Stabilization and disturbance rejection for the beam equation

Stabilization and disturbance rejection for the beam equation

We consider a system described by the Euler–Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give various asymptotical and exponential stability results. We also consider the distur...

Adaptive Stabilization and Disturbance Rejection for First-Order Systems

Two Approaches to Stabilization for Euler-Bernoulli Beam Equation with Boundary Moment Control and Disturbance

In this paper, we consider boundary stabilization for a one-dimensional Euler-Bernoulli equation with boundary moment control and disturbance. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By the ADRC approach, an extended state observer with time varying gain is designed to estimate the disturbance. It is shown that the ...

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

In this paper, we are concerned with the boundary stabilization of a one-dimensional anti-stable Schrödinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of th...

Exponential Stabilization of 1-d Wave Equation with Distributed Disturbance

In this paper, we consider the stabilization problem of a one-dimensional wave equation with unknown disturbance. In order to stabilize the system with disturbance, we design a distributed feedback controller by employing the idea of sliding mode control technology. For the resulted nonlinear closed-loop system, we prove its solvability by using the maximal monotone operator. Further we prove t...