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REFERENCES 259

r=0.1.
(b) Simulate the controller for various values of PD gains.
4.4–9 PD Computed Torque with Neglected Actuator Dynamics. Consider the
arm-plus-dynamics in Problem 4.4–8. Suppose, however, that the CT
controller was designed using only the arm dynamics and neglecting the
actuator dynamics. Use the PD gains in Example 4.4.1. Simulate the control
law on the arm-plus-dynamics for various values of gear ratio r. As r
decreases, the performance should deteriorate.
4.4–10 PD Computed Torque Using Only Actuator Dynamics. Consider the arm-
plus-dynamics in Problem 4.4–8. Design a CT controller using only the
actuator dynamics and no arm dynamics. Simulate the control law on the
arm-plus-dynamics for various values of gear ratio r. As r decreases, the
performance should improve. For fixed r, it is also instructive to try different
PD gains.
4.4–11 Classical Joint Control with Actuator Dynamics. Repeat Example 4.4.4
including actuator dynamics like those in Problem 4.4–8. Try different values
of gear ratio r. Compare to Problem 4.4–10.
4.4–12 PD Computed Torque with Flexible Coupling. Combine the flexible shaft in
Example 3.6.1 with the two-link arm in Example 4.4.1 to study the effects of
using CT control on a robot with compliant motor coupling. Try different
values of the coupling shaft parameters.
4.4–13 Error Dynamics with Approximate CT Control. Considzer the two-link
polar arm in Example 3.2.1 with friction of the form Find the error
dynamics (4.4.44) for the cases:
(a) Friction is not included in the CT control law.
(b) Payload mass m 2 is not exactly known in the CT control law.
(c) PD-gravity CT is used.
(d) PD classical joint control is used with no nonlinear terms.
Section 4.5
4.5–1 Digital Control Simulation
(a) Repeat Example 4.5.1 using a desired trajectory with period of 1

Copyright © 2004 by Marcel Dekker, Inc.