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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
  • 5. V1
    FI1
    V1
    FI1
    V1
    FI1
    V1
    FI1
    G11
    C11
    G11
    C11
    G11
    C11
    G11
    C11
    G21
    G21
    G21
    G21
    FF
    R1
    FI2
    FI2
    FI2
    FI2
    V1
    FI1
    G22
    C22
    G22
    C22
    G22
    C22
    G22
    C22
    G11
    V2
    V2
    V2
    Consequences of loop interaction
    V2
    C
    FI2
    G22
    R2
    V2
    Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide5
  • 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(jk) 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
  • 16. Estimation of tr(PjQi) for a bark boiler
    • The tree bark is burnt and steam is produced
    • 17. Bark is added with a screw and air flows complete the combustion
    Miguel 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
  • 24.
    • The norm will be used to determine the weights of a graph.
    • 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
  • 26.
    • SPDT compares in frequencydomainthepowertransmissionrate of thedirectinterconnections.
    Structural Dynamic Power Transfer.
    Structural Analysis of a Process
    Miguel Castaño & Wolfgang Birk | MSC 2009| 2009-07-08 | Slide 24
  • 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
  • 35. Functional Analysis of a process
    • Ω(s) collects the transfer functions from the manipulated variables and process disturbances to the measured or estimated variables.
    • 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
  • 39. Structure of ProMoVis
    • Several layers of information.
    • 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
  • 42. Visualization Tool usefulness
    • Analysis of industrial processes for control structure selection.
    • 43. Visual understanding of industrial processes.
    • 44. Visualization of process interconnections.
    • 45. Visualization of process control.
    • 46. Communicating process knowledge.
    • 47. Implementation of the results developed in MeSTA for the communication with project partners.
    Miguel CastañoArranz |LicentiateSeminar| 2010-12-15 | Slide37
  • 48. Thanks for your attention
  • 49. Questions, suggestions and comments
    Miguel Castaño & Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 39