1 Structure of the process control system Benefits from MPC (Model Predictive Control) and RTO (Real...

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Structure of the process control system Benefits from MPC (Model Predictive Control) and RTO (Real Time Optimization)

Sigurd Skogestad

Department of Chemical EngineeringNorwegian University of Science and Tecnology (NTNU)Trondheim, Norway

Gassco Summit, 10 June 2004

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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

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Trondheim

Oslo

UK

NORWAY

DENMARK

GERMANY

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Sigurd Skogestad

• Born in 1955• 1978: Siv.ing. Degree (MS) in Chemical Engineering from NTNU (NTH)• 1980-83: Process modeling group at the Norsk Hydro Research Center in

Porsgrunn• 1983-87: Ph.D. student in Chemical Engineering at Caltech, Pasadena, USA.

Thesis on “Robust distillation control”. Supervisor: Manfred Morari• 1987 - : Professor in Chemical Engineering at NTNU• Since 1994: Head of process systems engineering center in Trondheim

(PROST)• Since 1999: Head of Department of Chemical Engineering• 1996: Book “Multivariable feedback control” (Wiley)• 2000, 2003: Book “Prosessteknikk” (Tapir)• Group of about 10 Ph.D. students

in the process control area

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Outline



II Bottom Up • Step 5: Regulatory control: What more to control ?• Step 6: Supervisory control (MPC)• Step 7: Real-time optimization (RTO)

• Case studies

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Plantwide control

Need to define objectives and identify main issues for each

layer

PID

RTO

MPC

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Outline


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?


• Case studies

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Outline




• Case studies

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Dynamic DOFs = valves = 5, Steady-state (economic) DOFs = 5 - 2 = 3 (incl. pressure)

Example: Distillation column with given feed

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Outline




• Case studies

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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) = 0Operational constraints: g(u0,x,d) < 0

• Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u0,x,d) = 0

J = cost feed + cost energy – value products

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Outline




• Case studies

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Implementation of optimal operation:Self-optimizing Control

Self-optimizing control is when acceptable operation can be achieved using constant set points (c

s)

for the controlled variables c

(without re-optimizing when disturbances occur).

c=csAcceptable loss )

self-optimizing control

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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

– Usually large economic benefit

– Requires good control system (PID/MPC)

• WHAT MORE SHOULD WE CONTROL?– Look for “self-optimizing” variables c for

remaining unconstrained degrees of freedom u.

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Example Active constraints control

• Optimal operation of 100m- runner, J=T– Active constraint: Maximum speed (energy)

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Example Self-optimizing Control – Marathon

• Optimal operation of Marathon runner, J=T– Any self-optimizing variable c (to control at constant

setpoint)?

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Example Self-optimizing Control – Marathon

• Optimal operation of Marathon runner, J=T– Any self-optimizing variable c (to control at constant

setpoint)?• c1 = distance to leader of race

• c2 = speed

• c3 = heart rate

• c4 = level of lactate in muscles

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Further examples self-optimizing control

• 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

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EXAMPLE: Recycle plant (Luyben, Yu, etc.)

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2

3

4

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Given feedrate F0 and column pressure:

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

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Recycle plant: Optimal operation

mT

1 remaining unconstrained degree of freedom

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Singular value rule: Steady-state gain

Luyben rule:

Not promising

economically

Conventional:

Looks good

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Control of recycle plant 1: Given feedrate

LC

XC

LC

XC

LC

xB

xD

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

Self-optimizing

variable

Active

constraint

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Control of recycle plant 2: Max. feedrate

LC

XC

LC

XC

LC

xB

xD

Rearrange loops (or use MPC)

Self-optimizing

variable

Active

constraintNew active constraint:

Max. vapor flow

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Outline




• Case studies

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Outline




• Case studies

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Step 5. Regulatory control layer

• 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 Exists many tuning rules, including Skogestad

(SIMC) rules: – Kc = 0.5/k (1/) I = min (1, 8)

• Structural issue: What loops to close. That is, which variables (y2) to control, and how to pair with “inputs” (u2) ?

u2

process

y2

y2s

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Objectives regulatory control layer

• Take care of “fast” control

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

• Allow for “slow” control in layer above (supervisory MPC control)

• Make control problem easy as seen from layer above

• Stabilization (mathematical sense, e.g. liquid level or reactor)

• Local disturbance rejection

• Local linearization (avoid “drift” due to disturbances)“stabilization”

(practical sense)

Implications for selection of y2:

1. Control of y2 “stabilizes the plant”

2. y2 is easy to control (favorable dynamics)

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Outline




• Case studies

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Step 6. Supervisory control layer (MPC)

• 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.

