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4.4 Computed-Torque Control 197

Figure 4.4.5: Torque inputs (N-m).

PID Outer-Loop Design
We have just seen that PD computed-torque control is very effective if all the
arm parameters are known and there is no disturbance d . However, from
classical control theory we know that in the presence of constant disturbances,
PD control gives a nonzero steady-state error. Consequently, we are motivated
to make the system type I by including an integrator in the feedforward loop-
this can be achieved using the PID computed-torque controller

(4.4.34)

(4.4.35)

which yields the arm control input

(4.4.36)

Copyright © 2004 by Marcel Dekker, Inc.