Simultaneous adjustment of balance maintenance and velocity tracking for a two-wheeled self-balancing vehicle

Abstract

The purpose of this research is the development a method for simultaneously adjusting the velocity tracking control and the inclination angle stabilization using control techniques for a two-wheeled self-balancing vehicle. The control tasks involve balancing the vehicle around its unstable equilibrium configuration along with steering and velocity tracking. In this study, the mathematical dynamic model of the vehicle is derived using the Lagrange method, under the assumptions of pure rolling and no-slip conditions which are expressed through nonholonomic constraint equations. Along with the mathematical descriptions, a multibody virtual prototype featuring advanced tire-ground interaction modeling has been developed using the MSC Adams software suite. Several classical and modern control strategies are investigated and compared to implement the method. These include Sliding Mode Control (SMC), Proportional Integral Derivative (PID), Feedback Linearization (FL), and Linear Quadratic Regulator Control (LQR) for the under-actuated and unstable subsystem that accounts for the pitch and longitudinal motions. The capabilities of these control strategies are verified and compared not only through Matlab simulation but also using Adams-Matlab co-simulation of the controller and the plant. Although every control technique has its advantages and limitations, the extensive simulation activities conducted for this study suggest that the SMC controller offers superior performances in keeping the system balanced and providing good velocity-tracking responses. Moreover, a Lyapunov-based analysis is used to prove that the sliding mode control achieves finite time convergence to a stable sliding surface. These advantages are counterbalanced by the complexity and the large number of parameters belonging to the designed SMC laws, the scheduling of which can be difficult to implement. For the comparison results another non-linear control strategy, that is, the feedback linearization method, is presented as an alternative. Through the Jacobian linearization approach the mathematical model of the system is linearized, allowing the use of control techniques such as linear quadratic regulation, which are deployed to treat the balancing, steering, and velocity tracking tasks. Finally, the empirical tuning of a PID controller is also demonstrated. The performance and robustness of each controller are evaluated and compared through several driving scenarios both in pure-Matlab and Adams-Matlab co-simulations.