Page 11 - Servo Motors and Industrial Control Theory

1.3 Linearization Technique 3

y y y

x x x

On_off control Saturation of linear system Transport lag
Fig. 1.2 Some discontinuous nonlinearities

Fig. 1.3 A continuous

nonlinearity Y

y

x X

This is shown in Fig. 1.3

1.3 Linearization Technique

If there is a continuous nonlinearity in the form of

Y = F X() (1.8)

Assuming small perturbation from the equilibrium point, Eq. (1.8) can be linearized
as
d Y
Y + y = FX +() x d (1.9)
x d

or it can be written as

d Y
y = x (1.10)
x d