Mechatronics: A Y2K Status Report

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Fault Diagnostics for the Longitudinal and
Lateral Control Systems
Prof. Karl Hedrick Prof. Masayoshi
Tomizuka Adam Howell Shashikanth Suran..
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Outline of Presentation

• Motivation
• Basic Terminology
• Longitudinal Control Diagnostics
• Closed-loop vehicle dynamics
• Nonlinear observer design
• Fault estimation
• Experimental testing
• Concluding Remarks

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Motivation

• Automated control frees human operator from
  repetitive tasks, provides improved performance
  and system stability, however
• Automated control relies on accurate sensor
  measurements and the assumption that actuators
  respond correctly
• Not always true in reality, so need some means of
  detecting, identifying, and correcting for these
  faults (preferably without a human operator)

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Basic Terminology

• Fault Detection determine when the system is not
  behaving as expected (generally easy)
• Need at least one measure of error between
  expected and true behavior
• Fault Identification determine the cause of the
  discrepancy (generally hard)
• Need at least three independent sources of
  information to correctly identify fault
• Fault Diagnostics Fault Detection and
  Identification

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Fault Tolerant Control

• Classical division of control, fault
  diagnostics, and fault management into separate
  subsystems
• Pro Allows for simplified independent design of
  diagnostics and control
• Con Conflicting goals of diagnostics and control
  can limit performance of each subsystem

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Fault Diagnostics System

• Residual generator uses model-based redundancy to
  create a set of signals sensitive to faults
  called residuals
• Each residual is an algebraic relationship
  between
• Actuator Commands
• Sensor Measurements
• Observer Estimates
• Also called parity equations
• Residual processor monitors residuals for changes
  to detect and identify faults
• Thresholding
• Pattern Identification

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AVCS in 1997 NAHSC Demo

• Automated control system relies on twelve
  sensors, three actuators, and intervehicle
  communication
• Longitudinal Control radar, longitudinal
  accelerometer, wheel speed sensor, engine speed
  sensor, throttle angle sensor, brake pressure
  sensor, manifold pressure sensor, throttle
  actuator, brake actuator
• Lateral Control magnetometer, steering angle
  sensor, wheel angle sensor, yaw rate gyro,
  lateral accelerometer, steering actuator
• Design of a complete fault diagnostic system
  covered in Rajamani, et al. (2001), but focus on
  three primary techniques used in system

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Physical Redundancy

• Basic concept Given three measurements of the
  same variable, create residuals by forming all
  possible differences
• Lateral Control Example
• R11 commanded steering angle-measured steering
  angle
• R12 commanded steering angle-measured vehicle
  wheel angle
• R13 measured steering wheel angle-measured
  vehicle wheel angle
• Similar concept used for
• Static relationship between wheel speed, engine
  speed, and range rate measurements
• Input/output relationships in throttle, brake
  system, and longitudinal acceleration

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Analytical Redundancy using Linear Observer

• Basic concept If enough direct measurements are
  not available, but related to other
  measurement(s) via linear dynamics, then estimate
  using a linear observer
• Inter-vehicle spacing example
• Similar concept used for fault diagnosis in
  magnetometer, yaw rate gyro, and both
  accelerometers

(nprec- n)Lmag
vprec
v
nprec
n
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Analytical Redundancy using Nonlinear Observers

• Basic concept If enough direct measurements are
  not available, but related to other
  measurement(s) via nonlinear dynamics, then
  estimate using a nonlinear observer
• Engine state observer example
• Concept used for fault diagnosis in throttle,
  brake system, and manifold pressure sensor

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Residual Processing

• Fault detection and identification are conducted
  as follows
• Thresholds are chosen apriori for each residual
  based on noise, disturbances, and modeling
  uncertainty
• Fault declared when at least one residual exceeds
  its threshold
• Fault identified by checking which residuals are
  greater than threshold
• Continuing with previous Lateral Control Example
• Complete fault diagnostic system was tested in
  simulations, and found to detect and identify all
  single faults in the monitored components

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Implementation for 1997 NAHSC Demonstration

• Limited diagnostics implemented for Demo to
  monitor critical components
• Brake Actuator and Pressure Sensor
• Throttle Actuator and Angle Sensor
• Radar Range
• Inter-vehicle observer estimate used for
  closed-loop control during radar failures

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Limitations in Longitudinal Diagnostics

• Although diagnostic system design worked well in
  simulation, several complications noticed in
  subsequent experimental testing
• Range rate numerically calculated, and not used
  in controller
• Magnetometer faults not persistent in residuals
• Torque converter unlocks during normal operation
• Grade has significant influence on vehicle
  dynamics
• Recent research for longitudinal control system
  diagnostics has focused on
• Using knowledge of closed-loop dynamics in
  residual generator
• Optimal design of nonlinear observers
• Processing of residuals for fault detection and
  identification

