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Plantwide control: Towards a systematic procedure

Sigurd Skogestad

Department of Chemical Engineering

Norwegian University of Science and Tecnology (NTNU)

Trondheim, Norway

Based om: Plenary Presentation at ESCAPE’12, , May 2002

Updated: August 2002 (for use in Advanced process control)

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• 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.

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Outline

• Introduction

• Plantwide control procedure – Top-down

– Bottom-up

• What to control I: Primary controlled variables

• Inventory control - where set production rate

• What to control II: Secondary controlled variables

• Decentralized versus multivariable control

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Related work

• Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice)

• Alan Foss (1973) - control system structure

• George Stephanopoulos and Manfred Morari (1980)

• Bill Luyben and coworkers (1975- ) - “snowball effect”

• Ruel Shinnar (1981- ) - “dominant variables”

• Jim Douglas and Alex Zheng (Umass) (1985- )

• Jim Downs (1991) - Tennessee Eastman process

• Larsson and Skogestad (2000): Review of plantwide control

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Idealized view of control(“Ph.D. control”)

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Practice I: Tennessee Eastman challenge problem (Downs, 1991)

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Practice II: Typical P&ID diagram(PID control)

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Practice III: Hierarchical structure

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Plantwide control

• 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 (PID, decoupler, MPC etc.).

• That is: All the decisions made before we get to “Ph.D” control

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Stepwise procedure plantwide control

I. TOP-DOWN

Step 1. DEFN. OF OPERATIONAL OBJECTIVES

Step 2. MANIPULATED VARIABLES and DEGREE OF FREEDOM ANALYSIS

Step 3. WHAT TO CONTROL? (primary variables)

Step 4. PRODUCTION RATE

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II. BOTTOM-UP (structure control system):

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)

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I. Top-down

• Step 1: Define operational objectives

• Step 2: Identify degrees of freedom

• Step 3: Identify primary controlled variables (look for self-optimizing variables)

• Step 4: Determine where to set the production rate

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Step 2. Manipulated variables and DOFs

Manipulated variables:

• Usually given by design (“valves”)

Degrees of freedom (DOFs):

• Nm : no. of dynamic (control) DOFs (valves)• Nss = Nm- N0 : steady-state DOFs• N0 : liquid levels with no steady-state effect (N0y)+ purely dynamic

control DOFs (N0m)

• Cost J depends normally only on steady-state DOFs

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Table 2. Typical number of steady-state degrees of freedom 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 fixed pressure)

• liquid phase reactor: 1 (volume)

• gas phase reactor: 1 (0 with fixed pressure)

• heat exchanger: 1 (duty or net area)

• distillation column excluding heat exchangers: 1 (0 with fixed pressure) + number of sidestreams

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• 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

…….

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Nm = 5, N0y = 2, Nss = 5 - 2 = 3 (2 with given pressure)

Distillation column with given feed

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Heat-integrated distillation process

Nm = 11 (w/feed), N0y = 4 (levels), Nss = 11 – 4 = 7

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Heat exchanger with bypasses

CW

Nm = 3, N0m = 2 (of 3), Nss = 3 – 2 = 1

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Alternatives structures for optimizing control

Step 3:What should we control?

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Step 3. What should we control? (primary controlled variables)

• Intuition: “Dominant variables” (Shinnar)

• Systematic: Define cost J and minimize w.r.t. DOFs– Control active constraints (constant setpoint is optimal)

– Remaining DOFs: Control variables c for which constant setpoints give small (economic) loss

Loss = J - Jopt(d)

when disturbances d occurs

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Loss with constant setpoints

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Self-optimizing control(Skogestad, 2000)

Self-optimizing control is achieved when a constant setpoint policy results in an acceptableloss L (without the need to reoptimize whendisturbances occur)

Loss L = J - Jopt (d)

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Effect of implementation error on cost

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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

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Example sharp optimum. High-purity distillation : c = Temperature top of column

Temperature

Ttop

Water (L) - acetic acid (H)Max 100 ppm acetic acid100% water: 100 C99.99 % water: 100.01C

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Procedure for selecting (primary) controlled variables (Skogestad, 2000)

• Step 3.1 Determine DOFs for optimization

• Step 3.2 Definition of optimal operation J (cost and constraints)

