Control structure design: What should we measure, control and manipulate? Sigurd Skogestad Department of Chemical Engineering NTNU, Trondheim First African Control Conference, Cape Town, 04 December 2003 1 Outline
2 About myself Control structure design A procedure for control structure design Selection of primary controlled variables Example stabilizing control: Anti slug control Conclusion Sigurd Skogestad
3 Born in 1955 1956-1961: Lived in South Africa (Durban & Johannesburg) 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 Research: Develop simple yet rigorous methods to solve problems of engineering significance.
Use of feedback as a tool to 1. reduce uncertainty (including robust control), 2. change the system dynamics (including stabilization; anti-slug control), 3. generally make the system more well-behaved (including self-optimizing control). 4 limitations on performance in linear systems (controllability),
control structure design and plantwide control, interactions between process design and control, distillation column design, control and dynamics. Natural gas processes Outline 5
About myself Control structure design A procedure for control structure design Selection of primary controlled variables Example stabilizing control: Anti slug control Conclusion Idealized view of control (Ph.D. control) 6 Practice: Tennessee Eastman challenge problem (Downs, 1991) (PID control)
7 Control structure design 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 (LQG, H-infinity, PID, decoupler, MPC etc.). 8 That is: Control structure design includes all the decisions we need make to get from ``PID control to Ph.D control Process control:
Control structure design = plantwide control Large systems Each plant usually different modeling expensive Slow processes no problem with computation time Structural issues important What to control? Extra measurements Pairing of loops 9
Control structure selection issues are identified as important also in other industries. Professor Gary Balas at ECC03 about flight control at Boeing: The most important control issue has always been to select the right controlled variables --- no systematic tools used! 10 Process operation: Hierarchical structure RTO
MPC PID 11 Need to define objectives and identify main issues for each layer Regulatory control (seconds) 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 Status: Many loops poorly tuned Most common setting: Kc=1, I=1 min (default) Even wrong sign of gain Kc . 12
Regulatory control... Trend: Can do better! Carefully go through plant and retune important loops using standardized tuning procedure Exists many tuning rules, including Skogestad (SIMC) rules: Kc = 0.5/k (1/) I = min (1, 8) Probably the best simple PID tuning rules in the world
13 Outstanding structural issue: What loops to close, that is, which variables (y2) to control? Supervisory control (minutes) Purpose: Keep primary controlled variables (y1) at desired values, using as degrees of freedom the setpoints y 2s for the regulatory layer. Status: Many different advanced controllers, including feedforward, decouplers, overrides, cascades, selectors, Smith Predictors, etc.
Issues: Which variables to control may change due to change of active constraints Interactions and pairing 14 Supervisory control... Trend: Model predictive control (MPC) used as unifying tool. Linear multivariable models with input constraints Tuning (modelling) is time-consuming and expensive
Issue: When use MPC and when use simpler single-loop decentralized controllers ? MPC is preferred if active constraints (bottleneck) change. Avoids logic for reconfiguration of loops Outstanding structural issue: What primary variables y1 to control? 15 Local optimization (hour) Purpose: Identify active constraints and possibly recompute optimal setpoints y1s for 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. Modelling is time-consuming and expensive
16 Outline 17 About myself Control structure design A procedure for control structure design
Selection of primary controlled variables Example stabilizing control: Anti slug control Conclusion 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 outputs, c= y1) Step 4. PRODUCTION RATE 18 II. BOTTOM-UP (structure control system):
Step 5. REGULATORY CONTROL LAYER Stabilization and Local disturbance rejection What more to control? (secondary outputs y2) Step 6. SUPERVISORY CONTROL LAYER Decentralized control or MPC? Step 7. OPTIMIZATION LAYER (RTO) 19 Outline
20 About myself Control structure design A procedure for control structure design Selection of primary controlled variables Example stabilizing control: Anti slug control Conclusion What should we control? y1 = c ? (economics) y2 = ? (stabilization)
21 Optimal operation (economics) Define scalar cost function J(u0,d) u0: degrees of freedom d: disturbances Optimal operation for given d: minu0 J(u0,d) subject to:
f(u0,d) = 0 g(u0,d) < 0 22 Active constraints 23 Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy active constraints, g(u 0,d) = 0
Implementation of active constraints is usually simple. We here concentrate on the remaining unconstrained degrees of freedom u. Optimal operation Cost J Jopt uopt 24
