Boundary Vibration Control Of Euler-Bernoulli Beam System

Flexible structure systems have widely applications in aerospace,marine riser,industrial production and other fields because of its lightweight,high speed,low energy consumption and flexible operation.However,due to the small stiffness characteristics of the flexible material,it is easy to vibrate under the effect of environmental disturbances,which will cause operational inaccuracies,reduce efficiency and even destroy safety.Therefore,it is of great significance to analyze the dynamic model of flexible structure system and study the control methods of vibration suppression.This thesis aims to study the vibration control of a typical model of flexible structural system,i.e.Euler-Bernoulli beam.For the problems of external disturbances,input constraints and parameter uncertainties,the corresponding design methods of boundary vibration controller are studied.The main contents of this thesis are as follows:For the Euler-Bernoulli beam system which is modeled as partial differential equations under time-varying distributed loads and boundary disturbance,a sliding surface which can reflect the vibration of the system is developed and a sliding mode boundary controller is further proposed by using the boundary signals and the exponential approach reaching law.Under the sliding mode controller,it is guaranteed that the system can reach the sliding surface in finite time and remain there afterwards.With aid of the Lyapunov method,it is proven that the closed-loop system is ultimately uniformly bounded on the sliding surface.In order to improve the chattering phenomenon,based on the disturbance observer and the equivalent control method,two sliding mode controllers with chattering suppression are proposed further.Numerical simulations are shown to illustrate the validity of the proposed boundary control methods.For the vibration control problem of Euler-Bernoulli beam system affected by damping,time-varying distributed loads and boundary disturbance,three robust boundary controllers with different disturbance suppression strategies are proposed to suppress the vibration and the effect of external disturbances.Firstly,a disturbance observer is designed to estimate the unknown boundary disturbance online,so as to directly reduce the effect of boundary disturbance in the feedback loop.Then,a robust controller with disturbance observer is further developed.In order to prevent the controller output from being too large at the initial stage of observer operation,a disturbance observer with the time-varying parameter is further proposed.Secondly,in order to remove the limitation that the derivative of boundary disturbance should be bounded in the above method,a robust boundary controller with signum function is proposed.However,due to the introduction of signum function,chattering phenomenon follows.In order to solve the chattering phenomenon,a robust controller with hyperbolic tangent function is proposed further.In addition,with aid of the Lyapunov method,it is proven that the closedloop system is ultimately uniformly bounded under the proposed controllers.Numerical simulations are shown to illustrate the validity of the proposed controllers.For the Euler-Bernoulli beam system with boundary disturbance and input constraint,an adaptive robust boundary controller is proposed to suppress the vibration of the system and to deal with input constraint effectively.Due to the saturation of the controller,an auxiliary system is constructed to compensate the control force.Furthermore,the auxiliary control law of the system is designed by using Nussbaum function.In addition,considering the uncertainties of system parameters,the corresponding adaptive laws are designed to adaptively select the controller gains.The ultimately uniformly bounded stability of the closed-loop system under the proposed controller and the adaptive laws is proven by using Lyapunov theory.Numerical simulations show that the proposed method can solve the input constraint problem of the system effectively.