• Step 3.3 Identification of important disturbances

• Step 3.4 Optimization (nominally and with disturbances)

• Step 3.5 Identification of candidate controlled variables

• Step 3.6 Evaluation of loss with constant setpoints for alternative controlled variables

• Step 3.7 Evaluation and selection (including controllability analysis)

Case studies: Tenneessee-Eastman, Propane-propylene splitter, recycle process, heat-integrated distillation

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Application: Recycle processJ = V (minimize energy)

Nm = 5 N0y = 2Nss = 5 - 2 = 3

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2

3

4

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Given feedrate F0 and column pressure:

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Recycle process: Selection of controlled variables

• Step 3.1 DOFs for optimization: Nss = 3

• Step 3.2 J=V (minimize energy with given feed)

• Step 3.3 Most important disturbance: Feedrate F0

• Step 3.4 Optimization: Constraints on Mr and xB always active(so Luybens structure is not optimal)

• Step 3.5 1 DOF left, candidate controlled variables: F, D, L, xD, ...

• Step 3.6 Loss with constant setpoints. Good: xD, L/F. Poor: F, D, L

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Recycle process: Loss with constant setpoint, cs

Large loss with c = F (Luyben rule)

Negligible loss with c = L/F

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Recycle process: Proposed control structurefor case with J = V (minimize energy)

Active constraintMr = Mrmax

Active constraintxB = xBmin

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Recycle systems:

Do not recommend Luyben’s rule of fixing a flow in each recycle loop

(even to avoid “snowballing”)

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Good candidate controlled variables c (for self-optimizing control)

Requirements:

• The optimal value of c should be insensitive to disturbances

• c should be easy to measure and control

• 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.

Singular value rule (Skogestad and Postlethwaite, 1996):Look for variables that maximize the minimum singular value of the appropriately scaled steady-state gain matrix G from u to c

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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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Definition of bottleneck

A unit (or more precisely, an extensive variable E within this unit) is a bottleneck (with respect to the flow F) if

- With the flow F as a degree of freedom, the variable E is optimally at its maximum constraint (i.e., E= Emax at the optimum) - The flow F is increased by increasing this constraint (i.e., dF/dEmax > 0 at the optimum).

A variable E is a dynamic( control) bottleneck if in addition - The optimal value of E is unconstrained when F is fixed at a sufficiently low value

Otherwise E is a steady-state (design) bottleneck.

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

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Reactor-recycle process:Reconfiguration required when reach bottleneck

(max. vapor rate in column)

MAX

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

bottleneck (column)

F0s

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II. Bottom-up

• Determine secondary controlled variables and structure (configuration) of control system (pairing)

• A good control configuration is insensitive to parameter changes

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Step 5. Regulatory control layer

• Purpose: “Stabilize” the plant using local SISO PID controllers to enable manual operation (by operators)

• Main structural issues:• What more should we control? (secondary cv’s, y2)

• Pairing with manipulated variables (mv’s)

y1 = c

y2 = ?

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Selection of secondary controlled variables (y2)

• The variable is easy to measure and control

• For stabilization: Unstable mode is “quickly” detected in the measurement (Tool: pole vector analysis)

• For local disturbance rejection: The variable is located “close” to an important disturbance (Tool: partial control analysis).

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Partial control

y1 = P1 u1 + Pr1 (y2s-n2) + Pd1 dP1 = G11 – G12 G22

-1 G21

Pd1 = Gd1 – G12 G22-1 Gd2 - WANT SMALL

Pr1 = G12 G22-1

Primary controlled variable y1 = c(supervisory control layer)

Local control of y2

using u2

(regulatory control layer)

Setpoint y2s : new DOF for supervisory control

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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?

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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 active constraints move

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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• 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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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)

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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).

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References• Skogestad, S. (2000), “Plantwide control -towards a systematic procedure”, Proc.

ESCAPE’12 Symposium, Haag, Netherlands, May 2002.

• Larsson, T., 2000. Studies on plantwide control, Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim.

• 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, 2002, “Control of reactor, separator and recycle process’’, Submitted to Ind.Eng.Chem.Res.

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

See also the home page of S. Skogestad:

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