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Serena Tyson
United States Naval Academy
Subject Listing - Engineering
Advisor: Dr. Richard T. O'Brien, Jr., Dr. Matthew G. Feemster
Thursday, Oral Session 3, Presentation 4, Health & Fitness Center 203
AN INVESTIGATION OF A ROBUST SWING-UP CONTROLLER
The objective of this project is to verify the performance and robustness of existing swing-up controller designs using a commercially available rotary inverted pendulum system, from Quanser, Inc., through analysis, simulation, and experimentation. The rotary inverted pendulum system consists of a pendulum connected through an arm to the shaft of a DC motor so that the pendulum hangs freely. A swing-up controller moves the motor arm so that the pendulum swings from its natural (stable) equilibrium to its upright (unstable) equilibrium position where it is held in this inverted state by a separate stabilizing controller. The swing-up control problem is challenging due to the nonlinear nature of the system.
The verification process consists of three steps. In the first step, the existing nonlinear model is confirmed using Lagrange methods. To verify the accuracy of this model, the pendulum is dropped from a horizontal position and the motor and pendulum positions are recorded as the pendulum settled to its stable equilibrium point. All the parameters of the nonlinear model except the viscous friction coefficients of the motor and pendulum are available from the manufacturer. A comparison of the nonlinear simulation with the experimental results leads to the identification of the unknown friction coefficients and a verification of the derived nonlinear model for this system. In the second step, the nonlinear model is linearized about the upright (unstable) equilibrium point and a state feedback controller is designed using Linear Quadratic Regulator (LQR) methods to stabilize the pendulum about the this equilibrium point. In the final step, swing-up controllers developed using bang-bang and energy-based approaches are evaluated numerically using the nonlinear simulation and experimentally using the inverted pendulum apparatus.
The contribution of this project is a thorough analysis and verification of existing swing up controller designs on commercially available apparatus. This work will lead to investigations of robustness of existing swing-up controllers to parameter and general modeling uncertainty. Furthermore, this analysis has applications to hydrofoil ships and commuter vehicles that have high centers of gravity and require advanced control systems to prevent tipping when larger deviations from the upright position occur.
Advisor: Dr. Richard T. O'Brien, Jr., Associate Professor, Weapons and Systems Engineering Department, United States Naval Academy, Annapolis, MD
Advisor: Dr. Matthew G. Feemster, Assistant Professor, Weapons and Systems Engineering Department, United States Naval Academy, Annapolis, MD