Diagnosis and FTC by Prof. Blanke [pdf] - NTNU

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Models of dynamical systems
Linearized system without faults
The general, linear case reads, for A, BCD , , ... time invariant:
dx() t
= Ax() t + Bu() t + Exd(), t x(0) = x0
dt
y() t = Cx() t + Du() t + E d()
t
Linearized system with additive faults
y
dx() t
= Ax() t + Bu() t + Fxf() t + Exd(), t x(0) = x
dt
y() t = Cx() t + Du() t + F f() t + E d()
t
y y
Ship - running example
δ
rudder
angle
b
+
+
∫
ω3
δ
steering
characteristic
wave
disturbance
ω3
f ω
ωw
ω3m
rate
measurement
∫
f ψ
0
ψ
ψm
heading
measurement
Ship steering. Input is rudder angle. Output is ship’s
heading. Measured variables are turn rate and
heading angle.
+
+
+
+
+
+
Mogens Blanke – Spring 2006
Mogens Blanke – Spring 2006
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