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236 Computed-Torque Control

was very small, in fact very similar to that in Example 4.4.1. However, as
the sampling period T increased the tracking performance deteriorated.
The torque input for joint 2 is depicted in Figure 4.5.6. For small T is is
virtually identical to the continuous CT controller in Example 4.4.1. A
very interesting phenomenon occurs when T=0.1 s. According to the plot
in Figure 4.5.6(c), there is a limit cycle, a form of nonlinear oscillation. It
is well known that sampling can induce such nonlinear effects in the closed-
loop system [Lewis 1992]. According to Figure 4.5.5(d), the limit cycle is
reflected in the tracking error as a periodic oscillation about e(t)=0. The
appearance of limit cycles is closely tied to a loss of observability in the
sampled system.

Copyright © 2004 by Marcel Dekker, Inc.