 Optimal operation (economics)– Active constraints– Selection of economic controlled variables (CV1). Self-optimizing variables.

Part 1.3 -Inventory (level) control structure– Location of throughput manipulator– Consistency and radiating rule

Part 1.4 Structure of regulatory control layer (PID)– Selection of controlled variables (CV2) and pairing with manipulated variables (MV2) – Main rule: Control drifting variables and "pair close"

Summary: Sigurd’s rules for plantwide control 

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Course Summary

1. Find active constraints + self-optimizing variables (CV1). (Economic optimal operation)

2. Locate throughput manipulator (TPM)• “Gas pedal”

3. Select stabilizing CV2 + tune regulatory loops• SIMC PID rules

4. Design supervisory layer (control CV1)• Multi-loop (PID) ++• MPC

Difficulties:1. Optimization! May need to guess active constraints (CV1)

2. Handling of moving active constraints• Want to avoid reconfiguration of loops

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Summary: Sigurd’s plantwide control rulesRules for CV1-selection:

1. Control active constraints• Purity constraint on expensive product is always active (overpurification gives loss):  

2. Unconstrained degrees of freedom (if any): Control “self-optimizing” variables (c).  

–The ideal variable is the gradient of J with respect to the inputs (Ju = dJ/du), which always should be zero, independent of disturbances d, but this variable is rarely available

• Exception (if available!): Parallel systems (stream split, multiple feed streams/manifold) with given throughput (or given total gas flow, etc.)

• Should have equal marginal costs Jiu = dJi/du, so Ju = J1u - J2u, etc.

• Heat exchanger splits: equal Jächke temperatures, JT1 = (T1 – Th1)^2/(T1-T0)

–In practice, one prefers to control single variables, c=Hy (where y are all available measurements and H is a selection matrix), which are easy to measure and control, and which have the following properties:

– Optimal value for c is almost constant (independent of disturbances): Want small magnitude of dcopt(d)/dd.

– Variable c is sensitive to changes in input: Want large magnitude of gain=dc/du (this is to reduce effect of measurement error and noise).• If the economic loss with single variables is too large, then one may use measurement combinations, c=Hy (where H is a “full” matrix).

 

3. Unconstrained degrees of freedom: NEVER try to control a variable that reaches max or min at the optimum (in particular, never control J)• Surprisingly, this is a very common mistake, even (especially?) with control experts

 

Ruke for TPM location: Locate TPM at the next constraint to become active as throughput is increased (bottleneck)

Rules for inventory control:1. Use Radiation rule (PC, LC, FC ++)

2. Avoid having all flows in a recycle system on inventory control (this is a restatement of Luyben’s rule of “fixing a flow inside a recycle system” to avoid snowballing)

Rules for selecting stabilizing CVs (CV2): Control sensitive variablkes

Rules for pairing:1. General: “Pair close” (large gain and small effective time delay)

2. CV1: Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”

3. CV2 (stabilizing loop): Avoid MV that may saturate

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PLANTWIDE CONTROLCASE STUDIES

• Distillation: regulatory control

• Distillation: Economics (CV1)– Single column

– Two columns in series

• Reactor/separator/recycle problem– Economics (CV1)

– TPM location

– Max. throughput (Bottleneck)

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Case study: Distillation control

• S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), 13-23 (2007).

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Typical “LV”-regulatory control

Assume given feed5 dynamic DOFs (L,V,D,B,VT)

Overall objective (CV1): Control compositions (xD and xB)

“Obvious” stabilizing loops (CV2):1. Condenser level (M1)2. Reboiler level (M2)3. Pressure (p)

+ “non-obvious” CV24. Column temperature (T)

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Issues distillation control

• The “configuration” problem (level and pressure control)– Which are the two remaining degrees of

freedom? • e.g. LV-, DV-, DB- and L/D V/B-

configurations

• The temperature control problem– Which temperature (if any) should be

controlled?

• Composition control problem– Control two, one or no compositions?

– Always control valuable product at spec

TCTs TC

L

V

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Control “configurations” (pairing u2-y2 for level control)

• “XY-configuration”

X: remaining input in top after controlling top level (MD):

X= L (reflux), D, L/D,…

Y: remaining input in bottom after controlling MB:

Y = V (boilup, energy input), B, V/B, ...

