Title: Control Design to Reduce the Effects of Torsional Resonance in Coupled Systems
Author: Daniel M. Lofaro
Advisors: Dr. Tom Chmielewski, Dr. Paul Kalata
Connecting two rotary mechanical devices utilizes a flexible coupler to accommodate various shaft misalignments. These couplers, including belts and gear boxes, exhibit a spring constant and a viscous damping term. The spring constant causes the system to have a resonant frequency while the damping controls its amplitude. In the frequency domain this characteristic is called Torsional Resonance (TR). The TR frequencies can not be allowed into the pass band of closed loop servo because it will cause instability.
Some conventional solutions to obtain stable operation include: reduction of the servo’s bandwidth below the TR frequencies; using stiffer, more expensive, components to increase the TR frequencies thus increasing the useable bandwidth; and using notch filters to reduce the resonant peak.
The objective of this work is provide a control solution to allow systems using elastic parts, including loose belt drives and plastic gears, achieve sufficient bandwidth to obtain their desired performance. A model of a commercial application exhibiting the TR characteristic has been made using Matlab and Simulink.
A test rig has been constructed with a brushless DC motor and a system able to control the location of the TR frequencies. This test rig is controlled by a hard real time target control system which accepts control through Matlab and Simulink.
The techniques described by Bigley and Rizzo and non-linear Sliding Mode Control (SMC), which has shown to reduce the error at resonance by approximately 50dB, is desired to be modeled and implemented on the physical system. The ability to reduce the effects of TR using electrical control allows mechanical system implementation using less costly components while achieving the desired specifications.
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