Vibration Of Flexible Link Research Articles

A novel combined control of flexible single-link manipulator based on singularly perturbed theory

PurposeThis study aims to improve the control accuracy and antidisturbance performance of the manipulator with the flexible link, a combined controller, which combines the novel backstepping sliding mode controller based on the extended state observer (ESO) and super-twisting sliding mode controller.Design/methodology/approachFirst, the dynamic of the system is constructed by Lagrange method and assumed mode method, and then the dynamic is decoupled by the singular perturbation theory to obtain the slow-varying subsystem and fast-varying subsystem. For the slow-varying subsystem, the novel backstepping sliding mode controller based on ESO is used to achieve joint tracking. For the fast-varying subsystem, the super-twisting sliding mode controller is used for vibration suppression. At the same time, to suppress chattering, the tanh function is used to replace the sign function in the reaching law.FindingsThe simulation results show that the combined control has better trajectory tracking performance, antiinterference performance and vibration suppression performance than traditional sliding mode control (SMC).Originality/valueA novel backstepping sliding mode controller based on ESO is designed to guarantee the performance of the tracking trajectory. The new controller improves the converge rate. A super-twisting sliding mode controller, which can stabilize the fast-varying subsystem, is used to suppress the vibration of flexible link.

Visual Servoing of Flexible-Link Manipulators by Considering Vibration Suppression Without Deformation Measurements.

Visual servoing and vibration suppression of spatial flexible-link manipulators with a fixed camera setup are addressed in this article. The singular perturbation method is adopted to decouple the dynamic equations of the flexible manipulator; hence, two subsystems that represent the rigid robot motion and flexible-link vibration are obtained, respectively. Then, for the slow subsystem related to the rigid motion, an image-based controller is designed to converge the image errors with the consideration of compensating for the errors of approximating the Jacobian matrix. For the fast subsystem corresponding to the elastic vibration, to eliminate the requirements of measuring the vibration states, an observer is designed to estimate the fast states and then a feedback controller of the fast subsystem is presented to suppress the vibration of the flexible manipulator by using the estimation values. The closed-loop stabilities of the slow and fast subsystem are both proved by employing the Lyapunov theory. Numerical simulations demonstrate the effectiveness of the proposed controller, which shows that the image errors approach zero with the vibration of the flexible manipulator damped out simultaneously.

Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network

In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.

Finite-time tracking control and vibration suppression based on the concept of virtual control force for flexible two-link space robot

The dynamic modeling, finite-time trajectory tracking control and vibration suppression of a flexible two-link space robot are studied. Firstly, the dynamic model of the system is established by combining Lagrange method with assumed mode method. In order to ensure that the base attitude and the joints of space robot can reach the desired positions within a limited time, a non-singular fast terminal sliding mode (NFTSM) controller is designed, which realizes the finite-time convergence of the trajectory tracking errors. Subsequently, for the sake of suppressing the vibrations of flexible links, a hybrid trajectory based on the concept of the virtual control force is developed, which can reflect the flexible modes and the trajectory tracking errors simultaneously. By modifying the original control scheme, a NFTSM hybrid controller is proposed. The hybrid control scheme can not only realized attitude stabilization and trajectory tracking of joints in finite time, but also provide a new method of vibration suppression. The simulation results verify the effectiveness of the designed hybrid control strategy.

Experimental Study of Active Vibration Control of Planar 3-RRR Flexible Parallel Robots Mechanism

An active vibration control experiment of planar 3-RRR flexible parallel robots is implemented in this paper. Considering the direct and inverse piezoelectric effect of PZT material, a general motion equation is established. A strain rate feedback controller is designed based on the established general motion equation. Four control schemes are designed in this experiment: three passive flexible links are controlled at the same time, only passive flexible link 1 is controlled, only passive flexible link 2 is controlled, and only passive flexible link 3 is controlled. The experimental results show that only one flexible link controlled scheme suppresses elastic vibration and cannot suppress the elastic vibration of the other flexible links, whereas when three passive flexible links are controlled at the same time, they are able to effectively suppress the elastic vibration of all of the flexible links. In general, the experiment verifies that a strain rate feedback controller is able to effectively suppress the elastic vibration of the flexible links of plane 3-RRR flexible parallel robots.

