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290 Robust Control of Robotic Manipulators

Figure 5.2.8: Two-degree-of-freedom controller structure.

an integral term to achieve static accuracy. Its relative degree may be -1 since
both q and are available.

EXAMPLE 5.2–5: Dynamic Two DOF Design
Consider the two-DOF structure of Figure 5.2.8, where

(1)

Then a two-DOF regulator is described by

(2)

3
2
where s +b 2s +b 1s+1 is a stable polynomial, and w 1, w 2, a 1, b 1, and b 2 are
design parameters. Note that K 2(s) is a PID controller and that the closed-
loop system given by K 1(S) is a second-order system with natural frequency
w 1 and damping ration . Note also that the input to the robot
becomes

Copyright © 2004 by Marcel Dekker, Inc.