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220 Computed-Torque Control

Figure 4.4.15: PD classical joint control: k v =100, k p =2500, k i =1000.

Adding the gravity terms in the control law, therefore, significantly increases
the tracking performance.
The associated control torques are shown in Figure 4.4.14.

b. PID Independent Joint Control
PID independent joint control for the two-link arm is

(3)

This simple law is easily implemented by adding two states, x(5) and x(6),
to subroutine arm(x, xp) in Figure 4.4.2 to account for the integrators (see
Example 4.4.2).
The simulation in Figure 4.4.13(c) was repeated, but now adding an
integral gain of k i=1000. The result is shown in Figure 4.4.15. After several
iterations of the sinusoidal motion, the do value of the tracking errors goes
to zero, so that the performance is much improved. That is, adding an
integral term can compensate for neglecting the gravity terms in the control

Copyright © 2004 by Marcel Dekker, Inc.