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  1. 1. Robust Methods for Control Structure Selection in Paper Making Processes<br />Candidate: Miguel Castaño Arranz<br />Supervisor: WolfgangBirk<br />Oponent: Fredrik Sandin<br />Examiner: Thomas Gustafsson<br />
  2. 2. Outline<br />Backgound and motivation. Basics on control structure selection.<br />Robust methods for control structure selection.<br />New methods for analysis of complex processes using weighted graphs.<br />ProMoVis: a tool for Process Modeling and Visualization.<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide2<br />
  3. 3. A complex process: Making paper<br />From virgin and recycled fibersPaper production: 50 ton/hour<br />Energy intensive process<br />Some Steam Producers:<br />Oil fired boiler 50 ton/hour <br />Recovery boiler 150 ton/hour<br />Some Steam Consumers:<br />Paper Machine 90 ton/hour<br />Evaporation plant 40 ton/hour<br />Turbine production 18MW<br />1500 control loops<br />Many storage vesselsand return flows<br />Long process chain<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide3<br />
  4. 4. A procedure for control design of complex processes<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide4<br />Subset of sensors and actuatos <br />Model structure<br />Model<br />Control structure<br />Performance specification<br />Controller Parameters<br />Implemented Controller<br />
  5. 5. V1<br />FI1<br />V1<br />FI1<br />V1<br />FI1<br />V1<br />FI1<br />G11<br />C11<br />G11<br />C11<br />G11<br />C11<br />G11<br />C11<br />G21<br />G21<br />G21<br />G21<br />FF<br />R1<br />FI2<br />FI2<br />FI2<br />FI2<br />V1<br />FI1<br />G22<br />C22<br />G22<br />C22<br />G22<br />C22<br />G22<br />C22<br />G11<br />V2<br />V2<br />V2<br />Consequences of loop interaction <br />V2<br />C<br />FI2<br />G22<br />R2<br />V2<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide5<br />
  6. 6. Control Structure Selection<br />Decentralized Controller<br />Plant<br />Sparse Controller<br />+<br />r<br />e<br />u<br />y<br />-<br />We will use norms for quantifying the importance of the input-output channels<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide6<br />
  7. 7. Representing linear systems (with no direct term)<br />Models for the tanks are created from balance equations<br />State Space representation<br />Laplace<br />Transfer Function representation<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide7<br />
  8. 8. Representing linear systems in frequency domain<br />j is the standard imaginaryunit<br />Substitutes for j<br /> Is frequency in rad/sec<br />G(j ) is a frequency dependant complex number <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide8<br />
  9. 9. Quantification of system dynamics with gramians<br />P and Q are the controllability and observabillityGramians.<br />The eigenvalues of the product PQ quantifies the connection of the input and output spaces through the state space. <br />The eigenvalues of PQ can be used to quantify process dynamics.<br />PQ is positive definite and therefore the sum of its eigenvalues equals its trace.<br />tr(PQ) has an interesting relationship with the frequency domain:<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide9<br />
  10. 10. Nominal Analysis of The Quadruple Tank Process<br />tr(PQ) indicates off-diagonal pairing<br />Need for robust analysis of process interactions<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide10<br />
  11. 11. Approximating the analytical bounds for tr(PQ)<br />Uncertainty Description:<br />Normal vector:<br />Minimum area is enclosed by:<br />Maximum area is enclosed by:<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide11<br />
  12. 12. Example. The Quadruple Tank Process.<br />Nominal Case<br />Uncertain case<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide12<br />
  13. 13. Estimation of tr(PjQi) in the frequency domain<br />2. Obtain at each excited frequency the value G(jk) with the estimator variance<br />1. Excite your process at multiple frequencies k<br />1<br />1<br />2<br />2<br />3<br />3<br />3. Robust estimation of process interactions<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide13<br />
  14. 14. Obtainingtr(PQ) from the impulseresponse<br />Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 14<br />The impulseresponsehij(k) can be obtainedusinglinear regression<br />with <br />
  15. 15. Estimation of tr(PjQi) in time domain<br />with <br />ImpulseResponse<br />Estimator<br />Biased<br />Expectedvalue of the estimator<br />UnbiasedEstimator<br />Estimator distribution<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide15<br />
  16. 16. Estimation of tr(PjQi) for a bark boiler<br /><ul><li> The tree bark is burnt and steam is produced
  17. 17. Bark is added with a screw and air flows complete the combustion</li></ul>Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide16<br />
  18. 18. Estimation of tr(PjQi) for a bark boiler<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide17<br />
  19. 19. Conclusions<br />Computing the uncertaintybounds on an Interaction Measurehelps to take robust decisions on controlstructureselection<br />Methods for robust estimation of Interaction Measuresallow to takedecisions in the controlstructureselectionwithout the need of creatingparametricmodels.<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide18<br />
  20. 20. New methods for interaction analysis of complex processes using weighted graphs<br />
  21. 21. Motivation<br />Motivation.<br />Control structure design requires process knowledge. <br />Requires information about how the process variables are interconnected.<br />Goal.<br />Provide visual and intuitive representation of the relationships between process variables. <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide20<br />
  22. 22. Visualization<br />Theory.<br />New theory based in brain connectivity.<br />Analyzing relationships between voltage signals in the brain helps to understand it’s behavior.<br /> Analyzing relationships between process signals helps to understand the process. <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide21<br />
  23. 23. Process description based on graph theory<br /> collects the frequency description of the direct interconnections<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide22<br />
  24. 24. <ul><li> The norm will be used to determine the weights of a graph.
