Page 815 - Mechanical Engineers' Handbook (Volume 2)

806 Neural Networks in Feedback Control Systems

τ
u
τ m
d –
d + u

Figure 12 Backlash response characteristic.

The NN precompensator shown in Fig. 13 effectively adds control energy to invert the
dynamical backlash function. The control input into the backlash element is given by
ˆ u(t) K ˜ y nn v 2
b
where ˜ (t) (t) (t) is the torque error, y (t) is the NN output, and v (t) is a certain
nn
des
2
robust control term detailed in Ref. 28. Weight-tuning algorithms given there guarantee
closed-loop stability and effective backlash compensation.
7 NN OBSERVERS FOR OUTPUT FEEDBACK CONTROL
Thus far, we have described NN controllers in the case of full state feedback, where all
internal system information is available for feedback. However, in actual industrial and com-

Estimate
of nonlinear
y (n) function
d
ˆ
fx
()
- •
[0 Λ ] τ des
T
Filter v
- - 2 Backlash
x d e [Λ Ι] r ϕ ˆ u ˆ τ Nonlinear x
T
- K v - τ des K b 1/s system
-
v 1 - y nn
NN compensator

x r Z ˆ
d
F
Backstepping loop

Figure 13 Dynamic inversion NN compensator for system with backlash.