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4.4 Computed-Torque Control 219

Figure 4.4.14 (Cont.) (c) n=50 rad/s.

(1)

with the tracking error e(t)=q d (t)-q(t). This control law is very simple and
direct to implement on an actual arm without even using a DSP. It is much
simpler than the control in Example 4.4.1.
The results of using the PD controller on the two-link arm are shown in
Figure 4.4.13 for several values of a closed-loop natural frequency w n . Recall
that the PD gains for critical damping are

(2)

The low-gain results (k p =100, k v =20) in part (a) of the figure are very bad
(note the scale). However, the high-gain results in part (c) are much better.
Even higher gains would cause a further tracking error decrease.
It is important to notice that there is in all cases a do component of the
tracking error. This is due to the fact that the gravity terms are neglected and
should be contrasted with the results of Example 4.4.3.

Copyright © 2004 by Marcel Dekker, Inc.