1 Sigurd Skogestad 1955: Born in Flekkefjord, Norway 1978: MS (Siv.ing.) in chemical engineering at...

1

Sigurd Skogestad

• 1955: Born in Flekkefjord, Norway• 1978: MS (Siv.ing.) in chemical engineering at NTNU• 1979-1983: Worked at Norsk Hydro co. (process simulation)• 1987: PhD from Caltech (supervisor: Manfred Morari)• 1987-present: Professor of chemical engineering at NTNU• 1999-2009: Head of Department

• 160 journal publications• Book: Multivariable Feedback Control (Wiley 1996; 2005)

– 1989: Ted Peterson Best Paper Award by the CAST division of AIChE – 1990: George S. Axelby Outstanding Paper Award by the Control System Society of IEEE – 1992: O. Hugo Schuck Best Paper Award by the American Automatic Control Council– 2006: Best paper award for paper published in 2004 in Computers and chemical engineering. – 2011: Process Automation Hall of Fame (US)– 2012: Fellow of American Institute of Chemical Engineers (AIChE)– 2014: Fellow of International Federation of Automatic Control (IFAC)

2

Trondheim, Norway

Thailand

3

Trondheim

Oslo

UK

NORWAY

DENMARK

GERMANY

North Sea

SWEDEN

Arctic circle

4

NTNU,Trondheim

5

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

6

– 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 1.1 Introduction

7

Why control?

• Operation

time

Actual value(dynamic)Steady-state (average)

In practice never steady-state:• Feed changes• Startup• Operator changes • Failures• …..

- Control is needed to reduce the effect of disturbances- 30% of investment costs are typically for instrumentation and control

“Disturbances” (d’s)

8

Countermeasures to disturbances (I)

I. Eliminate/Reduce the disturbance (a) Design process so it is insensitive to disturbances

• Example: Use buffertank to dampen disturbances

(b) Detect and remove source of disturbances• “Statistical process control” • Example: Detect and eliminate variations in feed composition

inflow outflow∞Tin Tout

9

Countermeasures to disturbances (II)II. Process control

Do something (usually manipulate valve)

to counteract the effect of the disturbances

(a) Manual control: Need operator(b) Automatic control: Need measurement + automatic valve + computer

Goals automatic control:• Smaller variations

• more consistent quality• More optimal

• Smaller losses (environment)• Lower costs• More production

Industry: Still large potential for improvements!

10

Classification of variables

Process(shower)

uinput (MV)

youtput (CV)

d

Independent variables (“the cause”):

(a) Inputs (MV, u): Variables we can adjust (valves)

(b) Disturbances (DV, d): Variables outside our control

Dependent (output) variables (“the effect or result”):(c) Primary outputs (CVs, y1): Variables we want to keep at a given setpoint

(d) Secondary outputs (y2): Extra measurements that we may use to improve control

11

Inputs for control (MVs)

• Usually: Inputs (MVs) are valves. – Physical input is valve position (z), but we often simplify and say that

flow (q) is input

12

Idealized view of control(“PhD control”)

Control: Use inputs (MVs, u) to counteract the effect of the disturbances (DVs, d) such that the outputs (CV=y) are kept close to their setpoints (ys)

d, ys = y-ys

13

Practice: Tennessee Eastman challenge problem (Downs, 1991)

(“PID control”)

TC PC LC CC x SRCWhere place ??

14

Notation feedback controllers (P&ID)

TC2nd letter: C: controller I: indicator (measurement) T: transmitter (measurement)

1st letter: Controlled variable (CV) = What we are trying to control (keep constant)

T: temperature F: flow L: level P: pressure DP: differential pressure (Δp) A: Analyzer (composition) C: composition X: quality (composition) H: enthalpy/energy

Ts

(setpoint CV)T(measured CV) MV (could be valve)

15

LCH

Hs

Inflow (d)

Outflow (u)

INPUT (u): OUTFLOW (Input for control!)OUTPUT (y): LEVEL DISTURBANCE (d): INFLOW

Example: Level control

CLASSIFICATION OF VARIABLES:

16

How we design a control system for a complete chemical plant?

• How do we get from PID control to PhD control?

• Where do we start?

• What should we control? and why?

• etc.

• etc.

17

Plantwide control = 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 “PhD” control

18

• 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

Previous work on plantwide control:

19

Main objectives control system

1. Implementation of acceptable (near-optimal) operation2. Stable operation

ARE THESE OBJECTIVES CONFLICTING?

