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4.4 Computed-Torque Control 191

(4.4.31)

Moreover (see the Problems),
(4.4.32)

so that
(4.4.33)

Thus, in the case of critical damping, the position error decreases with k pi and
the velocity error decreases with k vi .

EXAMPLE 4.4–1: Simulation of PD Computed-Torque Control
In this example we intend to show the detailed mechanics of simulating a
PD computed-torque controller on a digital computer.

a. Computed-Torque Control Law
In Example 3.2.2 we found the dynamics of the two-link planar elbow arm
shown in Figure 4.2.1 to be

(1)
These are in the standard form

(2)

Take the link masses as 1 kg and their lengths as 1 m.
The PD computed-torque control law is given as

Copyright © 2004 by Marcel Dekker, Inc.