The search for the self-optimizing control structure PLANTWIDE CONTROL:

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1 PLNTWIDE CONTROL: The search for the self-optimizing control structure Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Technology (NTNU) N-7491 Trondheim, Norway March 2 QUESTION: Why do we control all these variables for which there are no a priori specifications? (temperatures, pressures, internal compositions,... )

2 OUTLINE 1. Introduction: Theory and practice 2. Plantwide control and control structure design 3. Controlled variables 4. Self-optimizing control 5. Previous work on self-optimizing control. Procedure for selecting controlled variables 7. Distillation case study 8. Optimal operation: n ethical dilemma? 9. Conclusion

3 The Trondheim Plantwide control group : dun Faanes (ph-neutralization; control structure design) Marius Govatsmark (Refinery; HD plant) Ivar Halvorsen (Petlyuk distillation; self-optimizing control) Truls Larsson (methanol plants; control structure design) Tore Lid (Refinery) Sigurd Skogestad associated (earlier) members John Morud (Sintef Kjemi) Kjetil Havre (BB) Bjørn Glemmestad (Borealis) plus Morten Hovd, Department of Engineering Cybernetics, NTNU Stig Strand, Statoil

4 Ph.D. thesises of Morud (1995), Glemmestad (1997) and Havre (1998). review1.pdf review of plantwide control, S. Skogestad and T. Larsson, (Internal report, g. 1998). vailable at: Chapter 1: Control structure design (plantwide control) Chapter : Limations on performance in MIMO systems (more controllability) Chapter 5: Limations on performance in SISO systems (controllability) Multivariable Feedback Control, S. Skogestad and I. Postlethwaite, Wiley, Shorter version: Self-optimizing control: The missing link berween steady-state optimization and control, S. Skogestad, Symposium Process Systems Engineering PSE 2, Keystone, Colorado, July 2. vaialable at: Plantwide control: The search for the self-optimizing control structure, S. Skogestad (prepared for publication in J.Proc.Control). vaialable at: Written material:

5 to which counteracts the influence of : Disturbances ( : Manipulated inputs ( norm from Find a controller which based on the information in, generates a control signal on, thereby minimizing the closed-loop. : Control error, ) : Measurements ( ) and setpoints ( ) ) and setpoints ( ) control signals sensed outputs exogenous inputs (weighted) (weighted) exogenous outputs General controller design formulation (Ph.D.level) EXISTING CONTROL THEORY

6 PRCTICE Typical base level control structure PID level

7 PRCTICE Typical control hierarchy

8 Relevant questions in practice 1. Is the plant easy or difficult to control? (controllability analysis)? 2. How should the plant be controlled (plantwide control)? (THIS TLK) lan Foss ( Critique of chemical process control theory, IChE 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? The gap is present indeed, but contrary to the views of many, it is the theoretician who must close it.

9 PLNTWIDE CONTROL (Control structure design) The control philosphy for the overall plant with emphasis on the structural decisions: Not: Which boxes (controllers; decision makers) do we have and what information (signals) are send between them The inside of the boxes (design and tuning of all the controllers)

10 CONTROL STRUCTURE DESIGN TSKS 1. Selection of controlled outputs (a set of variables which are to be controlled to achieve a set of specific objectives) 2. Selection of manipulations and measurements (sets of variables which can be manipulated and measured for control purposes) 3. Selection of control configuration (a structure interconnecting measurements/commands and manipulated variables) 4. Selection of controller type (control law specification, e.g., PID, decoupler, LQG, etc.). Tasks 1 and 2 combined: input/output selection Task 3 (configuration): input/output pairing pproach Control structure design: Top-down consideration of control objectives and available degrees of freedom to meet these (tasks 1 and 2) Bottom-up design of the control system, starting with stabilization (tasks 3, 4, 5).

11 1 ( * (,-, * ( /..,.. *. ( $% $ &' & $ & $ & &! The setpoints of the controlled variables ( link two layers in a control hierarchy, whereby the upper layer computes the value of to be implemented by the lower layer. 1 ) are the (internal) variables that Figure.1: Typical control hierarchy in a chemical plant. control (seconds) Regulatory () Control layer *+, control (minutes) Supervisory Local optimization (hour) "# " " Site-wide optimization (day) Scheduling (weeks) Controlled variables

12 2 BUT second question: lmost no theory. Decisions mostly made on experience and intuition. First question: lot of theory. 2. Implementation: What should be the controlled variables? (includes open-loop by selecting ) )? 1. Optimization: What are the optimal values (e.g. Two distinct questions: TSK 1: Selection of controlled variables

