ADAPTIVE CONTROL OF FLEXIBLE BEAM WITH UNKNOWN DEAD-ZONE IN THE DRIVING MOTOR

Adaptive control of a flexible beam system preceded by an unknown dead-zonein the driving motor is investigated in state space form. By introducing an important lemma forsimplifying error equation between the flexible beam model and the matching reference model, arobust adaptive control scheme is developed by involving the dead-zone inverse terms. The newadaptive control law ensures global stability of the entire system and achieves desired trackingprecision even when the slopes of the dead-zone are not equal. Simulations performed on a typicalflexible beam system illustrate and clarify the validity of this approach.

Model reduction and active control of flexible beam using internal balance technique

The internal balance technique is effective for the model reduction in flexible structures, especially the ones with dense frequencies. However, due to the difficulty in extracting the internal balance modal coordinates from the physical sensor readings, research on this topic has been mostly theoretical so far, and little has been done in experiments or engineering applications. This paper studies the internal balance method theoretically as well as experimentally and designs an active controller based on the reduction model. The research works on a digital signal processor （DSP） TMS320F2812- based experiment system with a flexible beam and proposes an approximate approach to access the internal balance modal coordinates. The simulation and test results have shown that the proposed approach is feasible and effective, and the designed controller is successful in restraining the beam vibration.

STUDY ON ACTIVE CONTROL FOR A FLEXIBLE BEAM UNDER THE CONDITION OF ZERO GRAVITY

The system of coupling structure with controlling is a kind of dynamic feedback system in which the mechanical load and the actuator/controller interact. The mechanical system and the control system can be considered integrally as a close system, and the driving forces actuating the mechanical load can be taken as inner forces in the coupling structure system with controlling. Therefore, one can use the method for dealing with conservative systems to simplify greatly modeling and analyses. The relative equilibrium state of motion of the flexible beam under the condition of zero gravity is studied by using the energy method, in which the characteristics of structure and controlling are considered synthetically. And further, the stability conditions for the relative equilibrium state of the system have been found. If the stability conditions are used as controlling parameters of motion of the system, the kinetic energy of the flexible beam can be converted advantageously into the electromagnetic energy of the motor and controller as well as the vibration of the flexible structure can be reduced rapidly. The results in the research provide a kind of very simple and effective real time control method reducing the vibration of the flexible beam. The method has been verified in many kinds of experimental systems of flexible beams.

Experimental study of delayed positive feedback control for a flexible beam

Recently, some researches indicate that positive feedback can benefit the control if appropriate time delay is intentionally introduced into control system. However, most work is theoretical one but few are experimental. This paper presents theoretical and experimental studies of delayed positive feedback control technique using a flexible beam as research object. The positive feedback weighting coefficient is designed by using the optimal control method. The available time delay is determined by analyzing the maximal real part of characteristic roots of the system. A DSP-based experiment system is introduced. Simulation and experimental results indicate that the delayed positive feedback control may effectively reduce the beam vibration if time delay is appropriately selected.

Hysteretic Nonlinearity Observer Design Based on Kalman Filter for Piezo-actuated Flexible Beams with Control Applications

Piezoelectric actuators fundamentally possess hysteresis behavior. Estimation of the hysteresis is usually demanded for enhancing the performance of piezo-actuated systems. This paper presents an observer-based scheme to estimate the hysteresis in piezo—actuated flexible beams. The observer is based on a nonlinearity observer method. The discrete-time Kalman-filter algorithm is adopted for determination of the observer gains. The major advantages of the presented scheme include ease of implementation and robustness to uncertainty of hysteresis parameters. Simulation results demonstrate that the observer is able to estimate the hysteresis efficiently and has better robustness compared to the previous scheme existing in the literature. The present scheme was also successfully applied to a real-life system. Moreover, a control application example is included to demonstrate the effectiveness of the scheme.

