Vibration Of Flexible System Research Articles

Numerical Investigation on Vibration Performance of Flexible Plates Actuated by Pneumatic Artificial Muscle

This paper theoretically introduced the feasibility of changing the vibration characteristics of flexible plates by using bio-inspired, extremely light, and powerful Pneumatic Artificial Muscle (PAM) actuators. Many structural plates or shells are typically flexible and show high vibration sensitivity. For this reason, this paper provides a way to achieve active vibration control for suppressing the oscillations of these structures to meet strict stability, safety, and comfort requirements. The dynamic behaviors of the designed plates are modeled by using the finite element (FE) method. As is known, the output force vs. contraction curve of PAM is nonlinear generally. In this present finite element model, the maximum forces provided by PAM in different air pressure are adopted as controlling forces for applying for the plate. The non-linearity between the output force and displacement of PAM is avoided in this study. The dynamic behaviors of plates with several independent groups of controlling forces are observed and studied. The results show that the natural frequencies of the plate can be varying and the max amplitude decreases significantly if the controlling forces are applied. The present work also demonstrates the potential of the PAM actuators as valid means for damping out the vibration of flexible systems.

FEA based discrete-time sliding mode control of uncertain continuum mechanics MIMO vibrational systems

In this paper, a novel method for control of uncertain MIMO flexible systems is proposed. The control system is constructed such that it is capable of stabilizing a flexible dynamical system based on rigid approximation of continuum dynamics, resulting in facilitation of modeling and control procedures for complicated vibrational systems. In order to ensure system stability in real-time applications, the control system is obtained in discrete-time basis. To these ends, a sliding hyper-plane based sliding mode control (SMC) algorithm is constructed featuring sliding functions for individual subsystems. An approximated dummy model of the real system is used alongside the dynamical system in order to estimate parametric and unstructured uncertainties which are evaluated through comparisons between the dummy model, data obtained from the real system and corresponding mathematical model. Conventional SMC techniques introduce undesired effects of chattering which result in amplifying vibrations in flexible systems. To address this issue, an alternate algorithm based on selection of control signals within appropriate bounds is used in order to eliminate chattering and provide superior performance in comparison with conventional SMC techniques. The accuracy of proposed method has been verified through ANSYS® mechanical APDL-based simulations and its effectiveness has been verified in multiple operating conditions.

An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

One method used to reduce or eliminate residual vibrations is to modify the input signal by using previously determined system parameters. In order to eliminate the residual vibration completely, these system parameters must be very accurately determined. In real systems, achieving such accuracy may not always be possible. To address this problem and to provide a solution, a new residual vibration elimination method is introduced in this study, which has proven to be useful especially in cases of uncertain parameters of estimated or predicted systems. It is shown that the technique is capable of handling high levels of uncertainty and is able to successfully eliminate or reduce residual vibrations in flexible systems. In this approach, the desired position of the system is primarily divided into two equal parts, and the generated input signal is used to eliminate vibration. This study presents theoretical and experimental results of the techniques applied to a flexible mechanical system; a comparative study of robustness performance is also provided. Simulation and experimental results show that the oscillations are considerably decreased with a high degree of robustness in the presence of uncertainty regarding system parameters.

Design of Multi-Stage Optimal Arbitrary Time-Delay Filter

Input shaping is an effective method for suppressing residual vibration of flexible system. In this paper, the design processes of Zero Vibration (ZV), Zero Vibration and Derivative (ZVD) shapers are deduced. Based on the idea of the robustness input shaper, the Multi-stage Optimal Arbitrary Time-delay Filter (MOATF) is proposed. The proposed control method is implemented on the second-order linear time-invariant system. Simulation results show that the residual vibration can be reduced effectively and the proposed method have great robustness in system parameter uncertainty.

Using continuous function to generate shaped command for vibration reduction

This article describes a continuous function for limiting vibration in flexible systems by convolving the original command to the system. Unlike previous command shaping strategies, a continuous function shapes the original command to suppress vibration. The effectiveness of this method for robustness is explored and quantified. The theoretic analysis shows that this method has more insensitivity at higher frequencies. However, the robust input shaper gets more insensitive at lower frequencies. Experimental results for a planar bridge crane validate the simulated dynamic behavior and the effectiveness of the continuous function.

Vibration reduction for flexible systems by command smoothing

A method is presented for limiting vibration in flexible systems by smoothing the original command. The original command is smoothed to drive the flexible systems without inducing vibration. The proposed smoother is designed as a function of system natural frequency and damping ratio. The comparison between the new method and the zero vibration and triple derivative (ZVDDD) shaper for modeling error is explored and quantified. The theoretic analysis shows that the new method is more insensitive at higher frequencies, while the ZVDDD shaper has more insensitivity at lower frequencies. Moreover, the designed smoother benefits vibration reduction for multi-mode systems. Experimental results for single-mode and multi-mode systems validate the simulated dynamic behavior and the effectiveness of the new method.

