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198 Computed-Torque Control

Figure 4.4.6: PID computed-torque controller.

with e(t) the integral of the tracking error e(t). Thus additional dynamics have
been added to the linear outer-loop compensator.
This control law is conveniently described by defining the state as
x= and augmenting the error dynamics (4.4.8) with an
integrator, so that

(4.4.37)

A block diagram of the PID computed-torque controller appears in Figure
4.4.6. Then the closed-loop system is

(4.4.38)

The closed-loop characteristic polynomial is

2
∆c(s)=|s I+K v s +K p s+K i |. (4.4.39)
3

Copyright © 2004 by Marcel Dekker, Inc.