| The ball and beam system is a very simple and powerful control system problem. The easy construction of this system combined with its challenging control design requirement makes it one of the most favorable example models for control engineers. The model contains a horizontal beam which can pivot about its center; a DC Motor whose shaft is connected to the center of the beam; and a ball that can freely roll on top of the beam. The basic idea is to accurately tilt the beam about its center, using the motor, to indirectly control the position of the ball that freely rolls on the beam. In this thesis, the L1 adaptive control technique is considered for precise positioning of the rolling ball on the beam. Two different architectures of L1 adaptive control namely, the L1 adaptive state feedback control and the L1 adaptive output feedback control are designed and verified in simulation. L1 adaptive control guarantees transient performance and robustness in presence of fast adaptation without introducing or enforcing persistence of excitation. |