  25. 25. The norm measures the energy transmission rate of each interconnection.</li></ul>Structural Analysis of a Process<br />Structural Energy Transfer.<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide23<br />
  26. 26. <ul><li> SPDT compares in frequencydomainthepowertransmissionrate of thedirectinterconnections.</li></ul>Structural Dynamic Power Transfer.<br />Structural Analysis of a Process<br />Miguel Castaño & Wolfgang Birk | MSC 2009| 2009-07-08 | Slide 24<br />
  27. 27. Structural VS Functional<br />Questions arise from the structural analysis.<br />How is the energy provided to the manipulated inputs propagated?<br />How are process disturbances propagated?<br />What is affecting to a measured or estimated variable?<br />Structural Energy Transfer.<br />SET.<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide25<br />
  28. 28. Functional Analysis of a process<br />Ω(s) colletsthe transfer functionsfromthemanipulated variables and processdisturbancestothemeasuredorestimated variables.<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide26<br />
  29. 29. Functional Analysis. Effect of actuators<br />FETc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of energy transmission).<br />Conclusions<br />u1 mainly affects h1 <br />u1 mainly affects h1 <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide27<br />
  30. 30. Functional Analysis. Effect of actuators<br />FETc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of energy transmission).<br />Conclusions<br />u1 mainly affects h1 and u2 mainly affects to h2 <br />u2 mainly affects h2 <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide28<br />
  31. 31. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of energy transmission).<br />Conclusions<br />u1 mainly affects to h1 and u2 mainly affects to h2 <br />h1 is mainly affected by h1 <br />h1 is mainly affected by u1 <br />Functional Analysis. Effect on process variables.<br />Miguel Castaño & Wolfgang Birk | MSC 2009| 2009-07-08 | Slide 29<br />
  32. 32. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of energy transmission).<br />Conclusions<br />u1 mainly affects to h1 and u2 mainly affects to h2 <br />h1 is mainly affected by u1 and h2 is mainly affected by u2 <br />Functional Analysis. Effect on process variables.<br />h2 is mainly affected by u2 <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide30<br />
  33. 33. Functional Analysis. Propagation of disturbances.<br />Conclusions<br />u1 mainly affects to h1 and u2 mainly affects to h2 <br />h1 is mainly affected by u1 and h2 is mainly affected by u2 <br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide31<br />
  34. 34. Functional Analysis. Can Process Disturbances be rejected?<br />Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 32<br />
  35. 35. Functional Analysis of a process<br /><ul><li>Ω(s) collects the transfer functions from the manipulated variables and process disturbances to the measured or estimated variables.
  36. 36. FDPTc describes the effect of the manipulated inputs and process disturbances on the rest of the process (in terms of power transmission).
  37. 37. FTPTr describes how the states are affected by manipulated inputs and process disturbances (in terms of power transmission).</li></ul>Functional Dynamic Power Transfer<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide33<br />
  38. 38. ProMoVis<br />A tool for Process Modeling and Visualization<br />Process Knowledge<br />Analyze your Process<br />Build your process<br />Library of Icons<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide34<br />
  39. 39. Structure of ProMoVis<br /><ul><li> Several layers of information.
  40. 40. The user chooses which information is relevant to display </li></ul>Build your process<br />Analysis<br />Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide35<br />Process Components<br />Process Models<br />Controllers<br />
  41. 41. Analysis of a Stock Preparation Plant with ProMoVis<br />Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 36<br />Numericalquantification of the effect on measurements<br />Effect on PI represented in the frequencydomain<br />
  42. 42. Visualization Tool usefulness<br /><ul><li> Analysis of industrial processes for control structure selection.
  43. 43. Visual understanding of industrial processes.
  44. 44. Visualization of process interconnections.
  45. 45. Visualization of process control.
  46. 46. Communicating process knowledge.
  47. 47. Implementation of the results developed in MeSTA for the communication with project partners. </li></ul>Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide37<br />
  48. 48. Thanks for your attention<br />
  49. 49. Questions, suggestions and comments<br />Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 39<br />

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