1 A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL ( ) Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway DTU March 2011

2 Title: A systematic approach to plantwide control. Abstract: A chemical plant may have thousands of measurements and control loops. By the term plantwide control it is not meant the tuning and behavior of each of these loops, but rather the control philosophy of the overall plant with emphasis on the structural decisions. In practice, the control system is usually divided into several layers, separated by time scale: scheduling (weeks), site-wide optimization (day), local optimization (hour), supervisory (predictive, advanced) control (minutes) and regulatory control (seconds). Such a hiearchical (cascade) decomposition with layers operating on different time scale is used in the control of all real (complex) systems including biological systems and airplanes, so the issues in this section are not limited to process control. In the talk the most important issues are discussed, especially related to the choice of variables that provide the link the control layers.

3 A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL ( ) Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway PROST Feb. 2011

4 c s = y 1s MPC PID y 2s RTO u (valves) Follow path (+ look after other variables) Stabilize + avoid drift Min J (economics) OBJECTIVE Dealing with complexity Plantwide control The controlled variables (CVs) interconnect the layers

5 How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc.

6 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. Previous work on plantwide control: 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

7 Control structure design procedure I Top Down Step 1: Define operational objectives (optimal operation) –Cost function J (to be minimized) –Operational constraints Step 2: Identify degrees of freedom (MVs) and optimize for expected disturbances Step 3: Select primary controlled variables c=y 1 (CVs) Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory / stabilizing control (PID layer) –What more to control (y 2 ; local CVs)? –Pairing of inputs and outputs Step 6: Supervisory control (MPC layer) Step 7: Real-time optimization (Do we need it?) y1y1 y2y2 Process MVs

8 Step 1. Define optimal operation (economics) What are we going to use our degrees of freedom u (MVs) for? Define scalar cost function J(u,x,d) –u: degrees of freedom (usually steady-state) –d: disturbances –x: states (internal variables) Typical cost function: Optimize operation with respect to u for given d (usually steady-state): min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 J = cost feed + cost energy – value products

9 Step 2: Identify degrees of freedom and optimize for expected disturbances Optimization: Identify regions of active constraints Time consuming! Control: 2 active constraints (x A, x B ) + 2 “selfoptimizing” Example (Magnus G. Jacobsen): Two distillation columns in series. 4 degrees of freedom

10 Step 3: Implementation of optimal operation Optimal operation for given d * : min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 → u opt (d * ) Problem: Usally cannot keep u opt constant because disturbances d change How should we adjust the degrees of freedom (u)?

11 Implementation (in practice): Local feedback control! “Self-optimizing control:” Constant setpoints for c gives acceptable loss y FeedforwardOptimizing controlLocal feedback: Control c (CV) d

12 Question: What should we control (c)? (primary controlled variables y 1 =c) Introductory example: Runner Issue: What should we control?

13 –Cost to be minimized, J=T –One degree of freedom (u=power) –What should we control? Optimal operation - Runner Optimal operation of runner

14 Sprinter (100m) 1. Optimal operation of Sprinter, J=T –Active constraint control: Maximum speed (”no thinking required”) Optimal operation - Runner

15 2. Optimal operation of Marathon runner, J=T Unconstrained optimum! Any ”self-optimizing” variable c (to control at constant setpoint)? c 1 = distance to leader of race c 2 = speed c 3 = heart rate c 4 = level of lactate in muscles Optimal operation - Runner Marathon (40 km)

16 Conclusion Marathon runner c = heart rate select one measurement Simple and robust implementation Disturbances are indirectly handled by keeping a constant heart rate May have infrequent adjustment of setpoint (heart rate) Optimal operation - Runner

17 Step 3. What should we control (c)? (primary controlled variables y 1 =c) Selection of controlled variables c 1.Control active constraints! 2.Unconstrained variables: Control self-optimizing variables!

18 Example active constraint Optimal operation = max. throughput (active constraint) Time Back-off = Lost production Rule for control of hard output constraints: “Squeeze and shift”! Reduce variance (“Squeeze”) and “shift” setpoint c s to reduce backoff Want tight bottleneck control to reduce backoff!

19 Control “self-optimizing” variables 1. Old idea (Morari et al., 1980): “We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions.” 2. The ideal self-optimizing variable c is the gradient (c =  J/  u = J u ) –Keep gradient at zero for all disturbances (c = J u =0) –Problem: no measurement of gradient Unconstrained degrees of freedom u cost J J u =0 JuJu

20 H Ideal: c = J u In practise: c = H y

21 Optimal operation Cost J Controlled variable c c opt J opt Unconstrained optimum

22 Optimal operation Cost J Controlled variable c c opt J opt Two problems: 1. Optimum moves because of disturbances d: c opt (d) 2. Implementation error, c = c opt + n d n Unconstrained optimum

23 H

24 Guidelines for selecting measurements as CVs Rule 1: Optimal value for CV (c=Hy) is insensitive to disturbances d (minimizes effect of moving optimum) –|dc opt /dd| is small Rule 2: c should be easy to measure and control (small implementation error n) Rule 3: “Maximum gain rule”: c should be sensitive to input changes (large gain |G| from u to c) or equivalently the optimum J opt should be flat with respect to c (minimizes effect of implementation error n) –|G| = |dc/du| is large Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure”, Journal of Process Control, 10, (2000).

