## Graduate Theses, Dissertations, and Problem Reports

2015

Thesis

MS

#### College

Statler College of Engineering and Mineral Resources

#### Department

Mechanical and Aerospace Engineering

Yu Gu

Marvin Cheng

Jason Gross

Yu Gu

#### Abstract

The control of an inverted pendulum is a classical problem in dynamics and control theory. Without active control, the inverted pendulum by itself is inherently unstable, thus serving as an ideal platform for control algorithms design and testing. This study utilizes an inverted pendulum setup to investigate the characteristics of manual control in executing a single-axial compensatory task. An inverted pendulum with sliding base on a single-axial rail was built for this purpose. Human subjects were asked to stabilize the pendulum by sliding the base on the rail. To mathematically quantify the characteristics of human manual control, a quasi-linear lead-lag with time delay model was chosen for the human operator. The mathematical model for the inverted pendulum was derived using the LaGrange's method. Using these two models, a simulation of the closed-loop human-inverted pendulum system was built in Matlab/Simulink. The stability conditions of the closed-loop system were derived by applying the Routh-Hurwitz stability criterion to the system. This completes the modeling and simulation of the process of humans balancing an inverted pendulum. The Matlab simulation serves as a validation tool in this study. The data of the human subject's input and the inverted pendulum's output generated from the simulation were used to estimate the parameters assumed in the mathematical model for the human operator. The estimation algorithm employed is a Kalman filter. Results show that the estimations do converge very quickly to the parameters set in the simulated human controller and can stabilize the inverted pendulum when fed back into the simulation. This verifies the plausibility of the mathematical structure for the human operator and the validity of the estimator. Experimentally, the pendulum's angle deflections from the vertical position and the human subjects' hand positions were recorded using a motion capture system called VICON. Using the same estimator developed for processing the simulation data, the collected experimental data were processed to estimate the parameters in the model for the human operator when the human operator actually carries out the task of balancing the inverted pendulum. The estimated parameters from the experimental data were then fed into the simulation model. The characteristics of the human operator were analyzed using the estimated parameters.

COinS

#### DOI

https://doi.org/10.33915/etd.5498