1. 1 Outline 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-optimizing 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

2. 2 II. Bottom-up Determine secondary controlled variables and structure (configuration) of control system (pairing) A good control configuration is insensitive to parameter changes Step 5. REGULATORY CONTROL LAYER 5.1Stabilization (including level control) 5.2Local 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)

3. 3 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 issues: What more should we control? (secondary cv’s, y 2, use of extra measurements) Pairing with manipulated variables (mv’s u 2 ) y 1 = c y 2 = ?

4. 4 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

5. 5 Let us start with the conclusion: Summary of step 5 The systematic plantwide control procedure of Skogestad (2004) includes the following steps: TOP-DOWN PART Step 1. Define economics and constraints Step 2. Optimization to identify regions of active constraints Step 3. Each region of active constraints: Identify self-optimizing CV1s for remaining unconstrained degrees of freedom Step 4. Locate TPM (important effect of economics because of possible back-off, as well as important effect on the inventory control system because of the requirement of “local consistency”.) BOTTOM-UP PART 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. Step 6. Supervisory layer. Single-loop OK or need multivariable control (MPC)? Step 7. RTO layer

6. 6 Rules for pairing of variables and choice of control structure Main rule: “Pair close” 1.The response (from input to output) should be fast, large and in one direction. Avoid dead time and inverse responses! 2.The input (MV) should preferably effect only one output (to avoid interaction between the loops) 3.Try to avoid input saturation (valve fully open or closed) in “basic” control loops for level and pressure 4.The measurement of the output y should be fast and accurate. It should be located close to the input (MV) and to important disturbances. Use extra measurements y’ and cascade control if this is not satisfied 5.The system should be simple Avoid too many feedforward and cascade loops 6.“Obvious” loops (for example, for level and pressure) should be closed first before you spend to much time on deriving process matrices etc.

7. 7 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

8. 8 Clossing inner loops (cascade control): Use of (extra) measurements (y 2 ) as (extra) CVs GK y 2s u2u2 y2y2 y1y1 Key decision: Choice of y 2 (controlled variable) Also important (since we almost always use single loops in the regulatory control layer): Choice of u 2 (“pairing”) Primary CV Secondary CV (control for dynamic reasons)

9. 9 Degrees of freedom unchanged No degrees of freedom lost by control of secondary (local) variables as setpoints become y 2s replace inputs u 2 as new degrees of freedom GK y 2s u2u2 y2y2 y1y1 Original DOF New DOF Cascade control:

10. 10 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

11. 11 XCXC TC FC ysys y LsLs TsTs L T z XCXC Cascade control distillation With flow loop + T-loop in top

12. 12 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 y 2 ) is not much influenced by the presence of the upper (slow) layers (involving y 1 ) 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

13. 13 QUIZ: What are the benefits of adding a flow controller (inner cascade)? q z qsqs 1.Counteracts nonlinearity in valve, f(z) With fast flow control we can assume q = q s 2.Eliminates effect of disturbances in p1 and p2 Extra measurement y 2 = q

14. 14 Objectives regulatory control layer 1.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 Implications for selection of y 2 : 1.Control of y 2 “stabilizes the plant” 2.y 2 is easy to control (favorable dynamics)

15. 15 1. “Control of y 2 stabilizes the plant” A. “Mathematical stabilization” (e.g. reactor): Unstable mode is “quickly” detected (state observability) in the measurement (y 2 ) and is easily affected (state controllability) by the input (u 2 ). Tool for selecting input/output: Pole vectors –y 2 : Want large element in output pole vector: Instability easily detected relative to noise –u 2 : Want large element in input pole vector: Small input usage required for stabilization B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity): Intuitive: y 2 located close to important disturbance Maximum gain rule: Controllable range for y 2 is large compared to sum of optimal variation and control error More exact tool: Partial control analysis