25 Optimal measurement combination H Candidate measurements (y): Include also inputs u

26 Nullspace method No measurement noise

27 c s = constant K H y c u “Minimize” in Maximum gain rule ( maximize S 1 G J uu -1/2, G=HG y ) “Scaling” S 1 “=0” in nullspace method (no noise) Optimal measurement combination, c = Hy With measurement noise

28 Example: CO2 refrigeration cycle J = W s (work supplied) DOF = u (valve opening, z) Main disturbances: d 1 = T H d 2 = T Cs (setpoint) d 3 = UA loss What should we control? pHpH

29 CO2 refrigeration cycle Step 1. One (remaining) degree of freedom (u=z) Step 2. Objective function. J = W s (compressor work) Step 3. Optimize operation for disturbances (d 1 =T C, d 2 =T H, d 3 =UA) Optimum always unconstrained Step 4. Implementation of optimal operation No good single measurements (all give large losses): –p h, T h, z, … Nullspace method: Need to combine n u +n d =1+3=4 measurements to have zero disturbance loss Simpler: Try combining two measurements. Exact local method: –c = h 1 p h + h 2 T h = p h + k T h ; k = bar/K Nonlinear evaluation of loss: OK!

30 CO2 cycle: Maximum gain rule

31 Refrigeration cycle: Proposed control structure Control c= “temperature-corrected high pressure”

32 Step 4. Where set production rate? Where locale the TPM (throughput manipulator)? Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts

33 Production rate set at inlet : Inventory control in direction of flow* * Required to get “local-consistent” inventory control TPM

34 Production rate set at outlet: Inventory control opposite flow TPM

35 Production rate set inside process TPM

36 LOCATE TPM? Default choice: place the TPM at the feed Consider moving if there is an important active constraint that could otherwise not be well controlled.

37 Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s Degrees of freedom for supervisory control, MV1=CV2s + unused valves Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs) Optimizer (RTO) PROCESS Supervisory controller (MPC) Regulatory controller (PID) H2H2 H CV 1 CV 2s y nyny d Stabilized process CV 1s CV 2 Physical inputs (valves) Optimally constant valves Always active constraints

38 Step 5: Regulatory control layer Step 5. Choose structure of regulatory (stabilizing) layer (a) Identify “stabilizing” CV2s (levels, pressures, reactor temperature,one temperature in each column, etc.). 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) (b) Identify pairings (MVs to be used to control CV2), taking into account –Want “local consistency” for the inventory control –Want tight control of important active constraints –Avoid MVs that may saturate in the regulatory layer, because this would require either reassigning the regulatory loop (complication penalty), or requiring back-off for the MV variable (economic penalty) Preferably, the same regulatory layer should be used for all operating regions without the need for reassigning inputs or outputs.

39 Example: Distillation Primary controlled variable: y 1 = c = x D, x B (compositions top, bottom) BUT: Delay in measurement of x + unreliable Regulatory control: For “stabilization” need control of (y 2 ): –Liquid level condenser (M D ) –Liquid level reboiler (M B ) –Pressure (p) –Holdup of light component in column (temperature profile) Unstable (Integrating) + No steady-state effect Variations in p disturb other loops Almost unstable (integrating) TC TsTs T-loop in bottom

40 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

41 ”Advanced control” STEP 6. SUPERVISORY LAYER Objectives of supervisory layer: 1. Switch control structures (CV1) depending on operating region Active constraints self-optimizing variables 2. Perform “advanced” economic/coordination control tasks. –Control primary variables CV1 at setpoint using as degrees of freedom (MV): Setpoints to the regulatory layer (CV2s) ”unused” degrees of freedom (valves) –Keep an eye on stabilizing layer Avoid saturation in stabilizing layer –Feedforward from disturbances If helpful –Make use of extra inputs –Make use of extra measurements Implementation: Alternative 1: Advanced control based on ”simple elements” Alternative 2: MPC

42 Summary. Systematic procedure for plantwide control 1.Start “top-down” with economics: –Step 1: Define operational objectives and identify degrees of freeedom –Step 2: Optimize steady-state operation. –Step 3A: Identify active constraints = primary CVs c. Should controlled to maximize profit) –Step 3B: For remaining unconstrained degrees of freedom: Select CVs c based on self-optimizing control. –Step 4: Where to set the throughput (usually: feed) 2.Regulatory control I: Decide on how to move mass through the plant: Step 5A: Propose “local-consistent” inventory (level) control structure. 3.Regulatory control II: “Bottom-up” stabilization of the plant Step 5B: Control variables to stop “drift” (sensitive temperatures, pressures,....) –Pair variables to avoid interaction and saturation 4.Finally: make link between “top-down” and “bottom up”. Step 6: “Advanced control” system (MPC): CVs: Active constraints and self-optimizing economic variables + look after variables in layer below (e.g., avoid saturation) MVs: Setpoints to regulatory control layer. Coordinates within units and possibly between units cscs

43 Summary and references The following paper summarizes the procedure: –S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), (2004).``Control structure design for complete chemical plants'', 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, (2000).``Plantwide control: A review and a new design procedure''

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