Vibration Cancellation in a Plate Using Orthogonal Eigenstructure Control

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. A. Rastgaar ◽  
M. Ahmadian ◽  
S. C. Southward
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Control Method ◽  
Null Space ◽  
Flexible Structures ◽  
Element Model ◽  
Open Loop ◽  
Gain Matrix ◽  
Control Gain

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.

Orthogonal Eigenstructure Control for Vibration Suppression

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Mohammad Rastgaar ◽  
Mehdi Ahmadian ◽  
Steve Southward
Keyword(s):  
Closed Loop ◽  
Vibration Suppression ◽  
Control Method ◽  
Null Space ◽  
Output Feedback Control ◽  
Open Loop ◽  
Unique Property ◽  
Gain Matrix ◽  
Coefficient Vector ◽  
Value Decomposition

Orthogonal eigenstructure control is a novel active control method for vibration suppression in multi-input multi-output linear systems. This method is based on finding an output feedback control gain matrix in such a way that the closed-loop eigenvectors are almost orthogonal to the open-loop ones. Singular value decomposition is used to find the matrix, which spans the null space of the closed-loop eigenvectors. This matrix has a unique property that has been used in this new method. This unique property, which has been proved here, can be used to regenerate the open-loop system by finding a coefficient vector, which leads to a zero gain matrix. Also several vectors, which are orthogonal to the open-loop eigenvectors, can be found simultaneously. The proposed method does not need any trial and error procedure and eliminates not only the need to specify any location or area for the closed-loop eigenvalues but also the requirements of defining the desired eigenvectors. This method determines a set of limited number of closed-loop systems. Also, the elimination of the extra constraints on the locations of the closed-loop poles prevents the excessive force in actuators.

Effect of the Actuators’ Location on Vibration Suppression Using Minimum Modal Energy Eigenstructure Assignment

2007 ◽  
Author(s):  
Mohammad Rastgaar Aagaah ◽  
Steve C. Southward ◽  
Mehdi Ahmadian
Keyword(s):  
Closed Loop ◽  
Vibration Suppression ◽  
Null Space ◽  
Flexible Structures ◽  
Output Feedback Control ◽  
Open Loop ◽  
Loop System ◽  
Eigenstructure Assignment ◽  
Gain Matrix ◽  
Coefficient Vector

A new Eigenstructure Assignment (ESA) method for vibration confinement of flexible structures has been developed. This method is based on finding an output feedback control gain matrix in such a way that the closed-loop eigenvectors are orthogonal to the open-loop ones. Singular Value Decomposition (SVD) is used for finding the matrix that spans the null space of the closed-loop eigenvectors. It is shown that this matrix has a unique property that can be used to regenerate the open-loop system. This method finds a coefficient vector which leads to a zero gain matrix while several coefficient vectors can be found simultaneously which are orthogonal to the open-loop coefficient vector. As a result, the closed-loop eigenvectors are orthogonal to the open-loop ones. It is shown that the modal energy of the closed loop system is reduced. Moreover, the proposed method needs neither to specify the closed-loop eigenvalues nor to define a desired set of eigenvectors. Also it is shown that if the maximum force of the actuators and the consumed energy of the actuators need to be low, actuators have to be relatively close to input. If the amplitude of vibration in isolated area has to be minimized as much as possible, the actuators need to be relatively closer to isolated area. Also the algorithm of the minimum eigenstructure assignment method has been modified to eliminate the effect of the actuators that are located on the nodes of different vibrational modes.