Singular perturbation adaptive control and vibration suppression of free-flying flexible space manipulators

Singular perturbation adaptive control is designed for free-flying space manipulators with multiple flexible links and unknown physical parameters. The dynamical Lagrange equation was established based on assumed mode technique and linear momentum conservation theory. A singular perturbation model has been formulated and used for designing a reduced-order controller. This controller consisted of a slow control component and a fast control component. An adaptive control law was constructed for the slow counterpart of the flexible manipulator. The flexible-link fast subsystem controller would damp out the vibrations of flexible links by optimal linear quadratic regulator method. Numerical simulations by undertaking a computer simulation of a two-flexible-link space manipulator using the fourth-order Runge–Kutta integration method showed that the link vibrations had been stabilized effectively with good tracking performance.

A Simple Compound Control Method for Flexible-link Manipulator

This paper presents a composite control scheme based on singular perturbation theory, which decouples the system of flexible-link manipulator into rigid motion (slow subsystem) and flexible vibration (fast subsystem) two different time scale subsystems. For the slow subsystem, a controller combined computer torque method and robust control is employed to track the desired trajectory, while, a state feedback control is used to stabilize the fast subsystem to suppress the vibration. The simulation results show that the proposed control strategy has good tracking performance and suppress the flexible-link vibration effectively. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.3515 Full Text: PDF

Motion Planning for Vibration Reducing of Free-floating Redundant Manipulators Based on Hybrid Optimization Approach

This paper is concerned with optimal motion planning for vibration reducing of free-floating flexible redundant manipulators. Firstly, dynamic model of the system is established based on Lagrange method, and the motion planning model for vibration reducing is proposed. Secondly, a hybrid optimization approach employing Gauss pseudospectral method (GPM) and direct shooting method (DSM), is proposed to solve the motion planning problem. In this approach, the motion planning problem is transformed into a non-linear parameter optimization problem using GPM, and genetic algorithm (GA) is employed to locate the approximate solution. Subsequently, an optimization model is formulated based on DSM, and sequential quadratic programming (SQP) algorithm is used to obtain the accurate solution, with the approximate solution as an initial reference solution. Finally, several numerical simulations are investigated, and the global vibration or residual vibration of flexible link is obviously reduced by the joint trajectory which is obtained by the hybrid optimization approach. The numerical simulation results indicate that the approach is effective and stable to the motion planning problem of vibration reducing.

RBFNN CONTROL OF A TWO-LINK FLEXIBLE MANIPULATOR INCORPORATING PAYLOAD

This paper presents the dynamic modeling and control of a two-link flexible robot manipulator. A dynamic model of the system is developed using a combined Euler-Lagrange and assumed mode methods. The most problems of a two-link flexible manipulator are vibration of flexible link and unpredictable payload additional. Previous researchers have discussed control methods for this system; few presented the effect of a payload profile. The s imulation in this research is performed to assess the dynamic model and system responses at the hub and end-point of both links are presented and analyzed in time domains and show the advantages using radial basis function neural network (RBFNN) controller for solving flexible link vibration, achieve high-precision position tracking, and payload effect robustness. The results achieved by the proposed controller are compared with conventional PID to substantiate and verify the advantages the proposed scheme and its promising potential in control of a two-link flexible manipulator. It is shown that smaller overshoot, quickly steady state response and tracking performance of the proposed controller is good profile and better than PID controllers.

