Page 287 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

Identification and Control of Hammerstein Systems With Hysteresis Non-linearity 289

Table 18.4 Identification results of G(z) with T = 0.5s
Voltage a 1 a 2 b 1 b 2
4V −1.8786 0.4078 −0.4058 −0.0701
5V −1.8950 0.4177 −0.4157 −0.0660

Figure 18.6 Hysteresis of servo system and identification of Preisach density function.
(A) Input/output of motor system; (B) Identified hysteresis curve; (C) Increasing section;
(D) Decreasing section.

18.5.2 Identification of Hysteresis

With these parameters, the unmeasurable variable x(t) can be obtained by
using the identified model G(z) and the output measurement y(t),which
will be utilized for the identification of non-linearities. Fig. 18.6Ashows
the input u(t) and the calculated output x(t) of hysteresis non-linearity.
The identified hysteresis non-linearity is illustrated in Fig. 18.6B. The
Preisach density function μ can be obtained from (18.19)for anygiven
input u(t) and calculated variable x(t).Fig. 18.6C provides the average μ of