Configurations

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Top of Column

“Standard” :LY-configuration(“energy balance”)

LCLS

VT

L+DD

L

“Reversed”: DY-configuration(“material balance”)

LC

L

VT

D

DS

cooling

Set manually or from upper-layer controller (temperature or composition)

Set manually or from upper-layer controller

Configurations

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LY - configuration

D

L

VT

D

LC

x

D

(L/D)s

Set manually or from upper-layer controller

Similar in bottom... XV, XB, X V/B

Ls

Top of ColumnConfigurations

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How do the configurations differ?

1. Level control by itself(emphasized by Buckley et al., 1985)

2. Interaction of level control with composition control• Related to “local consistency” (Do not want inventory control to depend on

composition loops being closed)

3. “Self-regulation” in terms of disturbance rejection(emphasized by Skogestad and Morari, 1987)

4. Remaining two-point composition control problem

(steady-state RGA - emphasized by Shinskey, 1984)

•Has been a lot of discussion in the literature (Shinskey, Buckley, Skogestad, Luyben, etc.).•Probably over-emphasized, but let us look at it

Configurations

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LV-configuration (most common)

“LV-configuration”:• D and B for levels (“local consistent”)• L and V remain as degrees of freedom

after level loops are closed

Other possibilities:DB, L/D V/B, etc….

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LIGHT

HEAVY

F

D

B

TC

• To stabilize the column we must use feedback (feedforward will give drift)• Simplest: “Profile feedback” using sensitive temperature

Even with the level and pressure loops closed the column is practically unstable - either closeto integrating or even truly unstable ( e.g. with mass reflux: Jacobsen and Skogestad, 1991)

feedback using e.g. D,L,V or B

BUT: To avoid strong sensitivity to disturbances: Temperature profile must also be “stabilized”

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Stabilizing the column profile

• Should close one “fast” loop (usually temperature) in order to “stabilize” the column profile– Makes column behave more linearly

– Strongly reduces disturbance sensitivity

– Keeps disturbances within column

– Reduces the need for level control

– Makes it possible to have good dual composition control

• P-control usually OK (no integral action)– Similar to control of liquid level

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Stabilizing the column profile (T)

Regulatory layer

LV

TCTs

. loop

LV

TCTs

LV

TCTs

TCTC TS

(a) Common: Control T using V (b) If V may saturate: Use L

1. T at which end? Prefer “important” end with tightest purity spec,2. T at which stage? Choose “sensitive” stage (sensitive to MV change)3. Pair T with which input (MV)? Generally “pair close”

• But avoid input that may saturate• Dynamics: V has immediate effect, whereas L has delay• Prefer “same end” (L for Ttop, V for Tbtm) to reduce interactions

Note: may not be possible to satisfy all these rules

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Bonus 1 of temp. control: Indirect level control

TC

Disturbance in V, qF:Detected by TC and counteracted by L-> Smaller changesin D required to keepMd constant!

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Bonus 2 of temp. control: Less interactive

TC TsSetpoint T:New “handle” instead of L

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Less interactive: RGA with temperature loop closed

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Less interactive: Closed-loop response with decentralized PID-composition control

Interactions much smaller with “stabilizing” temperature loop closed

… and also disturbance sensitivity is expected smaller

%

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Integral action in inner temperature loop has little effect

%

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Note: No need to close two inner temperature loops

%

Would be even betterwith V/F

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Would be even better with V/F:

TC

x(V/F)s

F

V

Ts

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A “winner”: L/F-T-conguration

Only caution: V should not saturate

TC

x

Ts

(L/F)s

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Temperature control: Which stage?

TC

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Binary distillation: Steady-state gain G0 = ΔT/ΔL for small change in L

BTM

T / L

TOP

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• Rule 1. Avoid temperatures close to column ends (especially at end where impurity is small)

• Rule 2. Control temperature at important end (expensive product)

• Rule 3. To achieve indirect composition control: Control temperature where the steady-state sensitivity is large (“maximum gain rule”).

• Rule 4. For dynamic reasons, control temperature where the temperature change is large (avoid “flat” temperature profile). (Binary column: same as Rule 3)

• Rule 5. Use an input (flow) in the same end as the temperature sensor.