Vibration Confinement by Minimum Modal Energy Eigenstructure Assignment

2007 ◽  
Author(s):  
Mohammad Rastgaar Aagaah ◽  
Mehdi Ahmadian ◽  
Steve C. Southward
Keyword(s):  
Closed Loop ◽  
Null Space ◽  
Flexible Structures ◽  
Output Feedback Control ◽  
Open Loop ◽  
Loop System ◽  
Eigenstructure Assignment ◽  
Open Loop System ◽  
The Matrix ◽  
Value Decomposition

A novel Eigenstructure Assignment (ESA) method for vibration confinement of flexible structures has been developed. This method is an output feedback control and determines the closed-loop systems that their eigenvectors are orthogonalized to the open-loop eigenvectors. This method is a numerical method and used Singular Value Decomposition (SVD) to find the null space of the closed-loop eigenvectors. The matrix that spans the null space can be used to regenerate the open-loop system as well as the systems that have orthogonal eigenvectors to the regenerated open-loop system. As a result the isolation of vibration is independent of the type of the disturbance. Also in this method, the energy of the closed-loop system is minimized. As an important outcome, the proposed method needs neither to specify the closed-loop eigenvalues nor to define a desired set of eigenvectors.

Research of vibration and crack propagation controls on an asymmetrical cracked rotor

2021 ◽  
pp. 107754632199822
Author(s):  
Jun Liu ◽  
Zhu Han ◽  
Rong Hu
Keyword(s):  
Crack Propagation ◽  
Vibration Suppression ◽  
Control Method ◽  
Element Model ◽  
Electromagnetic Actuator ◽  
Contact Method ◽  
Cracked Rotor ◽  
Mapping Model ◽  
Differential Control ◽  
Opening And Closing

To investigate vibration characteristics and delay crack propagations of an asymmetric cracked rotor, the 3D finite element model of the rotor system with a nonlinear contact method is established. Resonance characteristics of the asymmetrical rotor without a crack and within different locations of a crack are investigated systematically. Numerical results show that a crack affects vibration frequencies and the unstable region of the rotor. Meanwhile, an improved proportional integral differential control method with the electromagnetic actuator is used to accomplish the delay crack propagation and the vibration suppression. Based on the mapping model of opening and closing states of a crack, the effects of rotational speeds, an unbalance, and asymmetries of the rotor are discussed in detail. Experimental results show that vibrations and the breathing behavior of cracks in the rotor with the electromagnetic actuator can be suppressed, and the effectiveness of the proposed mapping model of opening and closing states of a crack is verified.

scholarly journals Flatness-Based Control of a Two Degrees-of-Freedom Platform With Pneumatic Artificial Muscles

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
David Bou Saba ◽  
Paolo Massioni ◽  
Eric Bideaux ◽  
Xavier Brun
Keyword(s):  
Degrees Of Freedom ◽  
Control Method ◽  
Sliding Mode ◽  
Feedforward Control ◽  
Volume Ratio ◽  
Open Loop ◽  
Control Technique ◽  
Artificial Muscles ◽  
Two Degrees Of Freedom ◽  
Pneumatic Artificial Muscles

Pneumatic artificial muscles (PAMs) are an interesting type of actuators as they provide high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods taking into account their complex and nonlinear dynamics. This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves. An overactuation is present as three muscles are controlled for only two degrees-of-freedom. The contribution of this work is twofold. First, whereas most of the literature approaches the control of systems of similar nature with sliding mode control, we show that the platform can be controlled with the flatness-based approach. This method is a nonlinear open-loop controller. In addition, this approach is model-based, and it can be applied thanks to the accurate models of the muscles, the platform and the servovalves, experimentally developed. In addition to the flatness-based controller, which is mainly a feedforward control, a proportional-integral (PI) controller is added in order to overcome the modeling errors and to improve the control robustness. Second, we solve the overactuation of the platform by an adequate choice for the range of the efforts applied by the muscles. In this paper, we recall the basics of this control technique and then show how it is applied to the proposed experimental platform. At the end of the paper, the proposed approach is compared to the most commonly used control method, and its effectiveness is shown by means of experimental results.

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

2020 ◽  
pp. 107754632096194
Author(s):  
Haining Sun ◽  
Xiaoqiang Tang ◽  
Senhao Hou ◽  
Xiaoyu Wang
Keyword(s):  
Large Scale ◽  
Vibration Suppression ◽  
Control Method ◽  
External Disturbance ◽  
Flexible Structures ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Lyapunov Theory ◽  
Normal Operation ◽  
Control Methods

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.

