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introduce additional poles into the I.M. system at 3 Hz. The resulting response is shown in Figure 7-6.     Although the sinusoidal ripple has

been virtually eliminated, there is a very small dc error.        This dc

error would not be expected in linear servomechanism problems, however, it occurs here because the manipulator system is nonlinear. In order to eliminate the dc error we then introduce integration capabilities into the I.M. system. The resulting error curves are shown in Figure 7-7 and the steady-state error is essentially zero.

     Figures 7-8 through 7-10, show the responses obtained when both tracking and disturbance rejection is to occur.    Figure 7-8 shows the

result of using linear servomechanism theory.    That is, only the poles corresponding to the   frequencies of the    reference and disturbance signals (3 Hz and 1 Hz respectively) have been included in the I.M. system. A steady-state sinusoidal error at a frequency of 6 Hz is seen in the plots.   Figure 7-9 shows the response obtained when the I.M. system is adjusted to include poles corresponding to a 6 Hz sinusoidal signal.   A small ripple still occurs at an even higher frequency; however, for the most part, the error consists only of a dc component. Consequently,  in  the  next  phase  of  the   design,  integrators  are incorporated into the I.M. system. The response is given in Fiugre 7-10 and we note that the steady-state error in both joints is now very small.

     The simulations presented    in this section show that if small steady-state tracking error    is  required, it   may  be  necessary  to introduce dynamics into the internal model system which may not have been included in a design based only on linear servomechanism theory.