Transcript Slide 1

Hybrid System Modeling,
Control, and Diagnosis
on a Three Tank Testbed
SIPHER Project Final Presentation
August 3, 2006
Nathan Allotey
Brian Turnbull
Outline
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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
Three Tank System Configuration
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Eight valves control filling,
draining, and transferring
between the three tanks.
A variable speed pump can
fill tanks one and two.
Four nodes provide
distributed monitoring and
control for the system.
Each node provides an
HTTP-based API for commands and queries.
The nodes are interfaced with the system’s transducers
using the IEEE 1451.2 standard.
Bond Graphs
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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.
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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)
HBG of Three Tank Testbed
Estimating Model Parameters
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We first collected experimental data from the system,
and then estimated the parameter of interests using
Matlab fitting functions.
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Example: Estimating the draining resistance of Tank 3
Rdrain 3 
P
dP
C
dt
R drain3  -1.7984E8h2  2.3568E8h  0.0092E8
Software Architecture
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Interface
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DataServer
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Broadcasts processed
datasets (via UDP Multicast)
to the local network.
DataClient
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Provides basic read/write
operations on the system
(unparsed strings).
Reusable class which receives
and buffers data from the
multicast for client applications
ThreeTankController
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Abstract base class serves as
a controller framework.
Model Validation
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Experiment I: Filling tank 1 and
transferring to tank 3
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Experiment II: Filling both tanks
and transferring them to tank 3.
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.
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Limited Lookahead Control Procedure
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Trajectory generation (tree)
 Discrete
time model
 Adjacency Matrix
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Cost computation for
each trajectory.
Select the “best” trajectory (control sequence)
Implement first control signal of that sequence
Controller Experiment
The objective of the controller is to arrive
at and maintain the water levels at the prespecified 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.
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Controller Experiment Results
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Experiment: Maintain heights of 40, 30 and 15cm
Real-time Results
Simulation Results
Mean
Std. Deviation
Tank 1
40.102 cm
1.097 cm
1.063cm
Tank 2
29.81 cm
0.369 cm
0.582cm
Tank 3
15.568 cm
0.487 cm
Mean
Std. Deviation
Tank 1
40.203 cm
1.018cm
Tank 2
30.061 cm
Tank 3
15.998 cm
Fault Diagnosis using FACT Diagnoser
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Uses annotated hybrid bond graph of the system to
implement a hybrid observer.
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Observer monitors system state, generates expected
behavior from the model, and uses a Kalman filter to
adjust estimation based on real data.
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Fault detector uses statistical methods to identify faults
based on deviations between plant output and observer
estimations.
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When fault is detected, possible causes (components)
are identified by back-propagating through causality
relationships in the model.
Identifying and Estimating Faults
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For each possible candidate, the diagnoser
identifies what other deviations should occur.
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For a specified period collected data is used to
reduce the fault candidates
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Finally, the Diagnoser attempts a quantitative
estimation of each remaining candidate’s
change (scale factor).
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The candidate whose estimation produces the
smallest error is reported as the fault.
Integrating the Diagnoser
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Model Issues
 Fill delays
 Parameters
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C++ console and C#
GUI applications
developed.
First tested offline
using logged data.
Simple controller
written for running
online fault diagnosis
experiments.
Experiments
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Three classes of faults tested
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’.
 Transfer
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Diagnoser should identify the fault and estimate
precisely such that the observer can track the
faulty behavior
Diagnosis Results
Average Absolute Tracking Error (cm)
Nominal
Faulty
1st Est.
2nd Est.
Tank 1
0.4173
5.7250
2.8112
0.9488
Tank 2
0.0156
0.2079
0.0978
0.0394
Tank 3
0.8357
5.0180
3.2018
0.0845
Transfer Resistance
Successful after second PE
Nonlinear Estimation
Fault Manifestation and Detection Time (s)
Fault
Detected
Difference
Transfer 1-3 (R+)
119.2407
131.88
12.64
Tank 2 Drain (R-)
100.346
178.508
78.162
Tank 3 (C-)
92.9176
98.91
5.9924
Drain Resistance
Successful on first PE
Capacitance
Detects fault, but fails to identify as
a capacitance change.
Problems/Limitations
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Model Parameters Constantly Changing
 Example:
fill rates decreased to 2/3 of original
value over a 4 week period.
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Tracking Issues With Tank 3
 Remains
after
several PE attempts.
 Possibly related to
timing issue fixed
by data collection
libraries.
Conclusions
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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
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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.
References
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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.
Hybrid System Modeling,
Control, and Diagnosis
on a Three Tank Testbed
SIPHER Project Final Presentation
August 3, 2006
Nathan Allotey
Brian Turnbull