具有外部干扰的不稳定剪切梁的输入–状态稳定

In this paper, the input-to-state stabilization of an unstable shear beam with van der Waals forces at one end is considered. Through an invertible transformation, the equation is transformed into a 2 × 2 system of first-order transport equations, which convects in opposite directions cascaded with an ordinary differential equation (ODE). Using the active disturbance rejection control (ADRC) method, an extended state observer with the time-varying gain is given to estimate the disturbance. Applying the backstepping transformation and the disturbance estimation, the feedback control of the closed-loop system is proposed to compensate for the instability of the system itself and cancel the matched disturbance. By the C0-semigroup method and the Lyapunov method, the well-posedness and the input-to-state stability (ISS) of the closed-loop systems are proved, respectively. The validity of the theoretical results is verified by numerical simulations.