• Usually NOT – Different time scales

• Stabilization fast time scale

– Stabilization doesn’t “use up” any degrees of freedom• Reference value (setpoint) available for layer above• But it “uses up” part of the time window (frequency range)

20

Example of systems we want to operate optimally

• Process plant – minimize J=economic cost

• Runner – minimize J=time

• «Green» process plant– Minimize J=environmental impact (with given economic cost)

• General multiobjective:– Min J (scalar cost, often $)– Subject to satisfying constraints (environment, resources)

Part 1.2 Optimal operation (economics)

23

Process operation: Hierarchical structure

Manager

Process engineer

Operator/RTO

Operator/”Advanced control”/MPC

PID-control

u = valves

24

Translate optimal operation into simple control objectives:

What should we control?

CV1 = c ? (economics)

CV2 = ? (stabilization)

25

Part 1.2 Optimal operation (economics)

•Goal: Select economic controlled variables (CV1)– Active constraints

– Self-optimizing variables

26

Outline

• Skogestad procedure for control structure designI Top Down

• Step S1: Define operational objective (cost) and constraints

• Step S2: Identify degrees of freedom and optimize operation for disturbances

• Step S3: Implementation of optimal operation

– What to control ? (primary CV’s) (self-optimizing control)

• Step S4: Where set the production rate? (Inventory control)

II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?

• Step S6: Supervisory control

• Step S7: Real-time optimization

27

Step S1. Define optimal operation (economics)

• What are we going to use our degrees of freedom (u=MVs) for?

• Typical cost function*:

• *No need to include fixed costs (capital costs, operators, maintainance) at ”our” time scale (hours)

• Note: J=-P where P= Operational profit

J = cost feed + cost energy – value products

28

Optimal operation distillation column

• Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V (u)

• Cost to be minimized (economics)

J = - P where P= pD D + pB B – pF F – pVV

• 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 (d) 2) p free (u): pmin · p · pmax

Feed: 1) F given (d) 2) F free (u): F · Fmax

• Optimal operation: Minimize J with respect to steady-state DOFs (u)

value products

cost energy (heating+ cooling)

cost feed

29

Step S2. Optimize

(a) Identify degrees of freedom (b) Optimize for expected disturbances

• Need good steady-state model

• Time consuming! But it is offline

• Main goal: Identify ACTIVE CONSTRAINTSs

• A good engineer can often guess the active constraints

30

Step S2a: Degrees of freedom (DOFs) for operation

NOT as simple as one may think!

To find all operational (dynamic) degrees of freedom:

• Count valves! (Nvalves)

• “Valves” also includes adjustable compressor power, etc.

Anything we can manipulate!

BUT: not all these have a (steady-state) effect on the economics

Steady-state DOFs

31

Steady-state degrees of freedom (DOFs)

IMPORTANT!

DETERMINES THE NUMBER OF VARIABLES TO CONTROL!

• No. of primary CVs = No. of steady-state DOFs

CV = controlled variable

Methods to obtain no. of steady-state degrees of freedom (Nss):

1. Equation-counting • Nss = no. of variables – no. of equations/specifications • Very difficult in practice

2. Valve-counting (easier!)• Nss = Nvalves – N0ss – Nspecs

• N0ss = variables with no steady-state effect • Inputs/MVs with no steady-state effect (e.g. extra bypass) • Outputs/CVs with no steady-state effect that need to be controlled (e.g., liquid levels )

3. Potential number for some units (useful for checking!)

4. Correct answer: Will eventually find it when we perform optimization

Steady-state DOFs

32

Nvalves = 6 , N0y = 2* , NDOF,SS = 6 -2 = 4 (including feed and pressure as DOFs)

Typical Distillation column

*N0y : no. controlled variables (liquid levels) with no steady-state effect

4 DOFs:With given feed and pressure:NEED TO IDENTIFY 2 more CV’s - Typical: Top and btm composition

1

2

3

4

5

6

Steady-state DOFs

33

Steady-state degrees of freedom (Nss): 3. Potential number 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/speed)

• adiabatic flash tank: 0*

• liquid phase reactor: 1 (holdup reactant)

• gas phase reactor: 0*

• heat exchanger: 1 (bypass or flow)

• column (e.g. distillation) excluding heat exchangers: 0* + no. of sidestreams

• pressure* : add 1DOF at each extra place you set pressure (using an extra valve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or absorption column

• *Pressure is normally assumed to be given by the surrounding process and is then not a degree of freedom

• Ref: Araujo, Govatsmark and Skogestad (2007)

• Extension to closed cycles: Jensen and Skogestad (2009)

• Real number may be less, for example, if there is no bypass valve

Steady-state DOFs

34

“Potential number”, Nss= 0 (column distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4With given feed and pressure: N’ss = 4 – 2 = 2

Distillation column (with feed and pressure as DOFs)

split

Steady-state DOFs

35

…. BUT A GOOD ENGINEER CAN OFTEN GUESS THE SOLUTION (active constraints)

• What are the optimal values for our degrees of freedom u (MVs)?