MULTI-MODE VIBRATION CONTROL AND POSITION ERROR ANALYSIS OF PARALLEL MANIPULATOR WITH MULTIPLE FLEXIBLE LINKS

This paper presents multi-mode vibration control and analysis of moving platform position errors of a planar 3-PRR parallel manipulator with three flexible intermediate links using PZT transducers. The active vibration controller is designed in modal space with modal filters and modal synthesizers determined from the flexible link vibration characteristics. Estimation of the moving platform position error is conducted using measurements of the flexible link deflection from PZT sensors mounted on the flexible intermediate links. An effective strategy for determining the control gains to reduce the vibrations of higher order modes is proposed through modification of the independent modal space control (IMSC) method. The proposed independent modal control strategy is experimentally implemented with first two modes targeted for control on a parallel manipulator with multiple flexible links. The experimental results show that the vibrations of the first two modes are effectively suppressed, and the position error of the moving platform is substantially reduced.

Vibration Control of Nonholonomically Redundant Flexible Manipulators

Underactuated flexible manipulator with redundant degrees of freedoms is investigated. Position control method of a single active joint driving the passive joint is given. According to the characteristics of nonholonomiclly redundant flexible manipulators, the optimal control strategy of multiple active joints driving the passive joints is proposed. As the elastic vibration of flexible links can not be eliminated only through position control, the vibration control schemes are presented again. The simulation results show that the elastic vibration is suppressed effectively. Therefore, for nonholonomically redundant flexible manipulator, both position control and vibration control are implemented successfully, which verifies the validity of the control schemes.

Flexible linkage structural vibration control on a 3-PRR planar parallel manipulator: Experimental results

Piezoelectric actuators and sensors have been used for vibration control of flexible manipulators and mechanisms since the 1990s. However, very few attempts have been made toward experimental investigations compared with numerical simulations, especially for mechanisms and manipulators with multiple flexible links. This paper presents an experimental study on active vibration control of a moving 3-PRR parallel manipulator with three flexible intermediate links with bonded lead zirconate titanate (PZT) actuators and sensors. First, experimental modal tests are conducted with an impulse force hammer and an accelerometer to identify structural vibration mode shapes and natural frequencies of the flexible manipulator. These modal test results are used to provide guidance for the determination of the location of PZT transducers and the design of an active vibration controller. Then, a strain rate feedback (SRF) controller is designed in modal space. A state-space model is formulated with the control input voltage applied to PZT actuators, and output generated voltage from PZT sensors. The design of an optimal active vibration controller is addressed based on SRF. Furthermore, to suppress the noise introduced through the differentiation of the strain signal, a second-order auxiliary compensator is introduced to the SRF controller. The design of the SRF controller and the noise attenuation compensator is addressed utilizing vibration theories. Finally, active vibration control experiments are implemented to demonstrate that the proposed active vibration control strategy is effective. Power spectral density plots of vibrations illustrate that the structural vibration of flexible links is suppressed effectively when the proposed SRF vibration control strategy is employed.

Vibration control of elastodynamic response of a 3-PRR flexible parallel manipulator using PZT transducers

SUMMARYThis paper addresses the dynamic simulation and control of structural vibrations of a 3-PRR parallel manipulator with three flexible intermediate links, to which are bonded lead zirconate titanate (PZT) actuators and sensors. Flexible intermediate links are modelled as Euler–Bernoulli beams with pinned-pinned boundary conditions. A PZT actuator controller is designed based on strain rate feedback (SRF) control. Control moments from PZT actuators are transformed to force vectors in modal space and are incorporated in the dynamic model of the manipulator. The dynamic equations are developed based on the assumed mode method for the flexible parallel manipulator with multiple PZT actuator and sensor patches. Numerical simulation is performed and the results indicate that the proposed active vibration control strategy is effective. Spectral analyses of structural vibrations further illustrate that deformations from structural vibration of flexible links are suppressed to a significant extent when the proposed vibration control strategy is employed, while the deflections caused by inertial and coupling forces are not reduced.

