The Stabilization And Control Of Rotating Rigid-flexible Coupling Systems

The thesis considers the stabilization and control design for one kind of rigid-flexible coupled systems.This kind of systems consists of a rotating disk and flexible beam,and one end of the flexible beam is free,whereas another end is clamped to the center of the disk.The disk rotates freely around its axis with a time-varying angular velocity and the motion of the beam is confined to a plane perpendicular to the disk.Mechanical arm is,a kind of rigid-flexible coupled systems,widely used in engineering construction field such as spacecraft,vehicles and robots,and composed of center rigid body connected with flexible appendages(such as beam)by flexible joint.In the process of work,safety reliability is the core of the design and manufacture of mechanical arm.The vibration caused by slewing or external disturbance can affect the stability and the pointing accuracy of the system.Therefore,there is a need for further research on the dynamic behavior of rigid-flexible coupled systems.The research content of this thesis has three aspects:The first one is to design a controller for the rotating body-beam systems with the external disturbances,and consider the asymptotic stabilization of the closed-loop systems;The second is to con-sider the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls.Finally,we consider the exponential stability of a 2-dimensional Schrodinger-Heat interconnected system in a torus region.The thesis is organized as follows:In Chapter 1,we introduce the engineering background,development situation,and main results.Some preliminaries relevant to basic concepts,main theorems and the active disturbance rejection control(ADRC)are also presented.In Chapter 2,we deal with the stabilization of the rotating disk-beam system,where the control ends of beam and disk are suffered from disturbances respectively.The active disturbance rejection control(ADRC)approach is adopted in investigation.The disturbances are first estimated by the extended state observers,and the observer-based feedback control laws are then designed to cancel the disturbances.When the angular velocity of the disk is less than the square root of the first nature frequency of the beam,it is shown that the feedback control laws are robust to the external disturbances,that is,the vibration of the beam can be suppressed while the disk rotating with a desired angular velocity in presence of the disturbances.Finally,the simulation results are provided to illustrate the effectiveness of ADRC approach.In Chapter 3,we are concerned with nondissipative torque and shear force sta-bilization of a rotating flexible structure subject to matched input disturbances.The ADRC approach is adopted in investigation.However,compared with Chapter 2,there are two different points for the control law designed in this chapter:(1).The system op-erator generates a compact semigroup;(2).Imposing nonlinear control on the rotating disk weakens the effect that flexible beam has imposed on the disk.In Chapter 4,we consider the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls.To stabilize the sys-tem,we propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively.As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite opera-tor,we show that the torque and nonlinear distributed control laws suppress the system vibrations,in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.In Chapter 5,we study the exponential stability of a 2-dimensional Schrodinger-Heat interconnected system in a torus region,where the interface between the Schrodinger equation and the heat equation is of natural transmission conditions.By using a polar coordinate transformation,the 2-dimensional interconnected system can be reformulated as an equivalent 1-dimensional coupled system.It is found that the dissipative damping of the whole system is only produced from the heat part,and hence the heat equation can be considered as an actuator to stabilize the whole system.By a detailed spectral analysis,we present the asymptotic expressions for both eigenvalues and eigenfunctions of the closed-loop system,in which the eigenvalues of the system consist of two branches which are asymptotically symmetric to the line Re ? =-Im?.Finally,we show that the system is exponentially stable and the semigroup,generated by the system operator,is of Gevrey class.A summary of this thesis and some unsolved problems are presented at the end.