• Minimize J with respect to u for given disturbance d (usually steady-state):

minu J(u,x,d)subject to:

Model equations (e,g, Hysys): f(u,x,d) = 0Operational constraints: g(u,x,d) < 0

OFTEN VERY TIME CONSUMING – Commercial simulators (Aspen, Unisim/Hysys) are set up in “design mode” and

often work poorly in “operation (rating) mode”.– Optimization methods in commercial simulators often poor

• We use Matlab or even Excel “on top”


Step S2b: Optimize for expected disturbances

36

Step S3: Implementation of optimal operation

• Have found the optimal way of operation. How should it be implemented?

• What to control ? (primary CV’s). 1.Active constraints2.Self-optimizing variables (for unconstrained

degrees of freedom)

37

– Cost to be minimized, J=T

– One degree of freedom (u=power)

– What should we control?

Optimal operation - Runner

Optimal operation of runner

38

1. Optimal operation of Sprinter

– 100m. J=T– Active constraint control:

• Maximum speed (”no thinking required”)

• CV = power (at max)


39

• 40 km. J=T

• What should we control? CV=?

• Unconstrained optimum


2. Optimal operation of Marathon runner

u=power

J=T

uopt

40

• Any self-optimizing variable (to control at constant setpoint)?

• c1 = distance to leader of race

• c2 = speed

• c3 = heart rate

• c4 = level of lactate in muscles


Self-optimizing control: Marathon (40 km)

41

Conclusion Marathon runner

c = heart rate

select one measurement

• CV = heart rate is good “self-optimizing” variable• Simple and robust implementation• Disturbances are indirectly handled by keeping a constant heart rate• May have infrequent adjustment of setpoint (cs)


c=heart rate

J=T

copt

42

Expected active constraints distillation

• Both products (D,B) generally have purity specs

• Valuable product: Purity spec. always active– Reason: Amount of valuable product (D or B) should

always be maximized• Avoid product “give-away” (“Sell water as methanol”)

• Also saves energy

Control implications: 1. ALWAYS Control valuable product at spec. (active

constraint).

2. May overpurify (not control) cheap product

valuable product methanol + max. 0.5% water

cheap product(byproduct)water + max. 2%methanol

methanol+ water

Selection of CV1

43

Example with Quiz:Optimal operation of two distillation columns in series

44

Operation of Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)

DOF = Degree Of FreedomRef.: M.G. Jacobsen and S. Skogestad (2011)

Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2

> 95% BpD2=2 $/mol

F ~ 1.2mol/spF=1 $/mol < 4 mol/s < 2.4 mol/s

> 95% CpB2=1 $/mol

N=41αAB=1.33

N=41αBC=1.5

> 95% ApD1=1 $/mol

QUIZ: What are the expected active constraints?1. Always. 2. For low energy prices.

QUIZ 1

45

DOF = Degree Of FreedomRef.: M.G. Jacobsen and S. Skogestad (2011)

Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2

> 95% BpD2=2 $/mol

F ~ 1.2mol/spF=1 $/mol < 4 mol/s < 2.4 mol/s

> 95% CpB2=1 $/mol

1. xB = 95% BSpec. valuable product (B): Always active!Why? “Avoid product give-away”

N=41αAB=1.33

N=41αBC=1.5

> 95% ApD1=1 $/mol

2. Cheap energy: V1=4 mol/s, V2=2.4 mol/sMax. column capacity constraints active!Why? Overpurify A & C to recover more B

QUIZ: What are the expected active constraints?1. Always. 2. For low energy prices.

Hm….?

Operation of Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)

SOLUTION QUIZ 1

46

Control of Distillation columns in series

Given

LC LC

LC LC

PCPC

QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTSRed: Basic regulatory loops

QUIZ 2

47


Given

LC LC

LC LC

PCPC

Red: Basic regulatory loops

CC

xB

xBS=95%

MAX V1 MAX V2

1 unconstrained DOF (L1):Use for what?? CV=? •Not: CV= xA in D1! (why? xA should vary with F!) •Maybe: constant L1? (CV=L1)•Better: CV= xA in B1? Self-optimizing?

General for remaining unconstrained DOFs: LOOK FOR “SELF-OPTIMIZING” CVs = Variables we can keep constantWILL GET BACK TO THIS!

SOLUTION QUIZ 2

QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTS

Hm…….HINT: CONTROL ACTIVE CONSTRAINTS!