• Rule 6. Avoid using an input (flow) that may saturate.

Summary: Which temperature to control?

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Conclusion stabilizing control:Remaining supervisory control problem

TCTs

Ls

+ may adjust setpoints for p, M1 and M2 (MPC)

With V for T-control

Would be even better with L/F

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Summary step 5: Rules for selecting y2 (and u2)

Selection of y2

1. Control of y2 “stabilizes” the plant• The (scaled) gain for y2 should be large

2. Measurement of y2 should be simple and reliable• For example, temperature or pressure

3. y2 should have good controllability• small effective delay• favorable dynamics for control• y2 should be located “close” to a manipulated input (u2)

Selection of u2 (to be paired with y2):1. Avoid using inputs u2 that may saturate (at steady state)

• When u2 saturates we loose control of the associated y2. 2. “Pair close”!

• The effective delay from u2 to y2 should be small

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CASE STUDIES

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PROBLEM:

•Objective: “Keep p=ps (or T=Ts) if possible, but main priority is to evaporate a given feed”– CVs in order of priority:

• CV1 = level, CV2 = throughput, CV3 = p

•MV1 = feed pump, MV2 = heat fluid valve, MV3= vapor product valve– Constraints on MVs (in order of becoming active as throughput is increased):

• Max heat (MV2), Fully open product valve (MV3), Max pump speed (MV1)

•Where locate TPM? Pairings?

Example (TPM location): Evaporator(with liquid feed, liquid heat medium, vapor product)

Present structure has feed pump as TPM: May risk “overfeeding”

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• Pairing based on Sigurd’s general pairing rule**:• CV1=level with MV1 (top-priority CV is paired with MV that is least likely to saturate)

• CV2=throughput with MV3 (so TPM =gas product valve)

• CV3=p with MV2 (MV2 may saturate and p may be given up)

• Note: Fully open gas product valve (MV3) is also the bottleneck• Rules agree because bottleneck is last constraints to become active as we increase throughput

* General: Do not need a FC on the TPM**Sigurd’s general pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”

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CASE STUDY: Recycle plant (Luyben, Yu, etc.)Part 1 -3

1

2

3

4

5

Assume constant reactor temperature.Given feedrate F0 and column pressure:

Dynamic DOFs: Nm = 5 Column levels: N0y = 2Steady-state DOFs: N0 = 5 - 2 = 3

Feed of A

Recycle of unreacted A (+ some B)

Product (98.5% B)

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Recycle plant: Optimal operation

mT

1 remaining unconstrained degree of freedom, CV=?

Part 1: Economics (Given feed)

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J=V as a function of reflux L

With fixed active constraints:

Mr = 2800 kmol (max), xB= 1.5% A (max)

Optimum= Nominal point

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Control of recycle plant:Conventional structure (“Two-point”: CV=xD)

LC

XC

LC

XC

LC

xB

xD

Control active constraints (Mr=max and xB=0.015) + xD

TPM

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Luyben law no. 1 (to avoid snowballing):

“Fix a stream in the recycle loop” (CV=F or D)

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Luyben rule: CV=D (constant)

LCLC

LC

XC

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“Brute force” loss evaluation:Disturbance in F0

Loss with nominally optimal setpoints for Mr, xB and c

Luyben rule:

Conventional

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Loss evaluation: Implementation error

Loss with nominally optimal setpoints for Mr, xB and c

Luyben rule:

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Conclusion: Control of recycle plant

Active constraintMr = Mrmax

Active constraintxB = xBmin

L/F constant: Easier than “two-point” control

Assumption: Minimize energy (V)

Self-optimizing

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Modified Luyben’s law to avoid snowballing

• Luyben law no. 1 (“Plantwide process control”, 1998, pp. 57): “A stream somewhere in all recycle loops must be flow controlled”

• Luyben rule is OK dynamically (short time scale),

• BUT economically (steady-state): Recycle should increase with throughput

• Modified Luyben’s law 1 (by Sigurd): “Avoid having all streams in a recycle system on inventory control” – Good economic control may then require that the stream which is not

on inventory control is chosen as the TPM (throughput manipulator).

