Page 80 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

APPC of Servo Systems With Continuously Differentiable Friction Model 71

Figure 4.6 Tracking errors of different controllers.

errors at the point of maximum amplitude, and thus provides smallest error
as shown in Fig. 4.6.
All the aforementioned experimental results clearly show that the pro-
posed APPC can retain the prescribed control performance. Moreover,
compared with other model-based friction compensations [1], [2], and [3],
a continuous differentiable friction model with online updated parameters
is adopted so that the time-consuming offline system identification proce-
dure can be avoided and reduced computational costs are required.

4.5 CONCLUSION
An adaptive control is proposed for a class of non-linear servo systems with
guaranteed transient and steady-state tracking performance. The difficulty
from the friction is circumvented by adopting a new continuously dif-
ferentiable friction model, which is lumped into the neural network for
approximating unknown dynamics. A novel high-order neural network
with a scalar weight parameter is developed allowing for reduced computa-
tional costs. Consequently, primary friction model parameters are updated
together with NN weight to avoid time-consuming and costly offline iden-
tification of friction. Moreover, a prescribed performance function and an
output error transform are investigated such that both transient and steady-
state performance (e.g., overshoot, convergence speed, steady-state error)
of the tracking error are guaranteed by stabilizing the transformed system.