Model Matching Control Applied to Bicycles

Abstract

Model matching control allows for a virtual change in the vehicle's physical parameters, removing the need to alter the system physically. These vehicles are used as a versatile test bed for safe and repeatable experiments, and allow for safer vehicle operation by virtually keeping the driving behaviour constant in the face of physical changes such as wet roads. Although already applied on planes and cars, it has not been applied to bicycles. The proposed control method accomplishes model matching control by equating the state derivative of the physical system to that of the the virtual system. Theoretical analysis shows model matching control is applicable to bicycle dynamics, even if only the steer torque is available for control. Via experiments, I identify the bicycle's weave mode eigenvalue at different speeds, and the Bode gain between steer torque to lean rate and to fork angle for frequencies between one and three Hz. The experimentally identified values follow the theoretically predicted values closely but do not overlap perfectly. The effect of artifacts during the experiment and unmodelled dynamics are analysed with the use of simulations and are able to explain these perceived differences. From the results, this research concludes that model matching control is applicable to bicycles and is able to virtually change the bicycle's physical parameters. Future work will look into making the controller more robust to modelling errors.