Presentation corfu (uncertain gramians)

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<ul><li> 1. Uncertainty Bounds for Gramian-Based Interaction Measures Bjrn HalvarssonUppsala University Miguel Castao ArranzLule University of Technology Wolfgang BirkLule University of Technology</li></ul> <p> 2. A procedure for control design of complex processes Miguel Castao | CSCC2010| 2010-07-24 | SlideModel structure Model Control structure Subset of sensors and actuatosPerformance specification Controller Parameters ImplementedController 3. A complex process: Making paper </p> <ul><li>From virgin and recycled fibers </li></ul> <ul><li>Energy intensive process </li></ul> <ul><li>More than 3000 control loops </li></ul> <ul><li>Many storage vessels and return flows </li></ul> <ul><li>Long process chain </li></ul> <p>Miguel Castao | CSCC2010| 2010-07-24 | Slide 4. Control Structure Selection &amp; Interaction Measures. e u - y + r Gramian-based Interaction Measuresquantify the importance of the input-output channels Decentralized Controller Plant Sparse Controller Miguel Castao | CSCC2010| 2010-07-24 | Slide 5. Quantification ofsystem dynamics with gramians. </p> <ul><li>P and Q are the controllability and observabillity Gramians. </li></ul> <ul><li>The eigenvalues of the product PQ quantifies the connection of the input and output spaces through the state space.</li></ul> <ul><li>The Hankel matrix maps the past process inputs into the future process outputs. </li></ul> <ul><li>The non-zero Hankel Singulat Values (HSV:s)are equal to the positive square root of the eigenvalues of PQ. </li></ul> <ul><li>Conclusion: The eigenvalues of PQ and/or the HSV:s can be used to quantify process dynamics </li></ul> <p>Miguel Castao | CSCC2010| 2010-07-24 | Slide 6. Quantification ofsystem dynamics with gramians. Hankel Norm( ||G|| H)We consider two different factors to quantify process dynamics Sum of the eigenvalues of PQ( tr(PQ) ) Both factors have important implications in time domain . tr(PQ) has an interesting relationship with the frequency domain.Miguel Castao | CSCC2010| 2010-07-24 | Slide 7. NominalAnalysis of The Quadruple Tank Process Bothmeasures indicate off-diagonal pairing. Miguel Castao | CSCC2010| 2010-07-24 | Slide 8. Improved bounds for ||G ij || Hand for tr(P j Q i ). </p> <ul><li>Previous bounds for the additive uncertainty in the Hankel-Norm were derived by Moaveni and Khaki-Sedigh: </li></ul> <ul><li>whereW cois the cross-Gramian matrix,obtained from</li></ul> <ul><li>The new potentially tighterproposed bounds for the Hankel norm and tr(P j Q i ): </li></ul> <p>DONT PANIC Miguel Castao | CSCC2010| 2010-07-24 | Slide 9. Example 1Performed Monte-Carlo simulations revealed that both bounds are still too loose. Previous bound: New bound: Miguel Castao | CSCC2010| 2010-07-24 | SlideUncertainty level 10. Approximating the analytical bounds for tr(PQ) Miguel Castao | CSCC2010| 2010-07-24 | SlideUncertainty Description: Normal vector: Minimum area is enclosed by: Maximum area is enclosed by: 11. Example 2. The Quadruple Tank Process. Nominal Case Boundsobtained from the inequality(loose bound) : Boundsobtained from integratingthe Nyquist Diagram(numerical approach): Miguel Castao | CSCC2010| 2010-07-24 | SlideUncertainty level 12. Conclusions and Future Work </p> <ul><li>Previously existing bounds for two Gramian-Based interaction measures have been improved and evaluated. </li></ul> <ul><li>These bounds have been found to be insufficiently tight in some examples. </li></ul> <ul><li>A novel method for numerically obtaining the bounds of tr(PQ) is suggested. </li></ul> <ul><li>Analyze which numerical approach for integrating the areas in the Nyquist array is more adequate. </li></ul> <ul><li>Methods to create robust decisions in control structure selection form the Gramian-based interaction measures and their computed bounds. </li></ul> <ul><li>Empirical estimation of interaction measures. </li></ul> <p>Miguel Castao | CSCC2010| 2010-07-24 | SlideConclusions Future Work 13. Other research topics in Control Structure Selection </p> <ul><li>Analysis of complex industrial processes with signal flow graphs and methods based on brain connectivity theory. </li></ul> <p>Miguel Castao &amp; Wolfgang Birk | MSC 2008| 2008-09-03 | Slide 14. Thanks for your attention Miguel Castao | CSCC2010| 2010-07-24 | Slide[email_address] </p>