Comparison of Polynomial Cam Profiles and Input Shaping for Driving Flexible Systems

Polynomial profiles can be used as reference commands to limit induced vibration in flexible systems. Due to their ease of design and low-pass filtering effects, polynomial profiles are often found in cam-follower systems. Polynomial profiles have also been used as smooth reference commands for automated machines. However, despite extensive work to develop and improve such profiles, inherent tradeoffs still exist between induced vibration, rise time, and ease of design. Input shaping is an alternative method for generating motion commands that reduce residual vibration. This paper compares polynomial profiles to input-shaped commands for the application of reducing vibration in flexible systems. Analyses using Laplace transforms reveal that input shapers suppress vibration at regularly spaced frequencies. However, polynomial profiles do not share this property. Simulations and experimental results show that input shaping improves rise time and reduces residual vibration in comparison to polynomial profiles.

A multi-modal control using a hybrid pole-placement-integral resonant controller (PPIR) with experimental investigations

Control of multi-modal structural vibrations has been an important and challenging problem in flexible structural systems. This paper proposes a new vibration control algorithm for multi-modal structural control. The proposed algorithm combines a pole-placement controller with an integral resonant controller. The pole-placement controller is used to achieve a target equivalent modal viscous damping in the system and helps in the suppression of higher modes, which contribute to the vibration response of flexible structures. The integral resonant controller successfully reduces the low frequency vibrations e.g. caused by broad-band turbulent wind excitations. Hence, the proposed hybrid controller can effectively suppress complex multi-modal vibrations in flexible systems. Both numerical and experimental studies have been carried out to demonstrate the effectiveness of the proposed algorithm using a limited number of sensors/actuators. Copyright © 2009 John Wiley & Sons, Ltd.

Designing unity magnitude input shaping by using PWM technique

This paper proposes a method for reducing vibrations in flexible systems by using the input shaping. A new input shaper technique based on Pulse Width Modulation (PWM) is used to shape the input. Since unity magnitude (UM) input shaping is easy to implement and provides less control duration, it has been preferred for many application areas. An analytical solution to time locations of the UM shaper requires very complex mathematical expressions due to involving in dependent constraint equations. This paper presents a simple PWM based input shaping method. The proposed technique allows designing UM shapers without analytical solution especially for the shapers having higher order impulse sequence. The method requires only the estimated value of system natural frequency and damping ratio. Desired numbers of impulses can be obtained by comparing reference signal amplitude and carrier wave frequency of a PWM. Analysis and experimental results demonstrate the effectiveness of the proposed method.

Simultaneous estimation of two bending vibration frequencies for attitude control of a flexible launch vehicle

Current developments in the aerospace flight devices have led to a control system being designed in the presence of elastic behaviour. However, there are several ways to reduce the destructive effects of vibration in flexible systems. In this paper, a practical approach called ‘rigid model reference’ is extended to two vibration modes based on the gradient method. Furthermore, the existence of two dominant bending vibration modes in the output of measurement devices leads to a redesign of the control system. Robust stability of the new algorithm is investigated by using Kharitonov theorem. Simulation results illustrate considerable reduction of vibration effects on the output of measurement system considering the first and the second bending vibration modes.

Estimation Based PID controller-Sensorless Wave Based Technique

AbstractThis paper presents a sensorless estimation algorithm for estimating flexible system parameters, dynamics and externally applied forces or torques due to system interaction with the environment. The proposed algorithm makes it possible to design a chain of observers that require measuring actuator's current and velocity along with performing two off-line experiments that do not require any additional measurement from the flexible system. The output of these observers are estimates of the system parameters, estimates of the system dynamics in configuration, motion and acceleration level. Eventually, the estimated positions are used to control the motion and vibration of the flexible lumped system without taking any measurement from the system. Experimental results show the validity of the proposed sensorless estimation algorithm and the possibility of controlling motion and vibration of flexible systems by focusing all the measurements on the actuator side keeping the system free from any attached sensors.

大型柔軟ロボットアームの操作時振動抑制実験

In flexible long arm operation, residual vibration due to excitation degrades working efficiency. Input Shaping method decreases residual vibration in flexible systems by filtering the reference command with sequence of impulses known as input shaper. The principle of Input Shaping is very simple, but it is necessary to consider implementation hardware, especially in the space system. In this paper, ground experimental setup of an 8m long space robotic arm is constructed, and the effect on vibration suppression using Input Shaping is considered. The results of the ground experiment are discussed.

Robust Residual Vibration Suppression Using IIR Digital Filters

A method for suppressing residual vibrations in flexible systems is presented and experimentally demonstrated. This method is based on the preconditioning of the inputs to the system using Infinite Impulse Response (IIR) digital filters. The proposed method is robust to variations of the system dynamic parameters and simple to implement in practice. The method is experimentally verified using a flexible aluminum beam.

