Fault-Tolerant Control

Fault Tolerance

PassivePassive Tolerance achieved by the use of Tolerance achieved by the use of

feedback control laws that are robust to feedback control laws that are robust to possible system faults.possible system faults.

ActiveActive Tolerance achieved through a fault Tolerance achieved through a fault

diagnosis and accommodation diagnosis and accommodation architecture.architecture.

Overview

Detection Isolation Identification AccommodationDetection Isolation Identification Accommodation

Detection – Indicates the occurrence of a fault.Detection – Indicates the occurrence of a fault.

Isolation – Determines the type and/or location of the fault.Isolation – Determines the type and/or location of the fault.

Identification – Determines the magnitude of the fault.Identification – Determines the magnitude of the fault.

Accommodation – Fault is self-corrected, usually through Accommodation – Fault is self-corrected, usually through controller reconfiguration.controller reconfiguration.

Diagnosis

A Fault-Tolerant Control Architecture

Fault Accommodation

Nominal ControllerNominal Controller Guarantees the stability and tracking performance.Guarantees the stability and tracking performance. Maintains the system signal boundedness until the fault is Maintains the system signal boundedness until the fault is

detected.detected.

Fault-Tolerant Controller (I) Fault-Tolerant Controller (I) Used right after fault detection.Used right after fault detection.

Fault-Tolerant Controller (II) Fault-Tolerant Controller (II) Used after fault isolation.Used after fault isolation. Purpose – Improve/recover performance.Purpose – Improve/recover performance.

General (Nonlinear) Plant

),()(),,(),( 0 uxfTttuxuxx

0

: Dynamicsof nominal model.

: Modeling uncertainty.

: Thechangein system due toa fault.

: Represents the time profilesof the faults.

: State vector.

: Input vector.

: Unknown fault occurrence time.

φ

η

f

β

x

u

T

Represents the deviation in the

system dynamics due to the

occurrence of a fault.

Fault time profile )(,),(:)( 0010 TtTtdiagTt n

.0where

if1

if0)(

0)(

00 0

i

Tti Tte

TtTt

i

Unknown fault evolution rate

Small – slowly developing faults.

Large – abrupt faults (step function).

Only reflects the speed of

the fault.

Faults

equation. state

th- theaffectingfault th - theof structure functional therepresents while

equation, stateth - in thefault theof magnitude thezescharacteri where

,),(,),,(:),(

bydescribedis,,,1,functionfaultEach

.),(,),,(:

bygivenfunctionsofsetfiniteatobelongs),(

11

1

isg

i

uxguxguxf

Nsf

uxfuxfF

uxf

si

si

Tsn

Tsn

sTss

s

N

Modes of Behavior

General Controller

isoldI

isolddD

dd

isoldI

isolddD

dd

Tttxvh

TtTtxvh

Tttxvh

u

Tttxxvg

TtTtxxvg

Tttxxvg

v

for ),,,(

for ),,,(

for ),,,(

for ),,,,(

for ),,,,(

for ),,,,(

0

0

y.accordingl designed be tofunctionsnonlinear are ,, and ,,

.controller theof vector state :

00 IDID hhhggg

v

A More Detailed Architecture

Specific Plant Structure

1 0 1

0 1

1

0 1 1

1

( , , ) ( ) ( , , )

(

( , , ) , 1 1

( , , ) ( , , ) , , ) ( ) ( , , )i i i i

n n n n

i i i i

i n n n

x u t t T f x xx x x x i n

x x u t t T f x xx x u x x

y x

Tnsn

Tsn

sTssTsn

s xxgxxgxgxxf ),,(,),,(),(:),,( 121221111

Design of The Nominal Controller

1

( 2) ( 1)1 1 1

0

1 1 1 2

Based on backstepping methodology, a new state vector

: ( , , ) is defined recursively by the following

coordinate transformation:

( , , , , , ) , 1, ,

0

n

i ii i i i r r r

z col z z

z x x x y y y i n

c z c z

1 1

21 2 1( 1)1 1 1

1 1 2 12 ( )1 0 1

( )i i i

ji i ii i i i i r j jj

j j jj r j

c z z c z y xx y x

The Nominal Controller

( )0

0

It can be shown that the nominal controller is of the

following form

1( )

( )n

n ru t yx

The control laws for the First Controller Reconfiguration and Second Controller Reconfiguration take on similar forms.

Different Approaches of Fault Isolation

This paper dealt with determining the type of the This paper dealt with determining the type of the fault among a set of known possible fault types.fault among a set of known possible fault types.

Other approaches: Other approaches: For physically distributed systems, determining For physically distributed systems, determining

the physical location of the fault.the physical location of the fault. For complex systems, determining the faulty For complex systems, determining the faulty

subsystem among the set of all subsystems.subsystem among the set of all subsystems.

Multiple Faults

This paper assumed only a single fault This paper assumed only a single fault could occur at any time.could occur at any time.

In some applications, multiple faults may In some applications, multiple faults may occur simultaneously or sequentiallyoccur simultaneously or sequentially In this case, a diagonal fault sensitivity In this case, a diagonal fault sensitivity

structure is required.structure is required.