(t) = -H11t)H2(t)f(t)                     (6-24)


It is perhaps better to express (6-24) in terms of the measured force f(t) and the nominal force f(t). More precisely, we may write


                    e*(t) = -HI1(t)H2(t)[f(t)-T(t)]                 (6-25)



     By supplying ^6*(t) as the corrective reference signal for the

control scheme of Figure 6-1, end-effector tracking can be improved considerably.  In order to achieve this objective, it is necessary that the internal modal system contain the appropriate dynamics.        If the

external forces are not varying rapidly, it is likely that an internal model system consisting of just integrators will be sufficient.      As a

final point note that perfect end-effector tracking will not occur since equation (6-25) is only approximate.

     In the next chapter, simulations are provided to demonstrate the performance of the control schemes discussed in this chapter when

applied to a 2-link manipulator.