Vibration Suppression Of Flexible Structures Research Articles

Vibration suppression for large-scale flexible structures based on cable-driven parallel robots

Specific satellites with ultralong wings play a crucial role in many fields. However, external disturbance and self-rotation could result in undesired vibrations of the flexible wings, which affect the normal operation of the satellites. In severe cases, the satellites would be damaged. Therefore, it is imperative to conduct vibration suppression for these flexible structures. Utilizing fuzzy-proportional integral derivative control and deep reinforcement learning (DRL), two active control methods are proposed in this article to rapidly suppress the vibration of flexible structures with quite small controllable force based on a cable-driven parallel robot. Inspired by the output law of DRL, a new control method named Tang and Sun control is innovatively presented based on the Lyapunov theory. To verify the effectiveness of these three control methods, three groups of simulations with different initial disturbances are implemented for each method. Besides, to enhance the contrast, a passive pretightening scheme is also tested. First, the dynamic model of the cable-driven parallel robot which comprises four cables and a flexible structure is established using the finite element method. Then, the dynamic behavior of the model under the controllable cable force is analyzed by the Newmark-ß method. Finally, these control methods are implemented by numerical simulations to evaluate their performance, and the results are satisfactory, which validates the controllers’ ability to suppress vibrations.

Recent developments in semi-active control of magnetorheological materials-based sandwich structures: A review

Magnetorheological (MR) materials are kinds of smart materials whose rheological characteristics are controllable with the application of external magnetic fields. In the last few decades, MR materials are well established as one of the leading smart materials for use in adaptive sandwich structures and systems for salient vibration control. This article reviews the semi-active vibration suppression of flexible structures with smart materials of MR fluids (MRFs) and MR elastomers (MREs). Stiffness and damping characteristics of beams, plates, panels, and shells integrating the core layer of MRFs and MREs are discussed in terms of field-dependent controllability. To keep the integrity of the knowledge, this review includes a study on free and forced vibration characteristics of sandwich structures with fully and various configurations of partial MR treatments, stability analysis of MR sandwich structures under rotating conditions and developments in identifying the optimal locations of MR sandwich structures for better vibration control are also discussed. Further, this article focuses on the role of carbon nanotubes in enhancing the field-dependent stiffness and damping properties of MR materials. A few of the most relevant research articles are reviewed and presented here briefly.

Inverse Shaper Based Active Vibration Control of Flexible Structures with a Collocated Sensor-Actuator Pair

We propose a new control design for active vibration suppression of flexible structures with a collocated sensor-actuator pair. The proposed controller is based on the inverse form of a well-known input zero vibration (ZV) shaper. The inverse ZV shaper is utilized with a serially interconnected all-pass filter. This way, the appropriate controller frequency response properties for vibration suppression of collocated flexible systems is achieved, when the controller is applied in the positive feedback path. We propose two different cost functions to optimize the parameters of the proposed controller for efficient vibration suppression. The performance of the controller is investigated in both frequency and time domains through the vibration control of a cantilever beam model with a collocated piezoelectric sensor-actuator pair. Furthermore, its performance is compared with a recently improved version of the positive position feedback controller, which is a state-of-the-art work. It is shown via the simulations that the proposed controller suppresses vibrations more efficiently.

A MIMO data driven control to suppress structural vibrations

A novel data driven control method is presented to control vibrations of active flexible structures with multiple control inputs and multiple sensing outputs. The evaluation of vibration suppression performance and a MIMO stability criterion are formulated based on the sampled frequency response data, which results in a non-convex controller design problem solved by a global optimization technique. Such method is experimentally applied on an active cantilever beam, which demonstrates the low-order data driven controllers are very competitive with a model-based mixed sensitivity controller and can achieve promising vibration suppression for flexible structures. Without requiring dynamic models, significant advantages might be expected by the proposed method when the accurate reduced-order models of space structures are not available nor handy to be obtained.

