Control of a beam-hoverboard self-transportation system with model predictive control

Abstract

In recent years, self-balancing transportation systems for personal use have gained increased popularity, the most popular of which being the "Hoverboard" type system. These systems function as inverted pendulum systems, with the operator acting as the pendulum, rotating a platform which incites lateral motion of a cart to maintain stability. This sort of system can be modeled as an inverted pendulum on a cart, but with the rigid pendulum replaced by a flexible cantilever beam. This allows for the vibrational characteristics to be accounted for and controlled. In this thesis, a Model Predictive Controller (MPC) is developed to control both the stability of the flexible beam and to minimize the magnitude of the vibrations at the tip of the beam. Several theoretical MPCs are developed for multiple models of increasing complexity that represent the system simplified to different degrees; the first model is a linearized, lumped-parameter inverted pendulum on a cart, the second is a nonlinear, lumped parameter inverted-pendulum on a cart, and the third is a continuous flexible cantilever beam on a cart. Multiple models were used in order to determine the minimum amount of modelled complexity necessary to develop a controller that can adequately control the most complex system (the flexible cantilever beam). The three controllers developed are each used in simulations with the three different models, to determine the least complex controller that can maintain the stability of the most complex model. It was found that only the controller developed specifically for the flexible beam model was able to maintain the stability, keeping the angle of the base of the beam <2.5×10-3rad, and the deflection in the tip of the beam <0.01m. This result is not particularly surprising, as MPCs lack robustness when dealing with model uncertainty or mismatch. This presentation concludes by discussing possible next steps for future work, including reduction of the computational load of the controller, and a design for initial experimental tests of the system.