13 B 2 B B B 2 B B C > < 8 < > ;: DFEG HH 354 JI4K L H Free degrees of freedom after satisfying constraints 354 B < Degrees of freedom for optimization Gives = = >,, etc.? = >@ (2) subject to constraints = (1) Minimize cost 8with respect to the degrees of freedom Optimization

14 M O N M O N O O O N N N N M P N. P N N N (c) Integrated optimization and control. Reoptimize = > (b) Closed-loop. Constant = Q > (a) Open-loop. Constant = RQ > (a) (b) (c) Measurement noise n n Disturbance d Process d Process d Process u u u Controller - c s c m Optimizer Optimizer Optimizing Controller Objective Objective Objective Implementation Measurements v.

15 S S Used in practice. Insensitive to changes ( self-optimizing ). Optimizer : Cook book (look-up table) oven temperature 2. Closed-loop implementation: Constant temperature Problem: Sensitive to uncertainty and optimal value depends strongly on size of oven 1. Open-loop implementation: Constant heat input Implementation: Degree of freedom: Heat input Goal (purpose): Well-baked inside and nice outside Example: Cake baking

16 Self-optimizing control C = constant 2,s Cost J Loss C = constant 1,s Reoptimized J opt(d) d * Disturbance d Figure.2: Loss imposed by keeping constant setpoint for the controlled variable Self-optimizing control is when we can achieve an acceptable loss with constant setpoint values for the controlled variables (without the need to reoptimize when disturbances occur)

17 Effect of implementation error J J J [ c c c (a) (b) (c) Figure.3: Implementing the controlled variable (a) Implementation easy: ctive constraint control (b) Implementation easy: Insensitive to error in (c) Implementation difficult: Look for another controlled variable]

18 Previous work on self-optimzing control Morari, Stephanopoulos and rkun (198): Translate ecomomic objectives into control objectives Find a function of process variables, which when held constant leads automatically to the optimal adjustment of the manipulated variables Shinnar (1981); rbel, Rinard and Shinnar (199): Dominant variables (= natural choice for controlled variables ) Luyben (1988): Eigenstructure (= the best self-regulationg and self-optimizing structure) Fisher, Dohert and Douglas (1988, part 3): HD example Rijnsdorp (1991): on-line algorithms for adjusting the degrees of freedom for optimization Narraway and Perkins (1991, 1993, 1994): Base control structure selection on process economics Marlin and Hrymak (1997): Implementation of optimal solution; active constraints Zheng, Mahajannam and Douglas (1999): Minimize economic penalty

19 X Variables (and thus U) are scaled such that requirements 1 and 2) = > XZY [(takes care of W 7 U W (linearized model) Here Prefer a set of controlled variables with a large minimum singular value of the scaled gain matrix,. T =VU = > > The four requirements may be combined into the singular value rule: 4. Be independent (not closely correlated) (Equivalently, the optimum should be flat with respect to ). 3. Should be sensitive to the manipulated inputs ( ), i.e. have a large range. 2. Be easy to control accurately (small implementation error) 1. Have a small variation in optimal setpoints The selected set of variables should: Skogestad and Postlethwaite (199; Chapter 1). Requirements for controlled variables

20 Selecting controlled variables Today: Steady-state optimization is performed routinely Thus: Have the main tools needed for a proper selection of controlled variables: Steady-state model Information about operational constraints Well-defined economic objective (scalar cost function 8to be minimized)

21 BLeaves B 2 B HHdegrees of freedom: Typically, consider measured variables or simple combinations thereof. Want to use constant. Use above requirements, e.g look for variables where is constant ^5_ ] = > 1 ^5_ ] = RQ > D EG Normally implement active constraints Step 5: Identify candidate controlled variables. Find the optimal steady-state operation for various disturbances. Step 4: Optimization. Implementation errors ( Disturbances Q that occur after the optimization Step 3: Identify important disturbances (uncertainty). Step 2: Cost function and constraints. Define the optimal operation problem by formulating a scalar cost function 8to be minimized for optimal operation, and specify the constraints that need to be satisfied. Step 1: Degree of freedom analysis. Determine the number of degrees of freedom ( ) for the degrees of freedom. 354 < ) available for optimization, and identify a base set ( \ ) in controlled variables Procedure for selecting controlled variables

