Recently, design, modeling and manufacture of two-wheeled vehicles have most been of concern due to their special capabilities such as not polluting the environment and reducing the traffic problem because of their smaller geometry rather than Four-Wheeled vehicles as well as non-use of fossil fuels. As known, in design of these types of vehicles, the most significant issues are the accurate analysis of stability and design of the suitable controller for the vehicle in order to exert the continuous control signal for the movement of two-wheeled vehicle.
In this study, first, dynamic equations of the vehicle are derived. It is noted that for the purpose of this thesis, the vehicle comprises a two-link inverted pendulum in order to model the position of the human while riding on the vehicle. A control law is then developed to ensure the stability of the two-wheeled vehicle about the upright position based on Lyapunov's stability theory.
The control strategy, however, contains discontinuous terms. The discontinuous terms in the controller make the system dynamics non-smooth resulting in high frequency oscillations (chattering) in the control torques. The effects of chattering are clearly undesirable, so a continuous controller is devised by replacing the discontinuous terms with continuous ones. Subsequently, another stability analysis is completed using the continuous control strategy as well as Quasi-Lyapanuv's function. During all design stages, the model is simulated using Simulink® in order to validate the mathematical modeling of the system.