48

Comment: Distillation column control in practice

1. Add stabilizing temperature loops– In this case: use reflux (L) as MV because boilup (V) may

saturate

– T1s and T2s then replace L1 and L2 as DOFs.

2. Replace V1=max and V2=max by dpmax-controllers (assuming max. load is limited by flooding)

• See next slide

49


Given

LC LC

LC LC

PCPC

TC TCT1s

T2sT1 T2

Comment: In practice

MAX V2MAX V1

CC

xB

xBS=95%

50

a) If constraint can be violated dynamically (only average matters)• Required Back-off = “measurement bias” (steady-state measurement error for c)

b) If constraint cannot be violated dynamically (“hard constraint”) • Required Back-off = “measurement bias” + maximum dynamic control error

JoptBack-off

Loss

c ≥ cconstraint

c

J

More on: Active output constraints

Need back-off

Want tight control of hard output constraints to reduce the back-off. “Squeeze and shift”-rule

CV = Active constraint

51

Hard Constraints: «SQUEEZE AND SHIFT»

0 50 100 150 200 250 300 350 400 4500

0.5

1

1.5

2

OFF

SPEC

QUALITY

N Histogram

Q1

Sigma 1

Q2

Sigma 2

DELTA COST (W2-W1)

LEVEL 0 / LEVEL 1

Sigma 1 -- Sigma 2

LEVEL 2

Q1 -- Q2

W1

W2

COST FUNCTION

© Richalet SHIFT

SQUEEZE


Rule for control of hard output constraints:•“Squeeze and shift”!•Reduce variance (“Squeeze”) and “shift” setpoint cs to reduce backoff

52

Example. Optimal operation = max. throughput. Want tight bottleneck control to reduce backoff!

Time

Back-off= Lost production


53

Example back-off. xB = purity product > 95% (min.)

• D1 directly to customer (hard constraint)

– Measurement error (bias): 1%

– Control error (variation due to poor control): 2%

– Backoff = 1% + 2% = 3%

– Setpoint xBs= 95 + 3% = 98% (to be safe)

– Can reduce backoff with better control (“squeeze and shift”)

• D1 to large mixing tank (soft constraint)

– Measurement error (bias): 1%

– Backoff = 1%

– Setpoint xBs= 95 + 1% = 96% (to be safe)

– Do not need to include control error because it averages out in tank


D1

xB

8

xB xB,product±2%

54

More on: WHAT ARE GOOD “SELF-OPTIMIZING” VARIABLES?

• Intuition: “Dominant variables” (Shinnar)

• More precisely1. Optimal value of CV is constant

2. CV is “sensitive” to MV (large gain)

Unconstrained variables

55

1. Optimal value copt is constant (independent of disturbance d):

2. c is “sensitive” to MV=u (to reduce effect of measurement noise)

Equivalently: Optimum should be flat

Unconstrained optimum

BADGoodGood

GOOD “SELF-OPTIMIZING” CV=c

56

Control of Distillation columns. Cheap energy

Given

LC LC

LC LC

PCPC

Overpurified: To avoid loss of valuable product B

CC

xB

xBS=95%

MAX V1 MAX V2

1 unconstrained DOF (L1): What is a good CV? •Not: CV= xB in D1! (why? Overpurified, so xB,opt increases with F) •Maybe: constant L1? (CV=L1)•Better: CV= xA in B1? Self-optimizing?

Example.

Overpurified

Overpurified

57

More on: Optimal operation

Mode 1. Given feedrate

Mode 2. Maximum production

minimize J = cost feed + cost energy – value products

Two main cases (modes) depending on marked conditions:

58

Amount of products is then usually indirectly given and

Optimal operation is then usually unconstrained

“maximize efficiency (energy)”

Control:•Operate at optimal trade-off •NOT obvious what to control•CV = Self-optimizing variable

Mode 1. Given feedrate

J = cost feed– value products + cost energy

c

J = energy

copt

Often constant

59

• Assume feedrate is degree of freedom

• Assume products much more valuable than feed

• Optimal operation is then to maximize product rate

Mode 2. Maximum production

Control: •Focus on tight control of bottleneck• “Obvious what to control”•CV = ACTIVE CONSTRAINT

c

J

cmax

Infeasibleregion


60

Control structure design using self-optimizing control for economically optimal CO2 recovery*

Step S1. Objective function= J = energy cost + cost (tax) of released CO2 to air

Step S3 (Identify CVs). 1. Control the 4 equality constraints2. Identify 2 self-optimizing CVs (Use Exact Local method and select CV set with minimum loss)

4 equality and 2 inequality constraints:1. stripper top pressure2. condenser temperature3. pump pressure of recycle amine4. cooler temperature

5. CO2 recovery ≥ 80%6. Reboiler duty < 1393 kW (nominal +20%)

4 levels without steady state effect: absorber, stripper (2), make-up tank

Step S2. (a)10 degrees of freedom: 8 valves + 2 pumps

*M. Panahi and S. Skogestad, ``Economically efficient operation of CO2 capturing process, Part I: Self-optimizing procedure for selecting the best controlled variables'', Chemical Engineering and Processing, 50, 247-253 (2011).

