Optimal and H_∞ robust control of Euler-Bernoulli beams with uncertainties by Riccati approaches

Optimal and H_∞ robust control of an uncertain Euler-Bernoulli beam (EBB) by the distributed force are studied in this paper. The standard Euler- Bernoulli beam is assumed to be the nominal model for the control system. The variation in material properties, the rotatory inertia of the beams and other random disturbances are considered as the uncertainties of the system. The random disturbances are assumed to be the white Gaussian noise. Optimal and H_∞ robust control methods are employed to find the controllers for the beam with these uncertainties and disturbances. It is shown that the optimal and robust controllers are determined by the product of the solutions of the corresponding Riccati equation with the states of the system. Numerical simulations of uncontrolled and controlled responses of the beam demonstrate the effectiveness of the proposed technique. It is shown that the Euler-Bernoulli beam with or without rotatory inertia can be stabilized in the presence of uncertainties due to variations in the material characteristics and the white Gaussian random forcing.