On the modeling and composite control of flexible parallel mechanism

One of the key problems in high speed motion control of a flexible parallel mechanism (PM) is to damp out the mechanical vibration arising from high inertial force acting on the linkages and other components. In this paper, the dynamic equations of a 2 degree-of-freedom (DOF) planar PM with flexible links are established by taking the singular perturbation approach (SPA). Thus the model of the mechanism can be separated into slow time-scale and fast time-scale subsystems. Based on the feedback linearization theory and input shaping technique, the large range rigid motion controller and the flexible link vibration controller can be designed separately. A composite control with the two separate controllers can then be applied in the PM to achieve the desired fast and accurate positioning.

Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

Constrained Motion Control of Flexible Robot Manipulators Based on Recurrent Neural Networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.

Direct tip regulation of a single-link flexible manipulator by adaptive variable structure control

Direct tip position regulation of flexible manipulators is one of the most challenging control tasks. There are mainly three problems to be addressed in order to achieve good performance. The first two control problems arise owing to the unstable zeros and complex poles in the system nominal part which is dominated by a transfer function. The third problem is the existence of unstructured uncertainties owing to the truncation of high-order resonance modes and system nonlinearities. Because of the above difficulties and in particular the non-minimum-phase nature, tip regulation task of flexible manipulators is usually solved indirectly: direct control of joint angle and suppression of the flexible link vibration. The aim of this study is to investigate the direct approach for tip regulation. Since the tip transfer function contains unstable zeros and the first few dominant flexible modes (complex poles), a reference model of the same order is selected which does not have any finite zero but all negative re...

Direct tip regulation of a single-link flexible manipulator by adaptive variable structure control

Direct tip position regulation of flexible manipulators is one of the most challenging control tasks. There are mainly three problems to be addressed in order to achieve good performance. The first two control problems arise owing to the unstable zeros and complex poles in the system nominal part which is dominated by a transfer function. The third problem is the existence of unstructured uncertainties owing to the truncation of high-order resonance modes and system nonlinearities. Because of the above difficulties and in particular the non-minimum-phase nature, tip regulation task of flexible manipulators is usually solved indirectly: direct control of joint angle and suppression of the flexible link vibration. The aim of this study is to investigate the direct approach for tip regulation. Since the tip transfer function contains unstable zeros and the first few dominant flexible modes (complex poles), a reference model of the same order is selected which does not have any finite zero but all negative real poles. In order to force the system to follow the reference model in the presence of the unstructured uncertainties, a variable structure controller is adopted in which the switching surface is derived from the reference model. When in sliding mode, the system performs as the reference model. Hence there will be no vibration and the tip position regulation can be achieved when the system approaches steady state. To improve the system responses further, an adaptation law with dead-zone scheme is combined with the variable structure controller. Simulation results show that link vibrations have been eliminated and the control profile is fairly smooth.

Dynamics of systems with changing configuration and with flexible beam-like links

Dynamic analysis of spatial systems, in which reciprocal influence of base motion and vibrations of flexible links are taken into account, is the subject of the paper. The mathematical model of a beam-like link with bending and torsional flexibility is presented. The model has been obtained using the rigid finite element method. Formulae and computer programmes obtained have been indirectly verified by comparison of results of different methods. Experimental verification has also been carried out.

A computed torque/time delay approach to the end-point control of a one-link flexible manipulator

The problem of modelling end point control of a one-linkflexible manipulator has been considered. The assumed mode methodas well as the Lagrangian dynamics are used to develop the dynamicmodel. It has been shown that a conventional computed torquecontroller cannot deal with the end point vibrations of flexiblelinks. The non-minimum phase characteristic of the end pointcontrol of a one link flexible manipulator has been demonstratedby choosing the absolute angle of a point along the link as thecontrolled output. In order to introduce active damping intothe system, a computed torque/delayed deflection approach hasbeen proposed. In this approach, the actuator torque is computedfrom the joint angle and a delayed deflection of a point alongthe link. The choice of the delay time depends on the point atwhich the deflection is measured. Simulation results are presentedto demonstrate the effectiveness of the proposed controller.