Disturbances: flue gas flowrate, CO2 composition in flue gas + active constraints

(b) Optimization using Unisim steady-state simulator. Mode I (nominal feedrate): No inequality constraints active Unconstrained degrees of freedom = 10 – 4 – 4 = 2

Case study

61

Exact local method* for finding2 self-optimizing CVs

The set with the minimum worst case loss is the best

21max. Loss= σ(M)

2-11/2 y

uu nyM=J (HG ) H [FW W ]d

y -1 yuu ud dF=G J J -G

opt.ΔyF=

Δd

* 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)

Juu and F, the optimal sensitivity of the measurements with respect to disturbances, are obtained numerically

62

39 candidate CVs- 15 possible tray temperature in absorber- 20 possible tray temperature in stripper- CO2 recovery in absorber and CO2 content at the bottom of stripper- Recycle amine flowrate and reboiler duty

Best self-optimizing CV set in region I: • c1 = CO2 recovery (95.26%) • c2 = Temperature tray no. 16 in stripper

These CVs are not necessarily the best if new constraints are met

Use a bidirectional branch and bound algorithm* for finding the best CVs

* V. Kariwala and Y. Cao. Bidirectional Branch and Bound for Controlled Variable Selection, Part II: Exact Local Method for Self-Optimizing Control, Computers & Chemical Engineering, 33(2009), 1402-1412.

Identify 2 self-optimizing CVs

63

Proposed control structure with given

nominal flue gas flowrate (mode I)

64

Mode II: large feedrates of flue gas (+30%)

Feedrate flue gas (kmol/hr)

Self-optimizing CVs in region I Reboilerduty(kW)

Cost(USD/ton)

CO2 recovery

%

Temperaturetray no. 16

°C

Optimal nominal point 219.3 95.26 106.9 1161 2.49

+5% feedrate 230.3 95.26 106.9 1222 2.49

+10% feedrate 241.2 95.26 106.9 1279 2.49

+15% feedrate 252.2 95.26 106.9 1339 2.49

+19.38%, when reboiler duty saturates

261.8 95.26 106.9 1393(+20%)

2.50

+30% feedrate (reoptimized)

285.1 91.60 103.3 1393 2.65

Saturation of reboiler duty; one unconstrained degree of freedom left

Use Maximum gain rule to find the best CV among 37 candidates :

• Temp. on tray no. 13 in the stripper: largest scaled gain, but tray 16 also OK

region I

region II

max

65

Proposed control structure with large flue gas flowrate (mode II)

max

66

Switching policies CO2 plant(”supervisory control”)

• Assume operating in region I (unconstrained) – with CV=CO2-recovery=95.26%

• When reach maximum Q: Switch to Q=Qmax (Region II) (obvious)– CO2-recovery will then drop below 95.26%

• When CO2-recovery exceeds 95.26%: Switch back to region I !!!

67

Conclusion optimal operation

ALWAYS:

1. Control active constraints and control them tightly!!– Good times: Maximize throughput -> tight control of bottleneck

2. Identify “self-optimizing” CVs for remaining unconstrained degrees of freedom

• Use offline analysis to find expected operating regions and prepare control system for this!

– One control policy when prices are low (nominal, unconstrained optimum)

– Another when prices are high (constrained optimum = bottleneck)

ONLY if necessary: consider RTO on top of this

68

Part 1.3 -Inventory (level) control structure

– Location of throughput manipulator

– Consistency and radiating rule

69

Outline





– What to control ? (primary CV’s)

– Control Active constraints + self-optimizing variables





70

Step S4. Where set production rate?

• Very important decision that determines the structure of the rest of the inventory control system!

• May also have important economic implications

• Link between Top-down (economics) and Bottom-up (stabilization) parts– Inventory control is the most important part of stabilizing control

• “Throughput manipulator” (TPM) = MV for controlling throughput (production rate, network flow)

• Where set the production rate = Where locate the TPM? –Traditionally: At the feed

–For maximum production (with small backoff): At the bottleneck

71

TPM (Throughput manipulator)

• Definition 1. TPM = MV used to control throughput (CV)

• Definition 2 (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control.

