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August 3, 2006 Nathan Allotey Brian Turnbull

Hybrid System Modeling, Control, and Diagnosis on a Three Tank Testbed SIPHER Project Final Presentation. August 3, 2006 Nathan Allotey Brian Turnbull. Outline. Three Tank Testbed Configuration Modeling The System Hybrid Bond Graph Parameter Estimation and Derived equations

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August 3, 2006 Nathan Allotey Brian Turnbull

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  1. Hybrid System Modeling, Control, and Diagnosison a Three Tank TestbedSIPHER Project Final Presentation August 3, 2006 Nathan Allotey Brian Turnbull

  2. Outline • Three Tank Testbed Configuration • Modeling The System • Hybrid Bond Graph • Parameter Estimation and Derived equations • Software Architecture • Model-based Controller • Fault Diagnosis • Problems/Limitations • Conclusion and Future Work

  3. Three Tank System Configuration • Eight valves control filling,draining, and transferringbetween the three tanks. • A variable speed pump canfill tanks one and two. • Four nodes providedistributed monitoring andcontrol for the system. • Each node provides anHTTP-based API for commands and queries. • The nodes are interfaced with the system’s transducers using the IEEE 1451.2 standard.

  4. Bond Graphs (BGs)Energy-based diagrams which capture the common energy structure of the system and give concise description of system behavior. It applies to electrical, mechanical, hydraulic systems, etc. Hybrid Bond Graphs (HBGs)Introduce the notion of idealized switching junctions into bond graphs to represent the discontinuous mode changes of a hybrid system. (e.g. valves) Bond Graphs

  5. HBG of Three Tank Testbed

  6. Estimating Model Parameters • We first collected experimental data from the system, and then estimated the parameter of interests using Matlab fitting functions. • Example: Estimating the draining resistance of Tank 3

  7. Software Architecture • Interface • Provides basic read/write operations on the system (unparsed strings). • DataServer • Broadcasts processed datasets (via UDP Multicast) to the local network. • DataClient • Reusable class which receives and buffers data from the multicast for client applications • ThreeTankController • Abstract base class serves as a controller framework.

  8. Experiment I: Filling tank 1 and transferring to tank 3 Experiment II: Filling both tanks and transferring them to tank 3. Model Validation

  9. Model-based Control • Controller employs the validated model to decide the control sequences. • Particularly a limited lookahead approach is utilized. • In the following experiment controller accepts data from the client libraries at a rate of 3Hz.

  10. Limited Lookahead Control Procedure • Trajectory generation (tree) • Discrete time model • Adjacency Matrix • Cost computation for each trajectory. • Select the “best” trajectory (control sequence) • Implement first control signal of that sequence

  11. Controller Experiment • The objective of the controller is to arrive at and maintain the water levels at the pre-specified heights. • This experiment began with initial water heights of 30.29cm, 20.91cm, 17.39cm • Given the same parameters, a simulation was run to observe the expected results from the model.

  12. Controller Experiment Results Real-time Results Simulation Results • Experiment: Maintain heights of 40, 30 and 15cm

  13. Fault Diagnosis using FACT Diagnoser • Uses annotated hybrid bond graph of the system to implement a hybrid observer. • Observer monitors system state, generates expected behavior from the model, and uses a Kalman filter to adjust estimation based on real data. • Fault detector uses statistical methods to identify faults based on deviations between plant output and observer estimations. • When fault is detected, possible causes (components) are identified by back-propagating through causality relationships in the model.

  14. Identifying and Estimating Faults • For each possible candidate, the diagnoser identifies what other deviations should occur. • For a specified period collected data is used to reduce the fault candidates • Finally, the Diagnoser attempts a quantitative estimation of each remaining candidate’s change (scale factor). • The candidate whose estimation produces the smallest error is reported as the fault.

  15. Integrating the Diagnoser • Model Issues • Fill delays • Parameters • C++ console and C# GUI applications developed. • First tested offline using logged data. • Simple controller written for running online fault diagnosis experiments.

  16. Experiments • Three classes of faults tested • Transfer Resistance – increased by adjusting manual valve on transfer pipe. • Drain Resistance – Leak created in Tank 1 or 2 by opening its drain valve. • Capacitance – Object dropped into Tank 3 to create an instantaneous change in ‘C’. • Diagnoser should identify the fault and estimate precisely such that the observer can track the faulty behavior

  17. Diagnosis Results Average Absolute Tracking Error (cm) Transfer ResistanceSuccessful after second PENonlinear Estimation Drain ResistanceSuccessful on first PE CapacitanceDetects fault, but fails to identify as a capacitance change. Fault Manifestation and Detection Time (s)

  18. Problems/Limitations • Model Parameters Constantly Changing • Example: fill rates decreased to 2/3 of original value over a 4 week period. • Tracking Issues With Tank 3 • Remains afterseveral PE attempts. • Possibly related totiming issue fixedby data collectionlibraries.

  19. Conclusions • The controller can successfully maintain the given set points using the limited lookahead approach. • Diagnoser can detect, identify, and estimate several system faults on the testbed. Future Work • Tracking issue should be fixed by investigating the timing issue with tank 3. • Better parameter estimation process for parameters modeled as a non-linear function. • Integrate controller with fault diagnosis to explicitly adapt control algorithms in response to system faults. • Experiment with other failure scenarios including less significant faults.

  20. References • R. C. Rosenberg and D. C. Karnopp, Introduction to Physical System Dynamics, McGraw-Hill, New York 1983. • J. Lyons, “Distributed monitoring and control and physical system modeling for a laboratory three tank-system,” M.S. thesis, Dept. Electrical Engineering, Vanderbilt University, Nashville,TN, 2004. • P. J. Mosterman and G. Biswas, “Model Based Diagnosis of Dynamic Systems,” Seventh Journees du L.I.P.N., pp. 143-154, September 18-19, Villetaneuse, France, 1997. • J. Wu, G. Biswas, S. Abdelwahed, and E. Manders, “A Hybrid Control System Design and Implementation for a Three Tank Testbed,” in Proc. IEEE Conf. Contr. Applications, Toronto, Canada, Aug. 2005, pp. 645-650. • P. J. Mosterman and G. Biswas, “Diagnosis of Continuous Valued Systems in Transient Operating Regions”, IEEE Trans. on Systems, Man, and Cybernetics, 29, 9, pp. 554-565, November, 1999.

  21. Hybrid System Modeling, Control, and Diagnosison a Three Tank TestbedSIPHER Project Final Presentation August 3, 2006 Nathan Allotey Brian Turnbull

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