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4.4 Computed-Torque Control 221

Figure 4.4.16: PID classical joint control with torque limits of ±35 N-m. Tracking
error in rads.

law. However, it takes awhile for the error to converge to a zero do value,
and the results are still not as good as the PD-gravity controller in Example
4.4.3 for the same PD gains. On the other hand, the integral term can
reject other terms besides gravity (e.g., friction of some sorts). The torque
control input was virtually the same in form as Figure 4.4.14(c).

c. Actuator Saturation Limits
We discussed integrator windup due to actuator saturation limits earlier in
the section “PID Outer-Loop Design.” Here we should like to demonstrate
its deleterious effects.
The control torque in part (b) of this example is similar to the torque in
Figure 4.4.14(c); it is fairly well behaved, except for some frantic action
near time zero, where the maximum positive excursion is 78 N-m.
Suppose now that there are torque limits of t max=35 N-m, t min= -35 N-m.
This is easily simulated by modifying subroutine CTL(x) in Figure 4.4.2 to
include a saturation function by adding the lines

Copyright © 2004 by Marcel Dekker, Inc.