– The TPM is the “gas pedal” of the process

– Value of TPM: Usually set by the operator (manual control)• Operators are skeptical of giving up this MV to the control system (e.g. MPC)

– The TPM is usually a flow (or closely related to a flow), e.g. main feedrate, but not always.• It can be a setpoint to another control loop

• Example: Reactor temperature can be a TPM, because it changes the reactor conversion,

• Example: Pressure of gas product can be a TPM, because it changes the gas product flowrate

– Usually, only one TPM for a plant, but there can be more if there are• parallel units or splits into alternative processing routes

• multiple feeds that do not need to be set in a fixed ratio

– If we consider only part of the plant then the TPM may be outside our control. • throughput is then a disturbance

72

TPM and link to inventory control

• Liquid inventory: Level control (LC)– Sometimes pressure control (PC)

• Gas inventory: Pressure control (PC)

• Component inventory: Composition control (CC, XC, AC)

73

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

* Required to get “local-consistent” inventory control

TPM

74

Production rate set at outlet:Inventory control opposite flow*

TPM


75

Production rate set inside process*

TPM


76

General: “Need radiating inventory control around TPM” (Georgakis)

77

Consistency of inventory control

• Consistency (required property):

An inventory control system is said to be consistent if the steady-state mass balances (total, components and phases) are satisfied for any part of the process, including the individual units and the overall plant.

78

CONSISTENT?QUIZ 1

79

Local-consistency rule

Rule 1. Local-consistency requires that

1. The total inventory (mass) of any part of the process must be locally regulated by its in- or outflows, which implies that at least one flow in or out of any part of the process must depend on the inventory inside that part of the process.

2. For systems with several components, the inventory of each component of any part of the process must be locally regulated by its in- or outflows or by chemical reaction.

3. For systems with several phases, the inventory of each phase of any part of the process must be locally regulated by its in- or outflows or by phase transition.

Proof: Mass balancesNote: Without the word “local” one gets the more general consistency rule

80

CONSISTENT?QUIZ 1

81

Local concistency requirement -> “Radiation rule “(Georgakis)

82

Flow split: May give extra DOF

TPM

TPM

Split: Extra DOF (FC) Flash: No extra DOF

83

Consistent?Local-consistent?

Note: Local-consistent ismore strict as it impliesconsistent

QUIZ 2

84

Closed system: Must leave one inventory uncontrolled

QUIZ 3

85

OK? (Where is production set?

NO. Two TPMs (consider overall liquid balance).Solution: Interchange LC and FC on last tank

QUIZ 4

TPM1

TPM2

86

Example: Separator controlAlternative TPM locations

Compressor could be replaced by valve if p1>pG

87

Alt.1 Alt.2

Alt.3 Alt.4

Similar to original but NOT CONSISTENT (PC not direction of flow)

88

LOCATION OF SENSORS

• Location flow sensor (before or after valve or pump): Does not matter from consistency point of view– Locate to get best flow measurement

• Before pump: Beware of cavitation

• After pump: Beware of noisy measurement

• Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

89

OK? (Where is production set?

NO. Two TPMs (consider overall liquid balance).Solution: Interchange LC and FC on last tank

QUIZ 4

TPM1

TPM2

90

Where should we place TPM?• TPM = MV used to control throughput

• Traditionally: TPM = Main feed valve (or pump/compressor)– Gives inventory control “in direction of flow”

Consider moving TPM if:

1. There is an important CV that could otherwise not be well controlled– Dynamic reasons

– Special case: Max. production important: Locate TPM at process bottleneck* !• TPM can then be used to achieve tight bottleneck control (= achieve max. production)

• Economics: Max. production is very favorable in “sellers marked”

2. If placing it at the feed may yield infeasible operation (“overfeeding”)– If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM

inside recycle loop

BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)– Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**

**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control

91

QUIZ. Distillation. OK?

LV-configuration

TPM

92

DB-configuration OK???

TPM

93

cc

*But DB-configuration is not recommended!

DB-configuration: Level control NOT consistent by itself, but can still work* if we add one (or preferably two) composition/temperature loops

TPM

cc

94

QUIZ

* Keep p ¸ pmin

** Keep valve fully open

*

**

96

QUIZ

97

LOCATION OF SENSORS

• Location flow sensor (before or after valve or pump): Does not matter from consistency point of view– Locate to get best flow measurement

• Before pump: Beware of cavitation

• After pump: Beware of noise

• Etc.

• Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

98

Often optimal: Locate TPM at bottleneck!