A data driven control method for structure vibration suppression

High radio-frequency space applications have motivated continuous research on vibration suppression of large space structures both in academia and industry. This paper introduces a novel data driven control method to suppress vibrations of flexible structures and experimentally validates the suppression performance. Unlike model-based control approaches, the data driven control method designs a controller directly from the input-output test data of the structure, without requiring parametric dynamics and hence free of system modeling. It utilizes the discrete frequency response via spectral analysis technique and formulates a non-convex optimization problem to obtain optimized controller parameters with a predefined controller structure. Such approach is then experimentally applied on an end-driving flexible beam-mass structure. The experiment results show that the presented method can achieve competitive disturbance rejections compared to a model-based mixed sensitivity controller under the same design criterion but with much less orders and design efforts, demonstrating the proposed data driven control is an effective approach for vibration suppression of flexible structures.

An adaptive PID-like controller for vibration suppression of piezo-actuated flexible beams

Flexible structures have been increasingly utilized in many applications because of their light-weight and low production cost. However, being flexible leads to vibration problems. Vibration suppression of flexible structures is a challenging control problem because the structures are actually infinite-dimensional systems. In this paper, an adaptive control scheme is proposed for the vibration suppression of a piezo-actuated flexible beam. The controller makes use of the configuration of the prominent proportional-integral-derivative controller and is derived using an infinite-dimensional Lyapunov method. In contrast to existing schemes, the present scheme does not require any approximated finite-dimensional model of the beam. Thus, the stability of the closed loop system is guaranteed for all vibration modes. Experimental results have illustrated the feasibility of the proposed control scheme.

Improving the vibration suppression capabilities of a magneto-rheological damper using hybrid active and semi-active control

This paper presents a new hybrid active and semi-active control method for vibration suppression in flexible structures. The method uses a combination of a semi-active device and an active control actuator situated elsewhere in the structure to suppress vibrations. The key novelty is to use the hybrid controller to enable the magneto-rheological damper to achieve a performance as close to a fully active device as possible. This is achieved by ensuring that the active actuator can assist the magneto-rheological damper in the regions where energy is required. In addition, the hybrid active and semi-active controller is designed to minimize the switching of the semi-active controller. The control framework used is the immersion and invariance control technique in combination with sliding mode control. A two degree-of-freedom system with lightly damped resonances is used as an example system. Both numerical and experimental results are generated for this system, and then compared as part of a validation study. The experimental system uses hardware-in-the-loop to simulate the effect of both the degrees-of-freedom. The results show that the concept is viable both numerically and experimentally, and improved vibration suppression results can be obtained for the magneto-rheological damper that approach the performance of an active device.

Multi positive feedback control method for active vibration suppression in flexible structures

This paper presents a novel controller for active vibration reduction in piezoelectric-actuated flexible structures. The new Multi Positive Feedback (MPF) control consists of two sections where each operates using a set of actuators. One section uses position and the other uses velocity feedback to perform real-time vibration control. The 90° phase difference between the feedbacks leads to non-zero resultant control output. This property results in a more effective operation of the available actuators. Sections of the MPF controller are designed based on the concept of the Modified Positive Position Feedback (MPPF) control approach, where the damping of the control system is increased by addition of a first-order term parallel to a second-order compensator. The controller is designed to simultaneously control single or multi resonant frequency vibrations. Due to the high influence of gain values on the control performance, H2 and H∞ norms are used to optimize these gains. For validation purposes, the controller is verified here numerically and experimentally for vibration control of a clamped–clamped beam and a cantilever at resonance. According to the results, the MPF controller has a superior performance compared to the MPPF controller, in addition to effective suppression on both vibration displacement and velocity. Using the MPF controller in multimode and by utilizing the H∞ gain optimization method, vibration displacement amplitudes were reduced to 19.4% of the uncontrolled state for the beam.

