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This paper presents the development of a full-state observer for an Euler-Bernoulli beam system with simply supported boundary conditions. This problem is motivated by the necessity of estimators in control and diagnostic applications. The observer is developed using a backstepping procedure. The full state observer cannot be completed with a single observer system, and hence this paper presents the synthesis of two observer structures that together provide the desired convergence. The necessary feedback information is limited to the slope and the sheer force of the beam at one boundary, which are practically measurable values on a physical system. The observer estimates the full infinite dimensional beam system without any discretization of the model. The result of the technique developed in this paper is that the infinite dimensional observer estimates converge to the plant system states (representing the actual beam displacement) at an arbitrary exponential rate; numerical simulation results validating this behavior are provided. [ABSTRACT FROM AUTHOR]

In this paper, a control technique is presented for an undamped, pinned–pinned Euler–Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler–Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form; however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and “second order” techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler–Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances. [ABSTRACT FROM AUTHOR]