• "A bottleneck is a unit where we reach a constraints which makes further increase in throughput infeasible"

• If feed is cheap and available: Located TPM at bottleneck (dynamic reasons)

• If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered.

99

Single-loop alternatives for bottleneck controlBottleneck.Want max flow here

Alt.1. Feedrate controls bottleneck flow (“long loop”…):

FCFmax

Alt. 2: Feedrate controls lost task (another “long loop”…):Fmax

Alt. 3: Reconfigure all upstream inventory loops:Fmax

Traditional: Manual control of feed rate

TPM

TPM

TPM

TPM

100

May move TPM to inside recycle loop to avoid snowballing

Example: Eastman esterification processAlcohol recycle

Alcohol + water + extractive agent (e)

Ester product

Reach max mass transferrate: R increases sharply(“snowballing”)

101

First improvement: Located closer to bottleneck

102

Final improvement: Located “at” bottleneck + TPM is inside “snowballing” loop

Follows Luyben’s law 1 to avoid snowballing(modified): “Avoid having all streams in a recycle system on inventory control”

103

Where should we place TPM?• TPM = MV used to control throughput

• Traditionally: TPM = Main feed valve (or pump/compressor)– Operators like it. Gives inventory control “in direction of flow”

Consider moving TPM if:

1. There is an important CV that could otherwise not be well controlled• Dynamic reasons

– Special case: Max. production important: Locate TPM at process bottleneck* !• Because max. production is very favorable in “sellers marked”

• TPM can then be used to achieve tight bottleneck control (= achieve max. flow)

2. If placing it at the feed may yield infeasible operation (“overfeeding”)– If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM

inside recycle loop

BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)– Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**

**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control

104

A purely top-down approach: Start by controlling all active constaints at max. throughput (may give moving TPM)

Economic Plantwide Control Over a Wide Throughput Range: A Systematic Design Procedure

Rahul Jagtap, Nitin Kaisthaand Sigurd Skogestad

Step 0: Obtain active constraint regions for the wide throughput range

Step 1: Pair loops for tight control of economic CVs at maximum throughput – Most important point economically

– Most active constraints

Step 2: Design the inventory (regulatory) control system

Step 3: Design loops for ‘taking up’ additional economic CV control at lower throughputs along with appropriate throughput manipulation strategy

Moving TPM

Warning: May get complicated, but good economically because of tight control of active constraints

105

Figure 5. Plantwide control structure for maximum throughput operation of recycle process (Case Study I)

A + B CB + C D

Strippe

r

Column

A, B RecycleB

A

C

D

FC

PC

LCFC

TC

X

LC

FC

TC

TC

RC

LC

FC

FC

CCD

CCB

CCB

PC

LC

V1MAX V2

MAX

0.98%

0.02%

LVLRxrMAX

TPM for < max throughput

165 °C

xBRxr Opt HS3

TRxrOpt HS2

LS1

SP1

SP3

LC2

SP2

SP1 > SP2 > SP3

LC1

LC3

LS2

TRxrMAX

106

Conclusion TPM (production rate manipulator)

• Think carefully about where to place it!

• Difficult to undo later

107

Part 1.4 Structure of regulatory control layer (PID)

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"


108

Outline





– What to control ? (primary CV’s) (self-optimizing control)



– Distillation example



109

II. Bottom-up

• Determine secondary controlled variables (CV2) and structure (configuration) of control system (pairing, CV2-MV2)

• A good control configuration is insensitive to parameter changes

Regulatory layer

110

Step 5. Regulatory control layer

• Purpose: “Stabilize” the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades)

• Enable manual operation (by operators)

• Main structural decisions:• What more should we control?

(secondary cv’s, CV2, use of extra measurements)

• Pairing with manipulated variables (mv’s u2)

CV1

CV2 = ?

Regulatory layer

111

Objectives regulatory control layer1. Allow for manual operation

2. Simple decentralized (local) PID controllers that can be tuned on-line

3. Take care of “fast” control

4. Track setpoint changes from the layer above

5. Local disturbance rejection

6. Stabilization (mathematical sense)

7. Avoid “drift” (due to disturbances) so system stays in “linear region”– “stabilization” (practical sense)

8. Allow for “slow” control in layer above (supervisory control)

9. Make control problem easy as seen from layer above

10. Use “easy” and “robust” measurements (pressure, temperature)

11. Simple structure

12. Contribute to overall economic objective (“indirect” control)

13. Should not need to be changed during operation

Regulatory layer

112

Stabilizing control: Use inputs MV2=u2 to control “drifting” variables CV2

GKCV2s u2

CV2

CV1

Key decision: Choice of CV2 (controlled variable)

