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3.6 Actuator Dynamics 159

Figure 3.6.2: Step response of dc motor with no shaft flexibility. Motor speed in rad/s.

The shaft flexible mode has the poles s=-3.4 ± j5.6, and so has a damping
ration of ζ=0.52 and a natural frequency of ω=6.55 rad/s. Note that the system
is marginally stable, with a pole at s=0. It is BIBO stable due to pole-zero
cancellation.

Program TRESP yielded the step response shown in Figure 3.6.3. Several
points are worthy of note. Initially, the motor speed ω m rises more
quickly than in Figure 3.6.2, since the shaft flexibility means that only
the rotor moment of inertia J m initially affects the speed. Then, as the
load J L is coupled back to the motor through the shaft, the rate of
increase of ω m slows. Note also that the load speed ω L exhibits a delay

Copyright © 2004 by Marcel Dekker, Inc.