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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).