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

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 hamper the performance of a system, it is necessary to consider and prototype output-feedback control systems because all state variables are almost never available for full-state feedback.Committee Member/Second Reader: Wardi, Yorai; Faculty Mentor: Taylor, Davi