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4.4 Computed-Torque Control 217

Figure 4.4.13 (Cont.) (c) n=50 rad/s.

(4.4.62)

In using an integral term in the control law, it is important to be aware of
the possibility of integrator windup due to actuator saturation limits, which
was discussed earlier in the section “PID Outer-Loop Design.”

EXAMPLE 4.4–4: Classical Joint Control and Torque Saturation Limits
In Example 4.4.1 we simulated the exact computed-torque control law for
a two-link planar elbow arm. Here we want to show the results of using
PD and PID classical joint control on the same arm (with the same desired
trajectory). We are also interested in demonstrating the effects of torque
saturation limits. To highlight the effects without extraneous details, we
shall use only the arm dynamics and no actuator dynamics or gear ratio.
These may easily be included by making some slight modifications to the
subroutine arm(x, xp) in Figure 4.4.2.

a. PD Independent Joint Control

For the two-link arm, PD independent joint control is simply

Copyright © 2004 by Marcel Dekker, Inc.