Pulse-width control is a technique that has been used successfully to control robotic manipulators in the presence of static and kinetic friction. The technique of pulse-width control utilizes an approach where pre-calculated force pulses of set amplitude and variable time are used to move the manipulator. This avoids problems with the disparity between the static friction coefficient and the kinetic friction coefficient. As a result, pulse-width control can provide fine positioning in the presence of dry sliding friction.

However, pulse-width control has been fully developed only for limited types of systems. For bodies that can be considered rigid, connected by prismatic joints, stability proofs have been done and the application of pulse-width control is well refined. For prismatically jointed systems with flexibility, the technique of pulse-width control has also been relatively well developed. The application of pulse-width control to revolute systems, particularly those with flexibility, has only just begun.
This thesis details work done in developing models of revolute systems, both with and without flexibility, explains some of the control algorithms that were developed for the application of pulse-width control to revolute systems, and analyzes simulations performed to validate the approaches. The development of the dynamical equations of motion is given, showing the equations used in later simulation.

Descriptions of each model used in the thesis work are provided. These include a two-link rigid revolute system, a one-link flexible revolute system, and a two-link flexible revolute system. Each of these models was used in the creation and validation of the simulations developed for this project.

The results of the simulations are also given, along with explanations of the behavior observed. Evidence is given for the validity of two control algorithms. The first algorithm uses a series of inequalities to determine the relative magnitudes of the torque pulses needed to move the system to the setpoint. The pulse times are calculated as needed. To control unstable behavior, the base motor (in either the rigid or flexible case) is prevented from applying the full torque amplitude when the links must move in opposing directions.

The second algorithm developed utilizes an approach where a table of the relative torque pulse times is calculated offline for varying error in each link. The controller then interpolates values from the table to determine the required pulse times during operation. Though the table can be difficult to generate, it takes advantage of the known dynamical relationships in the system and produces a stable and rapid convergence to the desired setpoint. Both approaches described showed stability and convergence in all test cases, though no stability proof is yet available for either algorithm.

Conclusions are drawn from the simulation results in the final portion of the thesis. Primary findings are that both pulse-width controllers can sufficiently control two-link flexible revolute systems. However, the controller utilizing relative magnitudes of the torque pulses can cause undesired motion in both links before coming to rest, even when considering rigid links. The tabular controller gives smoother and more accurate motion. Additionally, the tabular controller lends itself to adaptive control techniques. For these reasons, the tabular controller is judged to be the more promising control technique.

Read the Thesis - Read the Defense