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230 Computed-Torque Control

which means that they store information or energy. Windup occurs when R(z)
is not a stable polynomial.
To correct integrator windup, it is necessary to limit the state of the controller
so that it is consistent with the saturation effects being experienced by the
plant input u k . This may be accomplished as follows. Select a desired stable
-1
observer polynomial A 0 (z) and add A 0 (z )u k to both sides to obtain
(4.5.22)

A regulator with antiwindup compensation is then given by

(4.5.23)

(4.5.24)

A special case occurs when A 0 (z) has all n of its poles at the origin. Then
the regulator displays deadbeat behavior; after n time steps its state remains
limited to an easily computed value dependent on the values of w k and u k (see
the Problems).

Figure 4.5.3: Control system including actuator saturation.

The next example demonstrates some aspects of digital control in robotics.

EXAMPLE 4.5–1: Simulation of Digital Robot Computed-Torque
Controller

In Example 4.4.1 we simulated a continuous-time PD computed-torque
(CT) controller for the two-link planar elbow arm. In this example some
issues in

Copyright © 2004 by Marcel Dekker, Inc.