22 \ > b \ \ > region of feasibility expected dynamic control performance (input-output controllability) See if they are adequate with respect to other criteria that may be relevant, such like Select for further consideration the sets of controlled variables with acceptable loss. Step 7: Further analysis and selection. with fixed setpoints errors. d e \ 1 for the defined disturbances d eand implementation ` = > 8 = > 8 = ^5_ ] = >a = 1c (3) Step : Evaluation of loss. Compute the mean value of the loss for alternative sets of controlled variables. This is done by evaluating the loss

23 B 2 v B yx f qp i g o h rp n (e.g. selected as}and ~, or`and ~) 354 B < Step 1: Degree of freedom analysis Given pressure and feedrate w {z [ [ a B w t u[ v[ Propylene-propane splitter m l s q s r m l i jk l Case study: Distillation

24 ˆ [ (andƒ ˆ ~ Š Œ Ž ) v Š Œ Ž (Maximum capacity) y y {(Distillate purity specification) Step 2b: Constraints. Maximum acceptable loss `:.4 $/min = 2 $/year Typical profit: Y $/min v a [ v a w [ Prices [$/kmol] 8 } c w ƒ Step 2a: Cost function

25 ~ v Y Implementation trivial : Constant drop (avoid flooding) and increase ~until achieve max. pressure kmol/min (to maximize yield of valueable distillate product) y y {(never overpurify valueable product) Both constraints active ~ Case 1: Cheap energy ( ) Case 3: Same as Case 2, but with feed rate as degree of freedom Case 2: [[$/kmol] Case 1: (cheap energy) Will consider three cases:

26 \ In addition : 2% implementation errors for : Safety margin on : increase purity from.995 to.99 : Liquid fraction from 1. (pure liquid) to.5 (5% vaporized) : w from.5 to.75 : w from.5 to.5 : 3% increase inƒ Step 3: Disturbances. More detailed analysis needed ~ Case 2: Trade-off between energy and yield ( [$/kmol])

27 Œ ` B [ ª «{[ { u u x { u x [ x [ { u { {[ { u v { v yu ƒ u {z u ž œ u {z u ž ` Œ } a } Œ ƒ a ` a ` Œ ƒ a ~ Œ ƒ a } Six alternative controlled variables are considered Control From Table 1: BUT: Expensive and control problems at.4 One unconstrained degree of freedom, DFEG HH Bottom product purity constraint always active: y y { Step 5: Candidate controlled variables. Table 1. Optimal operating point (with maximum profit Œ ƒ) Nominal values:,, y y z y y z v vu[ ž y [ zu v xv v u ž w y y { z yx {[ {[ vu žv v xu z Ÿ u { ž [ w {ž y y { { ž [ x {[ vu Ÿ y[ u zv { u zv w y y { xv Ÿ z {[ vu v x vu[ Ÿ ž Ÿ u[ x y y { z yx {[ {[ v {xu ž u { v Ÿ š ;:9 y y { z yx {[ {[ v {xu ž u { v Ÿ } Œ ƒ ` Œ ƒ ~ Œ ƒ Œ ƒ Step 4: Optimization

28 Œ `Relatively poor: } ~ ` Ä Å Å Å Å ªÅ ;: { { ;: ƒ œ u {z u {z u ž ` Œ } } ll insesnitive to feed enthalpy ( w ) Poor: lso small loss: Œ ƒ(or Œ ƒor constant }) constant Œ ƒconstant. Loss small with Table 2. Loss [$/min] for distillation case study. Unacceptable loss (larger than.4) shown in bold face 2% impl.error: Â Ã Æ Ç m È Ç m Å É Å Ç Ç m Æ Å Å ÁÀ denotes infeasible operation v º: 9» u ¼½ ½ ½ v[ u² ² µ u² ² µ u² ¾ u² y y z u ¹ u ¹ µ u µ ² u µ ² u µ ² u µ w [ [ x w {ž y[ u ± z z u² µ w v x [ ² u µ u[ x u ±² ³ š ;:9 z yx {[ {[ {[ v {xu ž } Œ ƒ ` ` Œ ƒ ~ Œ ƒ Step : Evaluation of loss

29 `ƒfor Include feedforward from and ~

30 f qp i g o h rp n Ì Ì ` Ì ~ Ë Ê Î Ë Ê Î Ë Ê Î Í Í Í m l s q s r m l i jk l ~ Œ ƒ {[ u ž is kept constant (because ~may reach constraint). `is used to keep y y {. Proposed control system. One-point or preferred Two-point structure : Difficult (interactive) control problem Ï a Œ ƒ Ï a Œ ƒ Ï a Step 7: Selection of controlled variables. Lowest loss:

