Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 3 / Sensors
_ _
Expressed in the frequency domain used in Figure 3-8 (rate limit omitted)
and in functional form,
y
( s )
: =
3.2-18
( − t ⋅ s )
2
2
( s + ω ) ⋅ ( s + 2 ⋅ ζ ⋅ ω + ω )
SN
2
SN ωD1L
⋅ SNωD
2L
⋅ exp SN TD
⋅
D1L
In the functional form this becomes,
SN
SN
DL2
SN
DL2
( x ( t ) ) : = ϕ ( ϕ ( ϕ ( ϕ ( x ( t ) ) ) ) )
y D2L
D1L
RL TD
x
( s )
Equation 3.2-3
Equation 3.2-4
In the simulation the sensor time delays are gathered together, excluding the
transport delay due to the output interface, and modelled to an accuracy
commensurate with the high frequency update rate (fR). When undertaking
linear systems analysis the exponential function is replaced by 1 st or 2 nd
order Pade approximations with unity gain,
ROR (DEGREES)
y
⎛ 2 ⋅
⎜
⎝ 2 ⋅
SN O
( s ) : = ⎜
⎟ ⋅ x ( s )
⎛
SN
f
f
O
− s ⎞
+ s ⎟
⎠
2
2
12 ⋅ f − 6 ⋅ f ⋅ s + s
y
⎜
2
2
12 ⋅ SNf
O + 6 ⋅ SNf
O ⋅ s + s
SN O SN O
( s ) : = ⎜
⎟ ⋅ x ( s )
10
9
8
7
6
5
⎝
Figure 3-9 : Time Delay Phase Error
( 1 st order – solid ; 2 nd order – dashed )
⎞
⎟
⎠
Equation 3.2-5
Equation 3.2-6