Hybrid Kapitza's Pendulum
SPRING 2023 MAE 156B SPONSORED PROJECT
UNIVERSITY OF CALIFORNIA, SAN DIEGO
SPONSORED BY JORGE POVEDA, ECE PROFESSOR @ UCSD
BACKGROUND INFORMATION
Kapitza's Pendulum is a mechanism that consists of a vertically hanging pendulum attached to a vertically vibrating pivot point. The system was first studied by Soviet physicist Pyotr Kapitza in the 1950s.
When the pivot point of the Kapitza's pendulum is vibrated at high frequency, the pendulum can be stabilized in an inverted position. This phenomenon is known as dynamic stabilization and occurs because the high-frequency vibrations of the pivot point induce a non-linear damping force on the pendulum, which counteracts its gravitational force.
WHY IS KAPITZA'S PENDULUM IMPORTANT?
Understanding the principles behind Kapitza's pendulum is important for several engineering applications, including the development of Segways, rockets, and walking robots. The physical properties of Kapitza's pendulum can give mechanisms vertical self-stabilization capabilities.
SEGWAY
For Segways, the principles behind Kapitza's Pendulum are applied to create a self-balancing mechanism. A Segway uses sensors to detect the rider's center of gravity and then applies forces to maintain balance by oscillating the platform's pivot point.
ROCKET
Kapitza's Pendulum principles are used in rocket design to control rocket stability during ascent. The use of high-frequency oscillations of the rocket's fins enables the rocket to maintain stability even in the face of aerodynamic forces and disturbances.
ROBOTIC DOG
For robot dogs, like the one created by Boston Dynamics, Kapitza's Pendulum principles are applied to enable dynamic stabilization while in motion. By mimicking the high-frequency oscillations of the pivot point in Kapitza's Pendulum, robot dogs can remain stable in any type of terrain.
PROJECT OBJECTIVES
The project objective is to design and manufacture a mechanism that is capable of oscillations at any arbitrary angle on a 2D plane. Once we have the mechanism, a controller needs to be implemented to stabilize a free-hanging pendulum to the vertical position without human intervention. This controller will need to track desired positions with desirable control properties such as critically damped, low rise time, and asymptotic tracking. Additionally, the controller needs to be robust for arbitrary initial and final angle and be able to remain stable when disturbances are applied.
Objectives Summarized
Objective #1: Design/manufacture a mechanism capable of oscillations at any arbitrary angle on a 2D plane
Objective #2: Achieve vertical stabilization with human intervention (standard Kapitza’s pendulum)
Objective #3: Achieve vertical stabilization without human intervention (open-loop control)
FINAL DESIGNS
Scotch Yoke Design
Variable-Angle Pin-Slot Design
PERFORMANCE RESULTS
Created the standard Kapitza's pendulum and achieved stabilization. Open loop control achieved vertical stabilization without intervention. Resistant to small disturbances.
IMG_8038.movDesign 1
Open-Loop Stabilization
Design 2.MOVDesign 2
Open-Loop Stabilization
FINAL POSTER
