Tracking and observer design for a motorized Euler-Bernoulli beam

In this paper, we consider the planar tracking problem and the observer design for an Euler-Bernoulli beam, clamped to a motor at one end and to a force actuator at the other. The control law for the motor is based on cancellation of terms at the boundary such that the desired error dynamics are obtained, and the control law for the force actuator is chosen such that the energy is extracted from the system. We also propose an exponential stable observer. The convergence of the observer is unaffected by the control laws. The stability analysis of the controlled system and the convergence of the observer are based on the semigroups theory. Numerical simulation results are included to illustrate the performance of the proposed control laws and the proposed observer. The simulation results are in agreement with the theoretical results.