Self-powered synchronized switch damping on negative capacitance for broadband vibration suppression of flexible structures

Synchronized switch damping (SSD)techniques using piezoelectric materials have been used by different researchers for many years for the structure vibration control. In these techniques, a piezoelectric patch is bonded on or embedded into the vibrating structure and connected to or disconnected from a network of electrical components through an electronic switch, which is controlled by a digital signal processor (DSP), in synchronous with the structure motion. Recently, Self-powered SSD techniques have emerged in which the DSP is replaced by a low pass filter, thus making the whole system self-powered. The control performance of the previously used Self-powered SSD techniques heavily relied on the electrical quality factor of the shunt circuit, thus limiting their control performance as the electrical quality factor could not be increased beyond certain limit. However, in order to bypass the influence of the electrical quality factor on the control performance, a new Self-powered SSD technique has been proposed in this paper in which the inductance in the previous Self-powered SSD techniques has been replaced with a negative capacitance thus making the whole circuit capacitive without resonance. However, it is found that the voltage on the piezoelectric patch can still be inverted. In order to access the control performance of the proposed technique in comparison with the previous Self-powered SSD techniques, experiments are performed on a cantilever beam subjected to both single mode and multimode excitations. Keeping the value of negative capacitance slightly greater than the inherent capacitance of the piezoelectric patch gave the optimum damping performance. Experiments results confirmed the effectiveness of the proposed technique as compared to the previous SSD techniques.

Active vibration suppression of membrane structures and evaluation with a non-contact laser excitation vibration test

To realize a vibration suppression of flexible structures like a membrane, our research focuses on introducing smart structures technology into the membrane structure. In this study, the membrane structure is composed of a vibration control system using a flexible Polyvinylidene fluoride (PVDF) film as an actuator. A non-contact vibration test system, which uses a high power Nd: YAG pulse laser for producing an ideal impulse excitation and laser Doppler vibrometers for measuring the response on the membrane, is employed to evaluate the vibration characteristics of the smart membrane structure. To confirm the effectiveness of the proposed method, using a flexible PVDF actuator installed on the membrane structure, control experiments with H ∞ control for reducing single mode and multiple modes vibration are conducted. In the results of the control experiments for single mode vibration suppression, a corresponding resonance peak is reduced by around 20 dB. In case of multiple modes vibration suppression, the first and second resonance peaks are reduced by 14 dB and 24 dB, respectively. This study demonstrates that the present control method using a flexible piezoelectric element and a non-contact vibration test system effectively suppress and evaluate the vibration responses of smart membrane structures.

Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures

A new controller is introduced in this paper as a novel method for active vibration suppression in flexible structures. The hybrid positive feedback (HPF) uses a second- and a first-order compensator that are fed by the displacement and velocity feedbacks, respectively. Parallel pairs of the HPF controller are implemented when suppression in multimode condition is issued. Since the controller uses two gains for each pair of the actuator/sensor patch for each mode, a suitable gain optimization method has to be used to ensure the optimum performance. To this end, ${\cal H}_2$ and ${\cal H}_{\infty}$ optimization approaches are utilized. For validation purposes, the controller is verified numerically and experimentally for vibration control of a cantilever beam. System identification is performed, then closed-loop system responses to simultaneous multimode and swept frequency excitations are obtained. According to the results, the HPF controller has a superior performance compared to the conventional method of positive position feedback. Vibration displacement amplitudes were reduced by more than 85% relative to the uncontrolled state. The best performance was achieved by the ${\cal H}_2$ -optimized HPF, as the net value for vibration displacement amplitude reduction in the multimode condition was 90% of the uncontrolled amplitude.

Multiple Mode Spatial Vibration Reduction in Flexible Beams Using H2- and H∞-Modified Positive Position Feedback

This paper develops H2 modified positive position feedback (H2-MPPF) and H∞-MPPF controllers for spatial vibration suppression of flexible structures in multimode condition. Resonant vibrations in a clamped–clamped (c–c) and a cantilever beam are aimed to be spatially suppressed using minimum number of piezoelectric patches. These two types of beams are selected since they are more frequently used in macro- and microscale structures. The shape functions of the beams are extracted using the assumed-modes approach. Then, they are implemented in the controller design via spatial H2 and H∞ norms. The controllers are then evaluated experimentally. Vibrations of multiple points on the beams are concurrently measured using a laser vibrometer. According to the results of the c–c beam, vibration amplitude is reduced to less than half for the entire beam using both H2- and H∞-MPPF controllers. For the cantilever beam, vibration amplitude is suppressed to a higher level using the H2-MPPF controller compared to the H∞-MPPF method. Results show that the designed controllers can effectively use one piezoelectric actuator to efficiently perform spatial vibration control on the entire length of the beams with different boundary conditions.

