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Vibration Suppression Control of 3D Printed Beams
Dynamic systems and control can be an abstract and mathematically intensive subject that seems theoretical to students. This paper presents a cost-effective active-learning project that helps students visualize frequency response and make connections between pole locations and the step-response of the system while applying root locus to a physical system.
The experimental system consists of a 3D printed beam with an accelerometer at its tip attached to a DC motor/encoder system. An H-bridge and AA battery pack are used to allow an Arduino microcontroller to drive the motor. The entire system costs roughly $120, not including the cost of 3D printing. Real-time feedback control experiments are performed using entirely open-source software: control design and data analysis are done in Python and experiments are run using the Arduino IDE. The Arduino prints real-time, delimited data to the serial monitor. This data can be copied and pasted into a text file and loaded into Python or Python can communicate directly with the Arduino using the serial library.
The project assignment was to develop a vibration suppression controller to minimize the settling time of both the encoder and accelerometer signals when the system was given a step input in the desired encoder position. The project began in the seventh week of the dynamic systems and control course. When the project began, root locus had not yet been introduced. So, the students started by tuning PD control of the motor based on encoder feedback; accelerometer feedback would not be introduced until a few weeks later.
One fairly common problem with experimental feedback control projects is that they often deteriorate into PID tuning. Because the accelerometer is being used in feedback, PID tuning really does not work. Students are forced to ask themselves what form the compensator for accelerometer feedback should take and this ultimately drives them into root locus design. The students learn to identify closed-loop pole locations that would potentially improve the system response and to evaluate the open-loop transfer function at those locations to determine whether phase needs to be added or subtracted. This process guides students toward using a low pass filter on the accelerometer feedback signal.
Before root locus design can begin, students need a transfer function between desired encoder angle and tip acceleration. The students find this transfer function based on Bode plots from swept-sine tests. The Bode plots initially appear noisy and somewhat difficult to interpret. The teams were able to identify the first two natural frequencies of the beam through this process and eventually come up with a fairly accurate transfer function.
The project ended with a competition to see which team could get the lowest settling time. If acceleration feedback is not used, rapid motion of the motor can cause tip vibrations that take 2-4 seconds to die out. All of the teams successfully designed a control system that led to an accelerometer settling time of less than 0.8 seconds. The winning settling time was 0.42 seconds.