Maximally Robust Input Preconditioning for Residual Vibration Suppression Using Low-Pass FIR Digital Filters

A method for suppressing residual vibrations in flexible systems is presented and experimentally demonstrated. The proposed method is based on the preconditioning of the inputs to the system using low-pass Finite Impulse Response (FIR) digital filters. Provided that the cutoff frequency of FIR filters is selected lower than the lowest expected natural frequency of the system and their stop-band is maximized, we show that these filters can be designed to exhibit maximally robust behavior with respect to changes of the system natural frequencies. To perform the proper design of FIR filters for robust vibration suppression, this paper introduces a series of dimensionless performance indexes and the Delay-Error-Order (DEO) curves that represent graphically the delay time introduced by the filter as a function of the remaining residual vibrations, and the filter order. Several classes of FIR filters such as: a) Parks-McClellan; b) Window-based methods (using Chebyshev window); and c) Constrained Least Squares method, are shown to present maximally robust behavior, almost identical to the theoretically predicted. Parallel, they demonstrate excellent vibration suppression while they introduce the minimum possible delay. Further advantages offered by the proposed method, is that no modeling of the flexible system is required, the method can be used in a variety of systems exhibiting vibrations, it is independent of the guidance function and it is simple to implement in practical applications. The results are experimentally verified on a flexible aluminum beam with a significantly varying mass, attached to the end-effector of a robot manipulator. The beam is rotated, using one joint of the manipulator, from an initial to a final position. It is shown that the preconditioned inputs to the flexible system induce very little amount of residual vibrations compared to the inputs with no preconditioning.

Optimal control of vibration suppression in flexible systems via dislocated sensor/actuator positioning

In this study, we present a new controller design method that not only effectively suppresses vibration in flexible systems, but also has the ability to save control energy. The proposed method allows integrated determination of sensor/actuator location and feedback gain by minimizing the sum of the integral flexible system energy and the integral control energy. Also, the cost function is characterized by an effective representation of control systems, and is determined via an efficient solution of the Lyapunov equation. The optimization problem is solved by a recursive quadratic programming algorithm. The feasibility of applying this method to a simple and flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression.

Vibration reduction in flexible systems using a time-varying impulse sequence

SummaryAn input shaping technique using a time-varying impulse sequence is presented to reduce the motion-induced vibration of flexible systems in a feedforward way.The decoupled modal responses for a general linear time-varying system are firstly approximated. Upon this approximation, the time-varying impulse sequences to suppress the vibrational modes are found. The reference inputs to the systems are shaped by convolving with the time-varying impulse sequence to suppress the multimode vibrations. This technique can be also applied to suppress the vibration of nonlinear time-varying systems.The performance of this method is demonstrated with two practical examples: a moving overhead crane and a two-link robot manipulator. Consequently, this study provides an input shaping technique applicable to the vibration suppression of broader classes of flexible systems.

Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs

This paper describes a method for limiting vibration in flexible systems by shaping the input to the system. Unlike most previous input shaping strategies, this method does not require a precise system model or lengthy numerical computation; only estimates of the system natural frequency and damping ratio are required. The effectiveness of this method when there are errors in the system model is explored and quantified. Next, an algorithm is presented, which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimate of the natural frequency. Finally, performance predictions are compared to hardware experiments.

Effective Active Damping Design for Suppression of Vibration in Flexible Systems via Dislocated Sensor/Actuator Positioning

In this paper we present a new controller design method that effectively suppresses vibration in flexible systems. The method allows integrated determination of sensor/actuator locations and feedback gain via minimization of an energy criterion which represents the integrated total energy stored in the system. This energy criterion is characterized by an effective representation of vibration, determined via an efficient solution of the Lyapunov equation and minimized with a quasi-Newton or recursive quadratic programming algorithm. The application of this method to a simple flexible structure confirms the direct relationship between our optimization criterion and effectiveness of vibration suppression.

Shaped Input Control of a System With Multiple Modes

This paper describes a method for limiting vibration in flexible systems that have more than one characteristic frequency and mode. It is only necessary to have knowledge of the component mode frequencies and damping ratios in order to be able to calculate the timing and magnitudes of the impulse sequence used in the shaping. Only two impulses, in the nonrobust case, or three impulses in a more robust case, are necessary regardless of the number of component frequencies. Simple tests are established to determine when this technique can be used and examples are presented.

Active vibration control of flexible beams using shape memory actuators

This paper demonstrates, theoretically and experimentally, the feasibility of utilizing Shape Memory Actuators (SMA) in controlling the flexural vibrations of a flexible cantilevered beam. The beam dynamics are modeled, by using the finite element method, and integrated with the thermal and dynamic characteristics of the SMA to develop a mathematical model of the composite beam-actuators system. The model accounts for the effect of the actuators' physical and geometrical parameters on the elastic and the inertial properties of the beam-actuators system. An active computer-controlled prototype of the system is designed based on the mathematical model developed. The performance of the control system is evaluated, at different operating conditions, when the beam is subjected to step displacements. The results obtained demonstrate the potential of the SMA as viable means for damping out the vibration of flexible systems.