Boundary and Distributed Control for a Nonlinear Three Dimensional Euler Bernoulli Beam Based On Infinite Dimensional Disturbance Observer
Control problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation PDE model of a nonlinear three dimensional Euler Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.