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Example Reactor-recycle process:Given feedrate (production rate set at inlet)

Part 2: TPM location

TPM

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Note: Temperature and pressure controllers shown; Otherwise as before

PC

TC

Part 2: TPM location

F0

F

L

V

B

D

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Alt.1

Alt.3

Alt.2

Alt.4

Follows Luyben law 1:TPM inside recycle

Not really comparable since T is not fixed

T fixed in reactor

More?Alt. 5?Alt.6?Alt. 7?

Unconventional TPM

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What about TPM=D (Luyben rule)?

• Control xB, xD, Md

• Not so simple with liquid feed…..

Alt. 5

PC

TC

LC

LC

TPM

XC

LC

XC?

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What about TPM=D (Luyben rule)?

Another alternative:

•Top level control by boilup

•Get extra DOF in top

•OK!

Alt. 5

PC

TC

LC

LC

XC

LC

XC

TPM

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NOTE: There are actually two recycles

• One through the reactor (D or F)

• One through the column (L)

• One flow inside both recycle loops: V

• Alt.6: TPM=V if we want to break both recycle loops!

PC

TC

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TPM = V

PC

TC

LC

LC

Alt. 6

LC

L and F for composition control: OK!

L

F

XC

XC

TPM

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What about keeping V constant?

With feedrate F0 fixed (TPM)L for compostion control in bottom (xB)Top composition floating

Alt. 7

PC

TC

LC

LC

LC

L

F

F0

VXC

NO! Never control cost J=V

TPM

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Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column

Bottleneck: max. vapor rate in column

TPM

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Reactor-recycle process with max. feedrate

Alt.A: Feedrate controls bottleneck flow

Bottleneck: max. vapor rate in column

FC

Vmax

VVmax-Vs=Back-off

= Loss

Vs

Get “long loop”: Need back-off in V

TPM

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MAX

Reactor-recycle process with max. feedrate: Alt. B Move TPM to bottleneck (MAX). Use feedrate for lost task (xB)

Get “long loop”: May need back-off in xB instead…

Bottleneck: max. vapor rate in column

=Alt.6 TPM

TPM

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Reactor-recycle process with max. feedrate: Alt. C: Best economically: Move TPM to bottleneck (MAX) + Reconfigure upstream loops

MAX

OK, but reconfiguration undesirable…

LC

=Alt.6 TPM

TPM

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Reactor-recycle process: Alt.C’: Move TPM + reconfigure (permanently!)

F0s

For cases with given feedrate: Get “long loop” but no associated loss

LC

CC

=Alt.6 TPM

TPM

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• 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!

Alt.4: Multivariable control (MPC)

•One approach: Put MPC on top that coordinates flows through plant•By manipulating feed rate and other ”unused” degrees of freedom (including level setpoints):

•E.M.B. Aske, S. Strand and S. Skogestad, •``Coordinator MPC for maximizing plant throughput'', •Computers and Chemical Engineering, 32, 195-204 (2008).

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Comments on case study

• Operate with L=0 (column is a flash).– Not optimal nominally, but good enough?

• Many papers, a lot of confusion– Stupid recommendations of “balanced schemes” with reactor level not at

maximum (Luyben , Yu)• Gives economic loss

– Not understood: Distillation column itself is also a recycle

• Recommended reading:– T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control

structure selection for reactor, separator and recycle processes'', Ind. Eng. Chem. Res., 42 (6), 1225-1234 (2003).

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Plantwide control. Main references

• The following paper summarizes the procedure: – S. Skogestad, ``Control structure design for complete chemical plants'',

Computers and Chemical Engineering, 28 (1-2), 219-234 (2004).

• There are many approaches to plantwide control as discussed in the following review paper: – T. Larsson and S. Skogestad, ``Plantwide control: A review and a new

design procedure'' Modeling, Identification and Control, 21, 209-240 (2000).

• The following paper updates the procedure: – S. Skogestad, ``Economic plantwide control’’, Book chapter in V.

Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent Developments and Applications”, Wiley (2012).

• More information:

All papers available at: http://www.nt.ntnu.no/users/skoge/

http://www.nt.ntnu.no/users/skoge/plantwide

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PC

TC