16. 16 Recall maximum gain rule for selecting primary controlled variables c: Controlled variables c for which their controllable range is large compared to their sum of optimal variation and control error Control variables y 2 for which their controllable range is large compared to their sum of optimal variation and control error controllable range = range y 2 may reach by varying the inputs optimal variation: due to disturbances control error = implementation error n Restated for secondary controlled variables y 2 : Want small Want large

17. 17 What should we control (y 2 )? Rule: Maximize the scaled gain General case: Maximize minimum singular value of scaled G Scalar case: |G s | = |G| / span |G|: gain from independent variable (u 2 ) to candidate controlled variable (y 2 ) –IMPORTANT: The gain |G| should be evaluated at the (bandwidth) frequency of the layer above in the control hierarchy! If the layer above is slow: OK with steady-state gain as used for selecting primary controlled variables (y 1 =c) BUT: In general, gain can be very different span (of y 2 ) = optimal variation in y 2 + control error for y 2 –Note optimal variation: This is often the same as the optimal variation used for selecting primary controlled variables (c). –Exception: If we at the “fast” regulatory time scale have some yet unused “slower” inputs (u 1 ) which are constant then we may want find a more suitable optimal variation for the fast time scale.

18. 18 Minimize state drift by controlling y 2 Problem in some cases: “optimal variation” for y 2 depends on overall control objectives which may change Therefore: May want to “decouple” tasks of stabilization (y 2 ) and optimal operation (y 1 ) One way of achieving this: Choose y 2 such that “state drift” dw/dd is minimized w = Wx – weighted average of all states d – disturbances Some tools developed: –Optimal measurement combination y 2 =Hy that minimizes state drift (Hori) – see Skogestad and Postlethwaite (Wiley, 2005) p. 418 –Distillation column application: Control average temperature column

19. 19 2. “y 2 is easy to control” (controllability) 1.Statics: Want large gain (from u 2 to y 2 ) 2.Main rule: y 2 is easy to measure and located close to available manipulated variable u 2 (“pairing”) 3.Dynamics: Want small effective delay (from u 2 to y 2 ) “effective delay” includes inverse response (RHP-zeros) + high-order lags

20. 20 Rules for selecting u 2 (to be paired with y 2 ) 1.Avoid using variable u 2 that may saturate at steady state (especially in loops at the bottom of the control hierarchy) Alternatively: Need to use “input resetting” in higher layer (“mid- ranging”) bit this is generally non-optimal (because we need some backoff). Example: Stabilize reactor with bypass flow (e.g. if bypass may saturate, then reset in higher layer using cooling flow) 2.“Pair close”: The controllability, for example in terms a small effective delay from u 2 to y 2, should be good.

21. 21 Effective delay and tunings θ = effective delay PI-tunings from “SIMC rule” Use half rule to obtain first-order model –Effective delay θ = “True” delay + inverse response time constant + half of second time constant + all smaller time constants –Time constant τ 1 = original time constant + half of second time constant –NOTE: The first (largest) time constant is NOT important for controllability! LATER !!

22. 22 Summary: Rules for selecting y 2 (and u 2 ) Selection of y 2 1.Control of y 2 “stabilizes” the plant The (scaled) gain for y 2 should be large 2.Measurement of y 2 should be simple and reliable For example, temperature or pressure 3.y 2 should have good controllability small effective delay favorable dynamics for control y 2 should be located “close” to a manipulated input (u 2 ) Selection of u 2 (to be paired with y 2 ): 1.Avoid using inputs u 2 that may saturate (at steady state) When u 2 saturates we loose control of the associated y 2. 2.“Pair close”! The effective delay from u 2 to y 2 should be small

23. 23 Extra For students that take PhD course!

24. 24 Selecting measurements and inputs for stabilization: Pole vectors Maximum gain rule is good for integrating (drifting) modes For “fast” unstable modes (e.g. reactor): Pole vectors useful for determining which input (valve) and output (measurement) to use for stabilizing unstable modes Assumes input usage (avoiding saturation) may be a problem Compute pole vectors from eigenvectors of A-matrix

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27. 27 Example: Tennessee Eastman challenge problem

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