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1. Robust Methods for Control Structure Selection in Paper Making Processes Candidate: Miguel Castaño Arranz Supervisor: WolfgangBirk Oponent: Fredrik Sandin Examiner: Thomas Gustafsson
2. Outline Backgound and motivation. Basics on control structure selection. Robust methods for control structure selection. New methods for analysis of complex processes using weighted graphs. ProMoVis: a tool for Process Modeling and Visualization. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide2
3. A complex process: Making paper From virgin and recycled fibersPaper production: 50 ton/hour Energy intensive process Some Steam Producers: Oil fired boiler 50 ton/hour Recovery boiler 150 ton/hour Some Steam Consumers: Paper Machine 90 ton/hour Evaporation plant 40 ton/hour Turbine production 18MW 1500 control loops Many storage vesselsand return flows Long process chain Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide3
4. A procedure for control design of complex processes Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide4 Subset of sensors and actuatos Model structure Model Control structure Performance specification Controller Parameters Implemented Controller
6. Control Structure Selection Decentralized Controller Plant Sparse Controller + r e u y - We will use norms for quantifying the importance of the input-output channels Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide6
7. Representing linear systems (with no direct term) Models for the tanks are created from balance equations State Space representation Laplace Transfer Function representation Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide7
8. Representing linear systems in frequency domain j is the standard imaginaryunit Substitutes for j Is frequency in rad/sec G(j ) is a frequency dependant complex number Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide8
9. Quantification of system dynamics with gramians P and Q are the controllability and observabillityGramians. The eigenvalues of the product PQ quantifies the connection of the input and output spaces through the state space. The eigenvalues of PQ can be used to quantify process dynamics. PQ is positive definite and therefore the sum of its eigenvalues equals its trace. tr(PQ) has an interesting relationship with the frequency domain: Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide9
10. Nominal Analysis of The Quadruple Tank Process tr(PQ) indicates off-diagonal pairing Need for robust analysis of process interactions Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide10
11. Approximating the analytical bounds for tr(PQ) Uncertainty Description: Normal vector: Minimum area is enclosed by: Maximum area is enclosed by: Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide11
12. Example. The Quadruple Tank Process. Nominal Case Uncertain case Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide12
13. Estimation of tr(PjQi) in the frequency domain 2. Obtain at each excited frequency the value G(jk) with the estimator variance 1. Excite your process at multiple frequencies k 1 1 2 2 3 3 3. Robust estimation of process interactions Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide13
14. Obtainingtr(PQ) from the impulseresponse Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 14 The impulseresponsehij(k) can be obtainedusinglinear regression with
15. Estimation of tr(PjQi) in time domain with ImpulseResponse Estimator Biased Expectedvalue of the estimator UnbiasedEstimator Estimator distribution Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide15
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17. Bark is added with a screw and air flows complete the combustionMiguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide16
18. Estimation of tr(PjQi) for a bark boiler Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide17
19. Conclusions Computing the uncertaintybounds on an Interaction Measurehelps to take robust decisions on controlstructureselection Methods for robust estimation of Interaction Measuresallow to takedecisions in the controlstructureselectionwithout the need of creatingparametricmodels. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide18
20. New methods for interaction analysis of complex processes using weighted graphs
21. Motivation Motivation. Control structure design requires process knowledge. Requires information about how the process variables are interconnected. Goal. Provide visual and intuitive representation of the relationships between process variables. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide20
22. Visualization Theory. New theory based in brain connectivity. Analyzing relationships between voltage signals in the brain helps to understand it’s behavior. Analyzing relationships between process signals helps to understand the process. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide21
23. Process description based on graph theory collects the frequency description of the direct interconnections Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide22
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25. The norm measures the energy transmission rate of each interconnection.Structural Analysis of a Process Structural Energy Transfer. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide23
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27. Structural VS Functional Questions arise from the structural analysis. How is the energy provided to the manipulated inputs propagated? How are process disturbances propagated? What is affecting to a measured or estimated variable? Structural Energy Transfer. SET. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide25
28. Functional Analysis of a process Ω(s) colletsthe transfer functionsfromthemanipulated variables and processdisturbancestothemeasuredorestimated variables. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide26
29. Functional Analysis. Effect of actuators FETc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of energy transmission). Conclusions u1 mainly affects h1 u1 mainly affects h1 Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide27
30. Functional Analysis. Effect of actuators FETc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of energy transmission). Conclusions u1 mainly affects h1 and u2 mainly affects to h2 u2 mainly affects h2 Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide28
31. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of energy transmission). Conclusions u1 mainly affects to h1 and u2 mainly affects to h2 h1 is mainly affected by h1 h1 is mainly affected by u1 Functional Analysis. Effect on process variables. Miguel Castaño & Wolfgang Birk | MSC 2009| 2009-07-08 | Slide 29
32. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of energy transmission). Conclusions u1 mainly affects to h1 and u2 mainly affects to h2 h1 is mainly affected by u1 and h2 is mainly affected by u2 Functional Analysis. Effect on process variables. h2 is mainly affected by u2 Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide30
33. Functional Analysis. Propagation of disturbances. Conclusions u1 mainly affects to h1 and u2 mainly affects to h2 h1 is mainly affected by u1 and h2 is mainly affected by u2 Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide31
34. Functional Analysis. Can Process Disturbances be rejected? Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 32
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36. FDPTc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of power transmission).
37. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of power transmission).Functional Dynamic Power Transfer Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide33
38. ProMoVis A tool for Process Modeling and Visualization Process Knowledge Analyze your Process Build your process Library of Icons Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide34
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40. The user chooses which information is relevant to display Build your process Analysis Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide35 Process Components Process Models Controllers
41. Analysis of a Stock Preparation Plant with ProMoVis Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 36 Numericalquantification of the effect on measurements Effect on PI represented in the frequencydomain
47. Implementation of the results developed in MeSTA for the communication with project partners. Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide37