Page 269 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

270 Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics

Figure 17.3 Identification results of θ 1 and θ 2 .

Figure 17.4 Identification results of backlash characteristic parameters.

control, we set r =˙e + λe =˙e +400e (e = y −y d , y d is the desired trajectory).
Then the unknown parameter θ and the backlash characteristic parameters
(l,d 1 ,d 2 ) are estimated by (17.15)–(17.24). Fig. 17.3 and Fig. 17.4 show
the identification results of the system parameters and the backlash char-
acteristic parameters, respectively. From these two figures, it can be seen
that the estimated parameters all converge to their true values after about 5
iterations with very accurate estimation performance.
Moreover, the proposed control based on the identified parameters will
be tested. From (17.49), the control (17.40) with the inverse compensation
(17.28) is implemented with the control parameters k p = 400, v = 0.01.
The presented control scheme in this chapter is compared with the methods
proposed in literature [13]and [14]. The results are shown in Figs. 17.5