Independent variable u (remaining unconstrained) Implementation: How do we deal with uncertainty? 1. Disturbances d 2. Implementation error n us = uopt(d*) nominal optimization n u = us + n d Cost J Jopt(d) 25
Problem no. 1: Disturbance d d Cost J d* Jopt Loss with constant value for u uopt(d0) 26 Independent variable u
Problem no. 2: Implementation error n Cost J d0 Loss due to implementation error for u Jopt us=uopt(d0) u = us + n Independent variable u
27 Obvious solution: Optimizing control Probem: Too complicated 28 Alternative: Look for another variable c to control Cost J Jopt
copt 29 Controlled variable c and keep at constant setpoint cs = copt(d*) Self-optimizing Control Define loss: Self-optimizing Control
Self-optimizing control is when acceptable loss can be achieved using constant set points (cs) for the controlled variables c (without reoptimizing when disturbances occur). 30 Controlled variable: Feedback implementation Issue: What should we control? 31 Constant setpoint policy:
Effect of disturbances (problem 1) 32 Effect of implementation error (problem 2) Good 33 Good BAD Self-optimizing Control Illustrating
Example Optimal operation of Marathon runner, J=T Any self-optimizing variable c (to control at constant setpoint)? 34 Self-optimizing Control Illustrating Example 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 35 Further examples 36 Central bank. J = welfare. c=inflation rate Cake baking. J = nice taste, c = Temperature Biology. J = ?, c = regulatory mechanism
Business, J = profit. c = KPI = response time to order Good controlled Variables c: Guidelines Requirements for good candidate controlled variables (Skogestad & Postlethwaite, 1996): Its optimal value copt(d) is insensitive to disturbances d (to avoid problem 1) It should be easy to measure and control accurately (n small to avoid problem 1) The variables c should be sensitive to change in inputs (to avoid problem 2) The selected variables c should be independent (to avoid problem 2)
Rule: Maximize minimum singular value of scaled G c=Gu 37 Candidate controlled variables Selected among available measurements y, More generally: Find the optimal linear combination (matrix H): 38 Candidate Controlled Variables: Guidelines
Recall first requirement: Its optimal value copt(d) is insensitive to disturbances (to avoid problem 1) 39 Can we always find a variable combination c=Hy which satisfies YES!! Provided
Derivation of optimal combination (Alstad) Starting point: Find optimal operation as a function of d: uopt(d), yopt(d) 40 Linearize this relationship: yopt = F d
Look for a linear combination c = Hy which satisfies: copt = 0 To achieve Always possible if Applications of self-optimizing control
41 Distillation Tennessee Eastman Challenge problem Power plant +++ Outline
42 About myself Control structure design A procedure for control structure design Selection of primary controlled variables Example stabilizing control: Anti-slug control Conclusion Application: Anti-slug control Two-phase pipe flow (liquid and vapor) 43
Slug (liquid) buildup Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU 44 Experimental mini-loop
45 z p2 Experimental mini-loop Valve opening (z) = 100% p1 46 z p2 Experimental mini-loop
Valve opening (z) = 25% p1 47 z p2 Experimental mini-loop Valve opening (z) = 15% p1 48 z
Experimental mini-loop: Bifurcation diagram No slug p2 p1 Valve opening z % 49 Slugging
z Avoid slugging: 1. Close valve (but increases pressure) No slugging when valve is closed p1 Valve opening z % 50 p2 Avoid slugging:
2. Build large slug-catcher z p2 p1 51 Most common strategy in practice Avoid slugging: 3. Other design changes to avoid slugging z p2
p1 52 Avoid slugging: 4. Control? Comparison with simple 3-state model: Valve opening z % Predicted smooth flow: Desirable but open-loop unstable 53 Avoid slugging: 4. Active feedback control PC
ref z PT p1 Simple PI-controller 54 Anti slug control: Mini-loop experiments p1 [bar]
z [%] 55 Controller ON Controller OFF Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999) 56
Poles and zeros Topside T Operation points: P1 z FT DP Poles
DP 0.175 70.05 1.94 -6.11 0.00080.0067i 0.25 69
0.96 -6.21 0.00270.0092i P1 Zeros: y z P1 [Bar] DP[Bar]
-4.6276 -0.0032 -0.0004 -7.7528 -0.0004 0 0.175 0.25 57 Topside measurements: Ooops.... RHP-zeros or zeros close to origin
Stabilization with topside measurements: Avoid RHP-zeros by using 2 measurements Model based control (LQG) with 2 top measurements: DP and density T 58 Summary anti slug control
Stabilization of smooth flow regime = $$$$! (or Rand!) Stabilization using downhole pressure simple Stabilization using topside measurements possible Control can make a difference! Thanks to: Espen Storkaas + Heidi Sivertsen and Ingvald Brdsen 59 Conclusion What would I do if I was manager in a large chemical company?
Define objective of control: Better operation (objective is not just to collect data) Define control as a function in my organization Define operational objectives for each plant ($ + other..) Unified approach (company policy): Stabilizing control. PID rules MPC Avoid rule-based systems / Artificial intelligens /operator support systems - people are better at this My view
Set high standards for acceptable control More information: Home page of Sigurd Skogestad - http://www.nt.ntnu.no/users/skoge/ 60
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