Instrumentation & Measurement Magazine 26-1 - 48
Fig. 10. Nonlinear broken line modeling by PCM, UBCM and BCM, when r=0.25, 0=15°. (a) and (b) Objective functions comparison. (c) Comparisons of the fifth
ordered f, fp
, fub and fb. (d)-(f) The distribution of ep
that Oub
/Op
and Ob
0.374, respectively.
Comparing Fig. 10d, Fig. 10e, and Fig. 10f, it could be observed
that for the nonlinear broken line, the calibration error
mainly occurs at the two inflection points. For the lower-ordered
PCM, both the boundary and inflection points will show
modeling error. Fig. 10c reveals that fp
produces a sudden decrement
around the boundary of x=1. This is a huge drawback
/Op
, eub and eb under different n.
could achieve a minimum of 0.190 and
of the PCM, since the monotonicity of the PCM could not be
guaranteed for the present condition. For a control system, a
change of the measurement monotonicity could lead to the unstability
of the control process. The same phenomenon could
also be observed from Fig. 7c, xϵ(-10,-5) and xϵ(5,10).
Strong Nonlinearity (r=0.5): In this case, the parameter r is
increased from 0.25 to 0.5 to enhance the nonlinearity of the
nonlinear broken line. The corresponding modeling results
Fig. 11. Nonlinear broken line modeling by PCM, UBCM and BCM, when r=0.5, 0=15°. (a) and (b) Objective functions comparison. (c) Comparisons of the fifth
ordered f, fp
, fub and fb. (d)-(f) The distribution of ep
48
, eub and eb under different n.
IEEE Instrumentation & Measurement Magazine
February 2023
Instrumentation & Measurement Magazine 26-1
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