Active vibration suppression of flexible structure using a LMI-based control patch

Based on the linear matrix inequality, a linear feedback control is presented to realize active vibration suppression of a class of flexible structure. By introducing an appropriate modal transformation, the controller design procedure can be simplified greatly. A specific Lyapunov function is adopted to induce the asymptotical stability of the flexible structure. Simulation results for flexible spacecraft are provided to illustrate the effectiveness of the proposed scheme.

Non-parametric modelling of a rectangular flexible plate structure

This research investigates the performance of dynamic modelling using non-parametric techniques for identification of a flexible structure system for development of active vibration control. In this paper, the implementation details are described and the experimental studies conducted in this research are analysed. The input–output data of the system were first acquired through the experimental studies using National Instruments (NI) data acquisition system. A sinusoidal force was applied to excite the flexible plate and the dynamic response of the system was then investigated. Non-parametric modelling of the system were developed using several artificial intelligent methodologies namely Adaptive Elman Neural Networks (ENN), Backpropagation Multi-layer Perceptron Neural Networks (MLPNN) and Adaptive Neuro-Fuzzy Inference System (ANFIS). The performance of all these methodologies were compared and discussed. Finally, validation and verification of the obtained model was conducted using One Step Ahead (OSA) prediction, mean squared error (MSE) and correlation tests. The prediction ability of the model was further observed with unseen data. The results verified that the MLPNN converge to an optimum solution faster and the dynamic model obtained described the flexible plate structure very well. The non-parametric models of the flexible plate structure thus developed and validated will be used as the representation of the transfer function of the system in subsequent investigations for the development of active vibration control strategies for vibration suppression in flexible structures.

A Neural Fuzzy System for Vibration Control in Flexible Structures

An adaptive neural fuzzy (NF) controller is developed in this paper for active vibration suppression in flexible structures. A recurrent identification network (RIN) is developed to adaptively identify system dynamics of the plant. A novel recurrent training (RT) technique is suggested to train the RIN so as to optimize nonlinear input-output mapping and to enhance convergence. The effectiveness of the developed controller and the related techniques has been verified experimentally corresponding to different control scenarios. Test results show that the proposed RIN can effectively recognize the time-varying dynamics of the plant. The RT-based hybrid training technique can improve the adaptive capability of the control system to accommodate different system conditions and enhance the training convergence. The developed NF controller is a robust and stable vibration suppression system, and it outperforms other related NF controllers.

Vibration Cancellation in a Plate Using Orthogonal Eigenstructure Control

Orthogonal eigenstructure control is a novel control method that can be used for vibration suppression in flexible structures. The method described in this study does not need defining the desired locations of the closed-loop poles or predetermining the closed-loop eigenvectors. The method, which is applicable to linear multi-input multi-output systems, determines an output feedback control gain matrix such that some of the closed-loop eigenvectors are orthogonal to the open-loop eigenvectors. Using this, the open-loop system’s eigenvectors as well as a group of orthogonal vectors are regenerated based on a matrix that spans the null space of the closed-loop eigenvectors. The gain matrix can be generated automatically; therefore, the method is neither a trial and error process nor an optimization of an index function. A finite element model of a plate is used to study the applicability of the method to systems with relatively large degrees of freedom. The example is also used to discuss the effect of operating eigenvalues on the process of orthogonal eigenstructure control. The importance of the operating eigenvalues and the criteria for selecting them for finding the closed-loop system are also investigated. It is shown that choosing the operating eigenvalues from the open-loop eigenvalues that are farthest from the origin results in convergence of the gain matrix for the admissible closed-loop systems. It is shown that the converged control gain matrix has diagonal elements that are two orders of magnitude larger than the off-diagonal elements, which implies a nearly decoupled control.

