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.

Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with Euler-Bernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.

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.

Structural Dynamic Optimization for Flexible Beam of Helicopter Rotor Based on GA

As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexible beam should satisfy both the strength and dynamic requirements.However,traditional optimization research focused only on either the strength or dynamical characteristics.To sufficiently improve the performance of the flexible beam,both aspects must be considered.This paper proposes a two-stage optimization method based on the Hamilton variational principle:Variational asymptotic beam section analysis(VABS)program and genetic algorithm(GA).Consequently,a two-part analysis model based on the Hamilton variational principle and VABS is established to calculate section characteristics and structural dynamics characteristics,respectively.Subsequently,the two parts are combined to establish a two-stage optimization process and search with GA to obtain the best dynamic characteristics combinations.Based on the primary optimization results,the section characteristics of the flexible beam are further optimized using GA.The optimization results show that the torsional stiffness decreases by 36.1%compared with the full 0°laying scheme without optimization and the dynamic requirements are achieved.The natural frequencies of flapping and torsion meet the requirements(0.5 away from the passing frequencies of the blade,0.25 away from the excitation force frequency,and the flapping and torsion frequencies keep a corresponding distance).The results indicate that the optimization method can significantly improve the performance of the flexible beam.

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.

FULMS algorithm based multi channel active vibration control of piezoelectric flexible beam

A multi-channel active vibration controller based on a filtered-u least mean square （FULMS） control algorithm is analyzed and implemented to solve the problem that the vibration feedback may affect the measuring of the reference signal of the filtered-x least mean square （FXLMS） algorithm in the field of active vibration control. By analyzing the multi-channel FULMS algorithm, the multi-channel controller structure diagram is given, while by analyzing multi-channel FXLMS algorithm and its algorithmic procedure, the control channel model identification strategy is given. This paper also provides an easy but practical way to configure the actuators based on the maximal modal force rule. Taking the configured piezoelectric beam as the research object, an active vibration control experimental platform is established to verify the effectiveness of the identification strategy as well as the FULMS control scheme. Simulation and actual control experiments are done after the model parameters are obtained. Both the simulation and actual experiment results show that the designed multi-channel vibration controller has a good control performance with low order model and rapid convergence.

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.

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.

Large Deflection Dynamic Response Analysis of Flexible Hull Beams by the Multibody System Method

In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.

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.

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.

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.

Active Control of Initial Disturbances for Rockets and Missiles

The active control theory and methods of initial disturbances for rockets and missiles are investigated. The rocket or missile/launcher is simplified as a flexible beam excited by a moving varying velocity rigid body which has two points in contact with the beam. The control force is applied at the supporting point on the beam. Active control strategies based on optimal control theory are proposed and computer simulation is carried out. Simulation results are consistent with the theoretical results, and show that the active control strategies proposed can accomplish the purpose to control the initial disturbances actively. The results show that active control of initial disturbances for rockets and missiles is feasible for application.

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.

Efficient Mesh Updating Scheme for the ALE Corotational Formulation of an Arbitrarily Curved Beam

This paper presents an efficient mesh updating scheme(MUS)for the arbitrary Lagrangian-Eulerian(ALE)formulation of an arbitrarily curved beam based on the corotational method.By discretizing the beam using both Lagrangian elements and ALE elements,the proposed MUS can take full advantage of the simple expression form of the Lagrangian formulation and the accurate moving-load description of the ALE node.The deleting-node and adding-node procedures of the MUS can avoid the negative influence of the variation of the ALE element length on the element accuracy and stiffness matrix singularity.In contrast to the adding-node procedure for Lagrangian elements,interpolation cannot be used directly.Inserting a Lagrangian node in an ALE element is investigated,and the displacement,velocity,and acceleration of the newly added node are evaluated accurately based on the corotational method.Three examples are investigated to verify the validity,computational accuracy and computational efficiency of the proposed MUS by comparing the results of the MUS with those from literature that utilized traditional ALE formulation.These examples show that the proposed MUS has significant advantages in terms of computational time and computer memory.