between each sampling interval of the controller. Since the controller samples every 40 milliseconds, the Runge-Kutta algorithm updates every 4 milliseconds. The total simulation time is always 4 seconds.
Now consider the disturbance and reference signals which are
applied in the simulations. These shall usually be sinusoidal in
nature. As indicated, the disturbance force acts vertically downward on the hand. In addition, we shall always choose the reference joint angles l(t) and _(t) to be identical. For example, if *(t) = lO0sint then 82(t) = l00sint (note that the amplitudes of the sinusoidal signals are given in degrees). Finally, we point out that in all simulations both the reference and disturbance signals are applied at 0.25 seconds.
Control about a Stationary Configuration
In this section we present simulations which have been obtained when the manipulator operates relative to a fixed nominal position. In
*0
all cases, the nominal position is eI = -180, 2 360. Since the control is designed relative to a fixed position, the stabilizing feedback gains are constant. The various responses are shown in Figure 7-2 through Figure 7-10.
We have adopted a certain notation for describing the figures. For example, if the figure caption reads "ref. = 6 Hz sinusoid with amplitude of 1001' then it will mean that the reference joint angles 6i(t)' i = 1,2 are both equal to the function lO0sin (21 • 6(t-0.25)) (recall that the reference is always applied at 0.25 seconds). In
addition, the notation "I.M. frequency = F Hz" will indicate that the internal model system has eigenvalues at e±j21FT where T is the sample