A novel technique for optimal placement of piezoelectric actuators on smart structures

The problem of positioning of actuators and sensors on smart materials has been a point of interest in recent years. This is due to the fact that in many practical applications there are limitations in space, weight, etc. of the smart structures, which make the problem of positioning more complex. In addition, it is required that the actuators/sensors have the best possible performance. The development of smart structures technology in recent years has provided numerous opportunities for vibration control applications. The use of piezoelectric ceramics or polymers has shown great promise in the development of this technology. The employment of piezoelectric material as actuators in vibration control is beneficial because these actuators only excite the elastic modes of the structures without exciting the rigid-body modes. This is important since very often only elastic motions of the structures are needed to be controlled. The purpose of this paper is to introduce a novel approach developed for optimizing the location of piezoelectric actuators for vibration suppression of flexible structures. A flexible fin with bonded piezoelectric actuators is considered in this study. The frequency response function (FRF) of the system is then recorded and maximization of the FRF peaks is considered as the objective function of the optimization algorithm to find the optimal placement of the piezoelectric actuators on the smart fin. Three multi-layer perceptron neural networks are employed to perform surface fitting to the discrete data generated by the finite element method (FEM). Invasive weed optimization (IWO), a novel numerical stochastic optimization algorithm, is then employed to maximize the weighted summation of FRF peaks. Results indicate an accurate surface fitting for the FRF peak data and an optimal placement of the piezoelectric actuators for vibration suppression is achieved.

Genetic Algorithm Optimization and Control System Design of Flexible Structures

This paper presents an investigation into the deployment of genetic algorithm (GA)-based controller design and optimization for vibration suppression in flexible structures. The potential of GA is explored in three case studies. In the first case study, the potential of GA is demonstrated in the development and optimization of a hybrid learning control scheme for vibration control of flexible manipulators. In the second case study, an active control mechanism for vibration suppression of flexible beam structures using GA optimization technique is proposed. The third case study presents the development of an effective adaptive command shaping control scheme for vibration control of a twin rotor system, where GA is employed to optimize the amplitudes and time locations of the impulses in the proposed control algorithm. The effectiveness of the proposed control schemes is verified in both an experimental and a simulation environment, and their performances are assessed in both the time and frequency domains.

Equivalent Mechanical and Electrical Models of the Vibration Suppression System Using Piezoelectric Elements

This paper describes the equivalent mechanical and electrical models for systems of the vibration suppression in flexible structures using piezoelectric elements. There are two main methods to suppress vibration of flexible structures. One is active vibration control and the other is passive vibration suppression. Because they include both mechanical and electrical systems, the mechanism of the vibration suppression is complicated and can not be understood easily. To make matters worse, the knowledge of the mechanical vibration suppression device and the electrical circuit are not utilized in those systems with piezoelectric elements. Hence, this paper describes the way to derive the equivalent mechanical and electrical models. Using those equivalent models, the mechanism of the vibration suppression can be easily comprehended and the knowledge of mechanical and electrical systems can be applied effectively.

Active vibration suppression of flexible structures: robust gain scheduled approach

The paper deals with robust gain scheduled controller design applied for active vibration suppression of flexible structures. The experimental set-up is a three-storey flexible structure with an active mass driver placed on the last storey. First, system identification experiments are performed and the plant's uncertainty is deduced. Next, robust controller design with constraint on the control signal is presented. For a better trade-off between control performance and control constraint a gain scheduling approach is investigated. Finally, the control system is tested experimentally, when the input disturbance is a scaled historical earthquake record (1940 El Centro). The experimental results show that the proposed robust gain scheduling control approach offers higher performance levels and can handle effectively extreme control conditions, such as reconnection of the control system after power failure. All results presented in the paper are experimental results. Copyright © 2004 John Wiley & Sons, Ltd.