Understanding Automotive Electronics 8th - Appendix D

APPENDIX

FDI FEEDBACK MATRIX DESIGN

D

This appendix presents the algorithm for the design of the feedback matrix in the failure detection and

identification (FDI) method of model-based diagnostics in Chapter 11. The feedback matrix determines

the output error residual vector and, in particular, its direction in the output vector space due to failure

or degradation in the performance of the component for which the FDI is designed. In Chapter 11,a

model for the system in which the failed/failing component is incorporated is repeated below ¼6p

_

where y ¼Cx

^

y ¼ C

^

An algorithm for designing the D matrix is outlined below in which the inputs are the failure event

vector f

P ¼ λ

d

T

These eigenvalues determine the dynamic response of the state estimator and must be negative or, if

complex, must be in complex conjugate pairs with negative real parts. Normally, the choice for λ

is for

all to be negative real numb ers. With these parameters and inputs, the algorithm consists of the follow-

ing steps:

s

¼ INðÞC

p

where I(N) ¼N-dimensional identity matrix

i

¼ C

s

C

d

¼λ

d

f

+ Af

i

ðÞC

P

T

C

s

d

+ D

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