• Trend: Model predictive control (MPC) used as unifying tool.

• Structural issues: 1. What primary variables c=y1 to control?2. When use MPC and when use simpler single-loop

decentralized controllers ?

process

y2

y2s

c=y1

cs

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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 steady-state active constraints move

- Logic needed to handle dynamic constraints

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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 (both dynamic and steady-state)• no need for logic

• smooth transition

- Requires multivariable dynamic model

- Tuning may be difficult

- Less transparent

- “Everything goes down at the same time”

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Outline




• Case studies

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Step 7. Optimization layer (RTO)

• Purpose: Minimize cost function J and: – Identify active constraints – Recompute optimal setpoints cs 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– Do we need RTO? (or is optimal policy

“obvious” – e.g. max. load – or min. energy)process

y2

y2s

c=y1

cs

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Summary: Objectives of layers

cs = y1s

MPC

PID

y2s

RTO

u (valves)

“Maintain setpoints”CV=y1; MV=y2s

“Stabilize”CV=y2; MV=u

“Optimize setpoints”Min J; MV=y1s

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Benefits of MPC and RTO

• “10% more capacity and 20% less energy”

EVEN MORE IMPORTANT: ORGANIZATIONAL CHANGES

• More focus on operation and control

• More professional operation

• Better control: Less variation

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Gassco 3PM project(Plant Production Performance model)

Benefits:• RTO: Optimized setpoints (including identification of optimal active

constraints) that will improve plant performance and increase plant utilization. • Optimized production planning, including the optimization of unscheduled

maintenance sequences of equipment related to production forecasts• Reliable and business oriented capacity figures for the booking• Identification of de-bottlenecking measures• Reliable capacity figures for alternative feed gas compositions• More accurate basis for tariffing• More efficient use of resources, including energy savings• Improved basis for future expansion projects

ACHIEVING BENEFITS: REQUIRES FUTURE COMMITMENT

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References• Halvorsen, I.J, Skogestad, S., Morud, J.C., Alstad, V. (2003), “Optimal selection

of controlled variables”, Ind.Eng.Chem.Res., 42, 3273-3284.• Larsson, T. and S. Skogestad (2000), “Plantwide control: A review and a new

design procedure”, Modeling, Identification and Control, 21, 209-240. • Larsson, T., K. Hestetun, E. Hovland and S. Skogestad (2001), “Self-optimizing

control of a large-scale plant: The Tennessee Eastman process’’, Ind.Eng.Chem.Res., 40, 4889-4901.

• Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu (2003), “Control of reactor, separator and recycle process’’, Ind.Eng.Chem.Res., 42, 1225-1234

• Skogestad, S. and Postlethwaite, I. (1996), Multivariable feedback control, Wiley

• Skogestad, S. (2000). “Plantwide control: The search for the self-optimizing control structure”. J. Proc. Control 10, 487-507.

• Skogestad, S. (2003), ”Simple analytic rules for model reduction and PID controller tuning”, J. Proc. Control, 13, 291-309.

• Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, 219-234. (Special issue from ESCAPE’12 Symposium, Haag, May 2002).

• … + more…..

See home page of S. Skogestad:

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

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Looking for “magic” self-optimizing variables to keep at constant setpoints.

What properties do they have?

Skogestad and Postlethwaite (1996):

• The optimal value of c should be insensitive to disturbances

• c should be easy to measure and control accurately

• The value of c should be sensitive to changes in the steady-state degrees of freedom

(Equivalently, J as a function of c should be flat)

• For cases with more than one unconstrained degrees of freedom, the selected controlled variables should be independent.

• Summarized by minimum singular value rule

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Optimizer

Controller thatadjusts u to keep

cm = cs

Plant

cs

cm=c+n

u

c

n

d

u

c

J

cs=copt

uopt

n

Minimum singular value rule (G)

Want the slope (= gain G from u to c)

as large as possible

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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

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

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Production rate set at outlet:Inventory control opposite flow

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Production rate set inside process

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