Instrumentation & Measurement Magazine 26-1 - 49

Table 1 - Calibration efficiency comparison of the UBCM, BCM, and PCM under different nonlinear models
Nonlinear type
Sensor inherent nonlinearity
Sine wave
Gauss wave
Nonlinear broken line
Characteristic parameters
-
-
a=1, b=0, c=2
a=1, b=0, c=0.1
r=0.25, 0=15°
r=0.5, 0=15°
are displayed in Fig. 11. As depicted in Fig. 11c, the nonlinear
break line will produce a sudden distortion at x=0.5 due to the
increment of the parameter r. In this circumstance, the PCM,
BCM, and UBCM could not guarantee the monotonicity of the
nonlinear broken line. Fig. 11a reveals that when r=0.5, Oub
Ob decrease faster than that of the Op
and
. As depicted in Fig. 11b,
Oub/Op and Ob/Op will achieve a minimum of 0.108 and 0.116,
respectively. Fig 11d, Fig. 11e, and Fig. 11f reveal that the residual
calibration error of the PCM is larger than that of the UBCM
and BCM under different model order n.
Modeling Accuracy Comparison
The computed Oub
/Op
/Op
and Ob
and Ob
/Op
/Op
are summarized in Table 1 to
make a more intuitive comparison of the calibration accuracy
of the PCM, BCM, and UBCM. It reveals that both the minimum
of the Oub
is smaller than 1. This means
that the calibration accuracy of the UBCM and BCM is better
than that of the PCM. According to the above comparison
study, it could be concluded that the proposed UBCM has better
nonlinearity modeling accuracy than that of the previous
PCM and BCM.
Conclusions
In this study, an Unconstrained Bezier Calibration Method
(UBCM) is presented for the nonlinear system modeling, in
which a series of handle points and local weight coefficients
are utilized to enhance its nonlinear modeling ability. The
proposed UBCM has broad application prospects such as sensor
inherent nonlinearity calibration, system modeling and
dynamic control. A sensor inherent nonlinearity calibration
example is given to exhibit the effectiveness of the proposed
UBCM in real applications. Several different nonlinear functions,
such as sine wave, gauss nonlinearity and nonlinear
broken line, are utilized to test the nonlinear modeling accuracy
of the UBCM. A comparison study between the UBCM,
BCM and PCM is performed to provide a reference for engineering
applications. The conclusions are as follows:
◗ For the present nonlinearity modeling examples, the
PCM, UBCM and BCM could improve their modeling
accuracy by increasing its model order n. However, for
the gauss nonlinearity and nonlinear broken line, the
PCM fluctuates and produces a periodical calibration
error that aggravate its modeling accuracy. The UBCM

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