Advanced modeling and optimal control of a cart-double pendulum system

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The Overhead Crane has evolved in scope since its inception in the late 1800's. Its early use as a hoist for material transport is now proceeded by new found applications, such as in the Active Response Gravity Offload System (ARGOS) at the NASA Johnson Space Center. ARGOS is an astronaut training facility designed to simulate reduced gravity environments such as Lunar, Martian, or microgravity. By industry standards, it is essentially a repurposed Overhead Crane; in academia it can be conceptualized as a cart-double pendulum system. Anti-sway control of cart-pendulum systems has been heavily researched; however, these methods are not typically designed for space simulation. The goal of this research is to design a controller that provides both energy and error minimization for the cart-pendulum, so that its payload moves as if it were floating freely in a microgravity environment (according to Newton's 1st law). The Euler-Lagrange equation is used to model the system and an optimal control technique called the [alpha]-shift is used to control the system. Most treatments on optimal linear control do not include the [alpha]-shift, but its addition allows one to stabilize the system faster and provides an extra tuning parameter while maintaining the simplicity of the solution. Numerical experiments show that the [alpha]-shift method significantly improves the cart-pendulum's ability to control its payload; especially for payloads in the cart-double-pendulum case.