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192 Computed-Torque Control

(3)

with the tracking error defined as

e=q d-q. (4)

b. Desired Trajectory

Let the desired trajectory q d(t) have the components

θ 1d=g 1 sin (2πt/T)
θ 2d=g 2 cos (2πt/T) (5)

with period T=2 s and amplitudes g i=0.1 rad≈6 deg. For good tracking select
the time constant of the closed-loop system as 0.1 s. For critical damping, this
means that K v=diag{k v}, K P=diag{k p}, where

(6)

It is important to realize that the selection of controller parameters such as the
PD gains depends on the performance objectives-in this case, the period of the
desired trajectory.

c. Computer Simulation
Let us simulate the computed-torque controller using program TRESP in
Appendix B. Simulation using commercial packages such as MATLAB and
SIMNON is quite similar.
The subroutines needed for TRESP are shown in Figure 4.4.2. They are
worth examining closely. Subroutine SYSINP (ITx, t) is called once per Runge-
Kutta integration period and generates the reference trajectory q d(t), as well
as q d(t), and q d(t). Note that the reference signal should be held constant
during each integration period.

Copyright © 2004 by Marcel Dekker, Inc.