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

Chapter 3 / Sensors
_ _
3.2.2 Common Error Models
Although sensors exhibit a wide variety of errors, many are common and
can dealt with using relatively few modelling elements. To avoid repetition
when describing particular sensors, the common generic error models are
grouped as shown in Figure 3-7, defined here, and characterised using
default values in-situ.
1
HF DELAY AND
DYNAMIC ERRORS
BIAS AND SCALE
FACTOR ERRORS
3.2-14
ANALOGUE
TO DIGITAL
Figure 3-7 : Sensor Model - Generic Error Grouping
The functional notation (ϕ) provides a concise mathematical framework for
sensor error definition. When treating the errors in the time domain the
functional notation between input (x) and the output (y) from a model is,
( t ) : = ( x ( t ) )
y ϕ
In the frequency domain the equivalent notation is,
( s ) : = ( x ( s ) )
y ϕ
1
Equation 3.2-1
Equation 3.2-2
The functions in Table 3-7 provide a cross-reference to their implementation
using the utilities defined in §22. For convenience, the function arguments
listed are not referred to explicitly, they are implicitly assumed. Default
arguments are characterised when describing a particular sensor using
subscripted prefix to identify the sensor according to the “descriptor” listed
in Table 3-1 - here the generic sensor descriptor “SN” is used.
3.2.2.1 Dynamic Errors
The common dynamic errors comprise the lumped time delay, rate limiting,
and 1 st and 2 nd order lags shown in Figure 3-8.
1
SN_TD SN_RL
SN_BW
SN_W^2
s+SN_BW s 2+2*SN_Z*SN_Ws+SN_W^2
SN_B_1 SN_B_2
SN_B_4
Figure 3-8 : HF Time Delay, Rate Limiting and Dynamic Errors
1