101
Here we have used (6-2), (6-3) and the fact that = e* = 0. Since e
is a constant, both T9(e*) and D(e*) are also constant. This means that
k
the frequencies of TA(t) are identical to the frequencies of w(t) and
hence only the dynamics of the disturbance signal need to be included in
the internal model system. In this case, assumption (A.2) is satisfied
exactly. Note that the internal model system should also include
dynamics (i.e., integrators) to accomodate for the constant
gravitational torque T9(e*) if this torque is not supplied separately.
Feedback Gain Calculation
In this section we discuss the feedback gain calculation for the
manipulator system when the linearized model is used. In conjunction
with the chosen control scheme, this linearized model is evaluated over
the nominal trajectory. The linearized closed-loop system takes the
following form
(t) $*(t)
m n*(t)
F*(t) G*(t)K1(t)
-G*(t)K2(t)
A
<|>(t) (i.e., e) are taken as the
output, is defined as
% cw (6-H)
where 1^ is the NxN identity matrix. Evaluation of the nominal
Jacobian matrices using a linearization of (6-6) leads to