Executive Summary

Executive Summary 

The Hybrid Control of Kapitza’s pendulum, sponsored by Dr. Jorge Poveda, focused on the development of a hybrid Kapitza’s pendulum to be installed at University of California, San Diego (UCSD).  This system could then be used to test various vibrational control algorithms. A standard Kapitza’s pendulum has a pivot point which oscillates up and down rapidly, generating a stable position directly above the pivot point. Once moved into this position, the pendulum is stable without the need for closed loop control and can even withstand minor disturbances. This property also works when Kapitza’s pendulum is set at an angle, as seen in Figure ES.1.

The main challenge that the standard Kapitza’s pendulum faces in implementation is that it needs to be moved into the stable position manually. This means that a standard Kapitza’s pendulum cannot be started from rest without a human or mechanism moving the pendulum into position. A hybrid Kapitza’s pendulum can theoretically do this by quickly adjusting the vibrational angle, however. Kapitza’s pendulum has potential to be used in vertical stabilization for self-landing rockets, walking robots, segways, etc. Vibrational control has potential to be used in vertical stabilization for self-landing rockets, walking robots, segways, and more as a low cost option.

The primary objective of this sponsorship was to design and manufacture a mechanism capable of oscillations at any arbitrary angle on a 2D plane (Figure ES.2). After the mechanism was manufactured, a controller needed to be implemented to stabilize a free-hanging pendulum to the upwards vertical position without human intervention. The theory and implementation of this controller was done by graduate student Daniel Ochoa Tamayo. As a secondary objective, the controller needed to track desired position with desirable control properties, to be robust for arbitrary initial and final angles, and to remain stable when disturbances are applied. The motivation for this project was to first prove the control theory written by Daniel Ochoa Tamayo, and later be used by students at UCSD to test various control algorithms.

The oscillation generation system consists of a rotary motor that spins a laser cut aluminum flywheel, which in turn generates linear motion of the CNC machined aluminum track along the polished steel guide rails built into the laser cut aluminum backing frame. The angle adjustment system is governed by the backing frame, which is rotated by the servo to change the angle of the oscillations relative to the base of the machine. The pendulum system consists of a laser cut aluminum pendulum that can rotate 360° mounted inside an encoder such that the angle is recorded instantaneously. The hybrid Kapitza’s pendulum begins in the resting position and oscillates in the vertical direction. With the control algorithm implemented by Daniel Ochoa Tamayo, it quickly adjusts the angle of oscillation repeatedly to stabilize the pendulum at different angles, eventually stopping with the stabilized position in the upwards vertical position. 

The mechanism needed to generate oscillations at frequencies of 60 rad/s and above, which results in accelerations upwards of 7g’s at times. As a result, the mechanism needed to be lightweight to reduce the forces generated by these accelerations, as well as strong to withstand the forces that are present during operation. Aluminum was chosen as the primary material for most of this design because of its low mass to strength ratio. It was relatively inexpensive to purchase, and easily machinable with various methods in the machine shop and Design and Innovation Building (DIB) at UCSD. This allowed the team to manufacture parts with very high precision to reduce wear due to friction and fatigue, as the nature of this mechanism is highly cyclical. 

After testing, the mechanism proved to be capable of producing oscillations at frequencies of 25 Hz and above for periods longer than a minute, and changing angles within fractions of a second. Angular position of the pendulum could be recorded with precision of .04 degrees using a rotary encoder.It reliably fulfilled the primary objectives of the project and has achieved hybrid control of Kapitza’s pendulum.