State-Space Modeling and Analysis of Bicycle Dynamics
Bicycles are amongst the most common modes of transportation in our world, and its use ranges from commuting to locations to use in competitive sport. While a bicycle might seem to be a simple vehicle, it is difficult to model as there are many complex variables to consider such as velocity, steering angle, tilt angle, torque, and inertia. In this report, we will model this machine as a state-space system and will examine the model’s linearity, time-invariance, stability, controllability, and observability. Once deemed usable, the system’s open-loop system will be evaluated using a linear quadratic regulator (LQR). Once these examinations are complete, we
can design an optimized controller so that we can control a bicycle with utmost efficiency and performance. This optimized controller will be compared to other variations of the controller and
open loop model.