Also important: Choice of MV2=u2 (“pairing”)

Primary CV

Secondary CV(control fordynamic reasons)

Process control: Typical «drifting» variables (CV2) are•Liquid inventories (level)•Vapor inventories (pressure)•Some temperatures (reactor, distillation column profile)

Regulatory layer

113

Degrees of freedom unchanged

• No degrees of freedom lost as setpoints y2s replace inputs u2 as new degrees of freedom for control of y1

GKCV2s u2

CV2

CV1

Original DOFNew DOF

Cascade control:

Regulatory layer

114

Example: Exothermic reactor (unstable)

• u = cooling flow (q)

• CV1 = composition (c)

• CV2 = temperature (T)

u

TCCV2=T

CV2s

CCCV1=c

CV1s

feed

product

cooling

LC

Ls=max

Active constraints (economics):Product composition c + level (max)

Regulatory layer

115

Details Step 5 (Structure regulatory control layer)

(a) What to control (CV2)?

1. Control CV2 that “stabilizes the plant” (stops drifting)

2. Select CV2 which is easy to control (favorable dynamics)

• In addition, active constraints (CV1) that require tight control (small backoff) may be assigned to the regulatory layer.*

*Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat

Regulatory layer

116

“Control CV2 that stabilizes the plant (stops drifting)” In practice, control:

1. Levels (inventory liquid)

2. Pressures (inventory gas/vapor) (note: some pressures may be left floating)

3. Inventories of components that may accumulate/deplete inside plant• E.g., amine/water depletes in recycle loop in CO2 capture plant

• E.g., butanol accumulates in methanol-water distillation column

• E.g., inert N2 accumulates in ammonia reactor recycle

4. Reactor temperature

5. Distillation column profile (one temperature inside column)

• Stripper/absorber profile does not generally need to be stabilized

Regulatory layer

117

(b) Identify pairings =Identify MVs (u2) to control CV2, taking into account:

• Want “local consistency” for the inventory control– Implies radiating inventory control around given flow

• Avoid selecting as MVs in the regulatory layer, variables that may optimally saturate at steady-state (active constraint on some region), because this would require either– reassigning the regulatory loop (complication penalty), or – requiring back-off for the MV variable (economic penalty)

• Want tight control of important active constraints (to avoid back-off)

• General rule: ”pair close” (see next slide)

Details Step 5b….Regulatory layer

118

Step 5b…. Main rule: “Pair close”

The response (from input to output) should be fast, large and in one direction. Avoid dead time and inverse responses!

Regulatory layer

119

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

• Main reason: Minimizes need for reassigning loops

• Important: Always feasible (and optimal) to give up a CV when optimal MV saturation occurs. – Proof (DOF analysis): When one MV disappears (saturates), then we have one less optimal CV.

• Failing to follow this rule: Need some “fix” when MV saturates to remain optimal, like – reconfiguration (logic) – backoff (loss of optimality)

• BUT: Rule may be in conflict with other criteria– Dynamics (“pair close” rule)– Interactions (“avoid negative steady-state RGA” rule)– If conflict: Use reconfiguration (logic) or go for multivariable constraint control (MPC which may provide “built-in” logic)

Regulatory layer

LV

TCTs

. loop

LV

TCTs

LV

TCTs

TCTC TS

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

120

•

TCTC TS

LV

TCTs

. loop

LV

TCTs

LV

TCTs

Normal: Control T using V

121

Why simplified configurations?Why control layers?Why not one “big” multivariable controller?• Fundamental: Save on modelling effort

• Other: – easy to understand

– easy to tune and retune

– insensitive to model uncertainty

– possible to design for failure tolerance

– fewer links

– reduced computation load

Regulatory layer

122

Hierarchical/cascade 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:

1. 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

2. 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

123

XC

TC

FC

ys

y

Ls

Ts

L

T

z

XC

Cascade control

distillation

With flow loop +T-loop in top

124

QUIZ: What are the benefits of adding a flow controller (inner cascade)?

q z

qs

1. Counteracts nonlinearity in valve, f(z)• With fast flow control we can assume q = qs

2. Eliminates effect of disturbances in p1 and p2

Extra measurement y2 = q

125

Summary: Sigurd’s plantwide control rules

Rules for CV-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 (is 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

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)

– A special case is a closed system

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

126

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"


127

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

1 Sigurd Skogestad 1955: Born in Flekkefjord, Norway 1978: MS (Siv.ing.) in chemical engineering at...

Documents

Transcript of 1 Sigurd Skogestad 1955: Born in Flekkefjord, Norway 1978: MS (Siv.ing.) in chemical engineering at...