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Residual Generator

• Diagnostics can be effectively decoupled between
  two levels of modeling
• Linear vehicle model resulting from closed-loop
  control
• Nonlinear vehicle model describing powertrain and
  chassis dynamics
• Both levels use observers and parity equations
  for redundancy
• Linear model diagnostics use 2 dedicated
  Luenberger observers to estimate range
• Nonlinear model diagnostics use 2 nonlinear
  observers to estimate the manifold pressure

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Dedicated Observers

• Lower level dynamic surface controller for
  nonlinear dynamics results in overall linear
  vehicle model
• Synthetic input usyn chosen to provide string
  stability
• First-order observer also used in practice
• Convert to state space model and design 2 linear
  observers to estimate , where each observer
  uses the given desired spacing and a single
  sensor measurement

Model
Observer
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Dedicated Observers (cont.)

• A third range estimate based on magnetometer
  count and communication
• Residuals formed from radar range measurement and
  three range estimates

Model
Observer
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Nonlinear Observer Design

• Several prior results for estimation of Lipschitz
  nonlinear systems (Raghavan, Rajamani) but only
  stability of estimation error dynamics considered
• In fact, nonlinear observer design for a more
  general class of systems can be formulated as a
  Lure or absolute stability problem solvable
  using convex optimization

z
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Nonlinear Observers (cont.)

• Additional performance measures can be easily
  included in this setting
• Guaranteed decay rate of estimation error
• Minimization of disturbances influence on state
  estimates
• Multi-criterion optimization of both performance
  measures
• Two engine state observers were designed using
  this methodology to provide pre-specified
  convergence rate
• Further details in
• A. Howell and J. Hedrick, Nonlinear observer
  design via convex optimization, in Proc. Of 2002
  ACC.

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Residual Processor

• Model faults effects on residuals as
• is the nonzero offset of the residual
  vector due to modeling uncertainty, sensor noise,
  and controller performance
• F is the fault signature matrix, where each
  column represents the fixed directional
  characteristics of a specific fault. Obtained by
  calculating steady state gain of residual
  generator
• is the fault mode vector, where each
  element is an unknown scalar function
  representing the magnitude of the fault at time t
• Estimate the fault magnitude vector using least
  squares
• Fault detected when any component of
  exceeds threshold
• Fault identified by pattern of elements
  exceeding thresholds

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Experimental Testing

• Diagnostic system implemented in C, using
  longitudinal controller developed for 1997 NAHSC
  Demonstration
• Faults generated in software while vehicle was
  under closed-loop control
• Following experimental data shows results for
  high-speed tests of a three-car platoon at I-15
  in San Diego
• Faults were artificially introduced in second car
  of the platoon
• Fault magnitudes were chosen to determine minimum
  detectable fault

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Velocity tracking of Lead vehicle under nominal
conditions
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Acceleration of Lead vehicle under nominal
conditions
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Control actuation of Lead vehicle under nominal
conditions
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Relative distance tracking of follower vehicle
under nominal conditions
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Dedicated observer performance under nominal
conditions
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Nonlinear observer performance under nominal
conditions
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Dedicated observer estimates under Wheel Speed
Sensor Fault
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Fault estimate under Wheel Speed Sensor Fault
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Nonlinear observer estimates under Manifold
Pressure Sensor Fault
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Fault Estimates under Manifold Pressure Sensor
Fault
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Status of Diagnostics for Longitudinal Control

• Fault diagnostics experimentally implemented and
  verified to provide diagnosis of all single
  faults in longitudinal control sensors throttle
  actuator when the torque converter is locked
• However, torque converter unlocks when brakes
  applied or gear drops below 3rd. This limits the
  effectiveness of diagnostic system under these
  operating conditions, since simplified model no
  longer holds
• Only detection of faults in braking control
  components possible, i.e. brake pressure sensor
  and brake actuator, but not isolation
• Same limitation for throttle angle sensor and
  throttle actuator
• Unable to detect faults in engine speed sensor

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Ongoing and Future Research

• Two short-term goals associated with current
  system
• Improve diagnostics during operating modes where
  simplified model invalid by
• Including torque converter model
• Access additional vehicle sensors (ie.
  speedometer) to provide physical redundancy
• Application to transit buses for 2003
  Demonstration
• Dedicated observer work should carry over
  directly
• However, engine dynamics significantly different
• Longer term goals
• Further experimental testing under large
  magnitude faults
• Extension of nonlinear observer design to develop
  nonlinear detection filter
• Integrated design of controller and diagnostic
  system