Sliding mode boundary control for an Euler-Bernoulli beam with boundary disturbances and parameter variations

This work addresses the problem of stability and control of an Euler-Bernoulli beam with sliding-pinned boundary conditions. The control comes in the form of an applied displacement and bending moment on the pinned end. The proposed controller accounts for bounded exogenous disturbances on the pinned end boundary conditions, representing a number of possible practical issues such as model parameter uncertainties or unknown external forces. This controller takes advantage of a technique for stabilizing an Euler-Bernoulli beam through a Schrödinger equation representation and a previously developed integral transformation which provides the opportunity to select arbitrary damping for the system. The contribution of this work is to introduce unknown boundary disturbances into the system boundary terms and the development of a Sliding Mode Controller which effectively drives the system states to an exponentially stable infinite-dimensional sliding surface which then eliminates the system vibration with arbitrary damping. The resulting control efforts developed are continuous functions and therefore do not create a chattering effect on control actuators.