Dynamic Analysis of Flexible Structures Using Component Mode Synthesis

1989 ◽  
Vol 56 (4) ◽  
pp. 874-880 ◽  
Author(s):  
M. De Smet ◽  
C. Liefooghe ◽  
P. Sas ◽  
R. Snoeys
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Flexible Structures ◽  
Element Model ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
Flexible Robot ◽  
Preliminary Calculation ◽  
Resonance Frequencies

In this paper a dynamic model of a flexible robot is built out of a finite element model of each of its links. The number of degrees-of-freedom of these models is strongly reduced by applying the Component Mode Synthesis technique which involves the preliminary calculation of a limited number of mode shapes of the separate links. As can be seen from examples, the type of boundary conditions thereby imposed in the nodes in which one link is connected to the others, strongly determines the accuracy of the calculated resonance frequencies of the robot. The method is applied to an industrial manipulator. The reduced finite element model of the robot is changed in order to match the numerically and experimentally (modal analysis) determined resonance data. Further, the influence of the position of the robot on its resonance frequencies is studied using the optimized numerical model.

scholarly journals Vibration Control of Double-Beam System with Multiple Smart Damping Members

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Dominik Pisarski ◽  
Tomasz Szmidt ◽  
Czesław I. Bajer ◽  
Bartłomiej Dyniewicz ◽  
Jacek M. Bajkowski
Keyword(s):  
Smart Materials ◽  
Closed Loop ◽  
Control Method ◽  
Bilinear System ◽  
Element Model ◽  
Strong Wind ◽  
Loop Control ◽  
Double Beam ◽  
Bang Bang Control ◽  
Wind Blow

A control method to stabilize vibration of a double cantilever system with a set of smart damping blocks is designed and numerically evaluated. The externally controlled magnetorheological sheared elastomer damping block is considered, but other smart materials can be used as well. The robust bang-bang control law for stabilization the bilinear system is elaborated. The key feature of the closed loop controller is the efficiency for different types of initial excitement. By employing the finite element model, the performance of the controller is validated for strong wind blow load and concentrated impact excitement of the particular point of one of the beams. For each of the excitations, the closed loop control outperforms the optimal passive damping case by over 27% for the considered energy metric.

Active vibration control experiments on an AgustaWestland W30 helicopter airframe

2011 ◽  
Vol 226 (6) ◽  
pp. 1504-1516 ◽  
Author(s):  
J E Mottershead ◽  
M Ghandchi Tehrani ◽  
S James ◽  
P Court
Keyword(s):  
Vibration Control ◽  
Frequency Response ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Active Vibration Control ◽  
Input Voltage ◽  
Open Loop ◽  
Control Technique ◽  
Response Functions ◽  
Frequency Response Functions

This article describes the practical application of a vibration control technique, developed by the authors and known as the receptance method, to the AgustaWestland W30 helicopter airframe in the vibration test house at Yeovil. The experimental work was carried out over a total of 5 days in two visits to the Yeovil site during February and March 2011. In the experiments, existing electro-hydraulic actuators were used; they were built into the airframe structure and originally designed for vibration suppression by the methodology known as active control of structural response developed at the AgustaWestland Helicopters site in Yeovil. Accelerometers were placed at a large number of points around the airframe and an initial open-loop modal test was carried out. In a subsequent test, at higher actuator input voltage, considerable non-linearity was discovered, to the extent that the ordering of certain modes had changed. The vibration modes were, in general, heavily damped. Control was implemented using measured frequency response functions obtained at the higher input level. After acquiring the necessary measurements, simulations were carried out and the controller was implemented using MATLAB/Simulink and dSPACE. The closed-loop poles were mostly assigned with small real parts so that the system would be lightly damped and sharp peaks would be clearly apparent in the measured closed-loop frequency response functions. Locations of the open- and closed-loop poles in the complex s-plane were obtained to verify that the required assignment of poles had taken place.

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