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The various responses obtained when the manipulator is tracking
relative to the nominal trajectory are shown in figures 7-13 through
7-21. Each figure is presented so that part (a) depicts the error in
the joint angles while part (b) shows the actual and desired trajec
tories of the hand. The trajectories of the hand are given for both the
x- and y- displacements. The notation used here for the figure captions
is identical to the notation used in the previous section.
Figures 7-13 and 7-14 show the error which results when a
sinusoidal disturbance is applied. In Figure 7-13 the I.M. system
contains poles at the frequency of the disturbance. The tracking error
is very small; however, a slight ripple, most likely due to the time-
varying feedback gains, is evident in the joint-angle error curves.
Nevertheless, it is difficult to distinguish the actual hand trajectory
from the desired hand trajectory. Figure 7-14 is included mainly to
show that the I.M. system should contain poles corresponding to the true
frequencies of the disturbance. Here only integrators are used. As can
be seen from either the joint-angle error curves or the curves showing
the trajectory of the hand, a sinusoidal tracking error at the frequency
of the disturbance signal is present.
Figures 7-15 through 7-18 show the responses obtained when a
reference signal (no disturbance) is applied. Figure 7-15 illustrates
the response obtained when the poles of the I.M. system are at the
frequency of the disturbance signal (i.e., 2 Hz). A sinusoidal error at
a frequency of 4 Hz and with a slight dc offset is seen to occur. To
eliminate the dc offset, integrators are included in the I.M. system and
the resulting response is shown in Figure 7-16. As expected, the 4 Hz
sinusoid is still present in the steady-state tracking error. In order