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TABLE OF DUAL-INPUT DESCRIBING
FUNCTIONS (DIDFs)
The DIDF sinusoidal gain is given by (cf. Sec. 6.1)
and the corresponding dc gain is given by (cf. Sec. 6.1)
NB(A,B,w) = &l u Y ( B + A sin y, Aw cos y) dy
In this table we employ the "saturation function" (cf. Sec. 2.3) denoted by
f(r) = -1 y < -1
= 1
and the associated function (cf. Sec. 6.2)
These functions are plotted in Fig. C.1. Two additional functions of considerable use are
p(y) = -4 y < -1
2 -and 7 ) = - 1 - y 171 5 1
7r
= 0 lyl > 1
These functions are plotted in Fig. C.2.
TABLE O F D U A L - I N P U T DESCRIBING F U N C T I O N S (DIDFs) (Continued)
Nonlinearity Comments
1. General odd quantizer
2. Uniform quantizer or granularity
3. Relay with dead zone
n -Q
I -I-:LO
Q.
TABLE OF DUAL-INPUT DESCRIBING FUNCTIONS (DIDFs) (Continued)
Nonlinearity Comments
n = 3 , 5 , 7 , ...
See Sec. 6.2
M y = Msinmx Ns= -
B Ju(mA) sin mB
2M n, = -Jl(rnA) cos mB
A
n, = 0
29. Harmonic nonlinearity
y = M sinh mx I, and I, are modified Bessel M
NB = -B Iu(mA) sinh mB functions o f orders 0 and 1 , respectively.
2M n, = -Il(mA) cosh mB
A
TABLE OF DUAL-INPUT DESCRIBING FUNCTIONS (DIDFs) (Continued)
Nonlinearity Comments
44. Negative deficiency
o o o Q l ? 213 o II II II II II II ,.$$ ." ." EO
554 D U A L - I N P U T D E S C R I B I N G F U N C T I O N S
0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10
Y
Figure C.1 Graphs of f ( y ) andg(y) .
DUAL- INPUT DESCRIBING FUNCTIONS 555
Figure C.2 Graphs of p(y) and q(y).