Optimal State-feedback and Output-feedback Controllers for the Wheeled Inverted Pendulum System

iii ACKNOWLEDGEMENTS First and foremost I owe my deepest gratitude to my advisor and mentor, Prof. David G. Taylor for mentoring me and supporting me throughout my thesis for the last one year. This thesis would not have been possible unless it was for his patience, motivation, enthusiasm and immense knowledge of the subject matter. Besides my advisor, I would like to thank Prof. Yorai Wardi for agreeing to be the second reader of my thesis and thus approving it. I would like to show my gratitude to my instructor for the thesis writing class, Prof. Jeffrey A. Donnell for giving me invaluable comments on my thesis and excellent instruction on the process of thesis writing. My sincere thanks also extends to Prof. Douglas B. Williams for helping me on various occasions with regards to completing the requirements of the Research Option. for donating a Freescale MPC-555 Microcontroller Board towards our project. Last but not the least, I am grateful to my parents for encouraging me throughout my life and eventually supporting my entire education at Georgia Tech. vi SUMMARY Vehicles characterized as wheeled inverted pendulums have received recent attention in the robotics community. This thesis illustrates the process of designing optimal state-feedback and output-feedback controllers for the wheeled inverted pendulum system. However, since the wheeled inverted pendulum is a complex system to analyze, the cart-stick system is analyzed first. The cart-stick system is a simpler representation of the wheeled inverted pendulum system. The first step in designing a control system for any dynamic system is to derive the equations of motion or the dynamic model of the system. The exact same methodology of dynamic modeling and control system design is followed for the cart-stick system and the wheeled inverted pendulum system. The dynamic modeling includes deriving the equations of motion using the Newtonian and Lagrangian methods, assigning appropriate state-space variables, determining the non-linear state-space model, and deriving the approximate linear model of the non-linear state-space model. The control system design includes the determination of controllability and observability, state-feedback design and output-feedback design. The optimal gain matrix for state-feedback design is determined using the Linear Quadratic Regulator (LQR) technique; whereas the optimal gain matrices for output-feedback design are determined using Loop Transfer Recovery (LTR). The results of the state-feedback and output-feedback designs are compared in the conclusions of the thesis. It is found that though output-feedback designs using an estimator …