31 ÑÐ sƒ ƒ ~~is kept at v ƒ ~~is adjusted to keep ƒ is increased from to 1.5, the optimal value.4 and.9. of increases from is kept at its maximum available valueƒ ÑÐ(active constraint). ÑÐ (active constraint). `is used to keep y y {(active constraint). Proposed control system: 2. Intermediate available feed rates; vu[ ž Ò ƒ ÑÐ Ò { u[ z z[kmol/min]. is kept at its maximum available valueƒ ÑÐ(active constraint). Œ ƒ {[ u ž constant `is used to keep y y {(active constraint). Proposed control system: 1. Low available feed rates;ƒ vu[ ž [kmol/min]). (Same as above) Consider available feed rateƒ ÑÐas a parameter. ÑÐ dditional constraint Three degrees of freedom Case 3: Feedrate as degree of freeedom

32 ~ ~ ƒ v In this case: y Œ ƒis better if the value of u[ { z ƒis adjusted to keep zconstant, but using ~ Œ ƒ v[ u ž žconstant (alternatively, we may keep ÑÐchanges) ÑÐ ~~is kept at (active constraint). `is used to keep y y {(active constraint). Proposed control system: 3. Large available feed rates;ƒ ÑÐ Ó { u[ z z[kmol/min]).

33 Œ ƒ ~ ¼ Ù Ü ÜÖ n environmental and ethical dilemma? Question: Less effective use of raw materials and energy than design Œ ƒthan design Smaller specific value increase Maximize profit limiting value increase; Often:ƒa degree of freedom (with no effect on prices) Operation Œ ƒ = maximize value increase Maximize profit [$/kg] ƒgiven Design } c w ƒ For example ½Ô Õ Ö ½Ô Ø Ù ÚÖ Øœ ¼ Û ¼ ¼ Ù Ü Ö Ý œ½: Þœ Both design and operation: Maximize profit [$/min] Optimal operation: n ethical dilemma? ƒ: Operate at capacity constraint(s) and increase until zero

34 2. PRODUCTION RTE: Where should the throughput be set? The throughput manipulator cannot be used for other control tasks, thus this choice will have a large effect on the structure of the control system. The optimal choice may follow from steadystate optimization, but may require continuous reconfiguration (may use MPC to avoid this) The throughput manipulator should have a strong and direct effect on the production rate. ßàâá What is the control objective and which variables should be controlled? Goal: Obtain primary controlled variables ( ã) Steady-state model and operational objectives Degree of freedom analysis. Determine the major distrubances. Evaluate the (economic) loss, with constant controlled variables and look for selfoptimizing control structure. Step Tools (in addition to insight) Top-down analysis: 1. CONTROLLED VRIBLES: plantwide control design procedure

35 ßä ) so that the ßà ) plantwide control design procedure Bottom up design: (With given controlled and manipulated variables) nalysis 1. REGULTORY CONTROL LYER. The purpose of this control layer is to enable manual operation of the plant Stabilization. Selection of measurements and inputs for stabilization (including slowly drifting modes). Pole vectors Give insight about which measurements and inputs can be used for each unstable mode. Select large elements: Small input energy needed and large noise tolerated. Local disturbance rejection. Often based on secondary measurements. Partially controlled plant Select secondary measurements ( effect of disturbances on the primary output ( can be handled by the operators. 2. SUPERVISORY CONTROL LYER. The purpose of this control layer is to control the primary control variables ( ã). Decentralized control. We use a decentralized control structure if the process is noninteracting and the constraints are not changing. Feed-forward control and ratio control may be useful here. Controllability analysis for decentralized control Pair on relative gain array close to identity matrix at crossover frequency, provided not negative at stead-state. Closed loop disturbance gain (CLDG) and performance gain array (PRG) may be used to analyze the interactions. Multivariable control Use for interacting process (coordination including feed-forward control). MPC is useful for tracking the active constraints (if the steady-state optimization shows that the active constraints are changing with disturbances).

36 CONCLUSION QUESTION Why do we control all these variables for which there are no a priori specifications? (temperatures, pressures, internal compositions,... ) NSWER: We have degrees of freedom that need to be specified to achieve optimal operation The controlled variables are the links between steady-state economics and process control Select the controlled variables to achieve self-optimizing control

The dos and don ts of distillation column control

The dos and don ts of distillation column control Sigurd Skogestad * Department of Chemical Engineering Norwegian University of Science and Technology N-7491 Trondheim, Norway Abstract The paper discusses