Substructuring Technique for Dynamics Analysis of Flexible Beams with Large Deformation

In this paper, the substructuring technique is extended for the dynamics simulation of flexible beams with large deformation. The dynamics equation of a spatial straight beam undergoing large displacement and small deformation is deduced by using the Jourdain variation principle and the model synthesis method. The longitudinal shortening effect due to the transversal deformation is taken into consideration in the dynamics equation. In this way, the geometric stiffening effect, which is also called stress stiffening effect, is accounted for in the dynamics equation. The transfer equation of the flexible beam is obtained by assembling the dynamics equation and the kinematic relationship between the two connection points of the flexible beam. Treating a flexible beam with small deformation as a substructure, one can solve the dynamics of a flexible beam with large deformation by using the substructuring technique and the transfer matrix method. The dynamics simulation of a flexible beam with large deformation is carried out by using the proposed approach and the results are verified by comparing with those obtained from Abaqus software.

Spacecraft Dynamic Characteristics While Deploying Flexible Beams

The attitude dynamic equations of a spacecraft while deploying two flexible beams and the beam equations were developed from momentum theory. The dynamic equations were solved numerically using the Runge-Kutta method to calculate the vibration amplitudes of the flexible beams and the attitude angular velocity. The results show that the vibration amplitudes increase as the beam length increases or as the initial attitude angular velocity increases. The results also show that the vibration amplitudes decrease as the deployment velocity increases.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

Delayed feedback control experiments on some flexible structures

In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward.

NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

The nonlinear dynamic equations of a multibody system composed of ?exible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation e?ect is employed and its deformation ?eld is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and e?ciency of the method proposed.

Robust distributed controller design of rotational single-link smart materials beam

A dynamic modelling and controller design were presented for a single-link smart materials beam, a flexible beam bonded with piezoelectric actuators and sensors for better control performance. Taking into account bounded disturbances, a robust distributed controller was constructed based on the system model, which was described by a set of partial differential equations (PDEs) and boundary conditions (BCs) . Subsequently, a finite dimensional controller was further developed, and it was proven that this controller can stabilize the finite dimensional model with arbitrary number of flexible modes. Keywords Dynamic modelling - Robust distributed controller - Flexible beam - Smart material

Nonlinear Dynamic Analysis of Three Dimensional Flexible Multibody Systems

The nonlinear dynamic problems of three dimensional flexible multibody systems are investigated. The elastic deformation fields of flexible space beams are decomposed into axial deformation and bending deformation, and described by each exact vibration modes in the body coordinate systems. The constrainted nonlinear dynamic equations are derived by using Lagrange multiplier method. A numerical procedure for solving the resulting differential algebraic equations is presented based on Newmark direct integration method combined with the modified Newton-Raphson iterative method. Numerical results verify the effectiveness of the proposed method.

Real-time Design Constraints in Implementing Active Vibration Control Algorithms

Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control （AVC） algorithm for a flexible beam system simulated using the finite difference （FD） method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments.

Stability of Nonlinear Vibrations of a Deploying Flexible Beam

A rigid flexible coupled system which consists of a central rigid body deploying a flexible appendage is considered. The appendage is modeled as a finite deflection beam having linear constitutive equations. By taking the energy integral as Lyapunov function, it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam, according to the partial stable theorem.

VIBRATION SUPPRESSION OF A FLEXIBLE PIEZOELECTRIC BEAM USING BP NEURAL NETWORK CONTROLLER

This paper aims at modeling and developing vibration control methods for a flexible piezoelectric beam. A collocated sensor/actuator placement is used. Finite element analysis （FEA） method is adopted to derive the dynamics model of the system. A back propagation neural network （BPNN） based proportional-derivative （PD） algorithm is applied to suppress the vibration. Simulation and experiments are conducted using the FEA model and BPNN-PD control law. Experimental results show good agreement with the simulation results using finite element modeling and the neural network control algorithm.

Flexible and high-efficiency generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere

We propose theoretically and verify experimentally a compact optical configuration to directly generate arbitrary vector vortex beams on a hybrid-order Poincare sphere with good flexibility and high efficiency based on a reflective phase-only liquid crystal spatial light modulator （LC-SLM）. The conversion system, consisting of an LC-SLM and a quarter-wave plate, can be considered a flexible dielectric metasurface to simultaneously modulate inhomogeneous polarization and helical phase-front. This approach has some advantages, including a simple experimental setup, good flexibility, and high efficiency. superposition existing in the conventional method are potential applications in many advanced domains. Orthogonally polarized modes alignment and an explicit not necessary in the proposed method, which exhibits