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.

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.

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.

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.

Enhanced Active Constrained Layer Damping Treatment for Broadband Vibration Suppression

2002 ◽  
Vol 8 (6) ◽  
pp. 777-803 ◽  
Author(s):  
Y. Liu ◽  
K. W. Wang
Keyword(s):  
Closed Loop ◽  
Noise Suppression ◽  
Vibration Suppression ◽  
Wide Frequency Range ◽  
Open Loop ◽  
Loop System ◽  
Constrained Layer Damping ◽  
Edge Elements ◽  
Modal Damping ◽  
Active Constrained Layer

In this paper, the Enhanced Active Constrained Layer (EACL) treatment is investigated for broadband damping augmentations on beam structures. The EACL concept was originally proposed to improve the damping performance of the Active Constrained Layer (ACL) by introducing edge elements at the treatment boundaries. It has been recognized that the edge elements can increase ACL performance by enhancing the direct active authority of the piezoelectric constraining layer. It has also been demonstrated that the edge element stiffness and the host structure strain field have significant influence on the overall closed-loop system damping and its various components: the active damping, the closed-loop passive damping, and the open-loop passive (fail-safe property - without any active action) damping. Through utilizing this finding, the present study explores how the EACL performance can be synthesized for multiple mode broadband applications using symmetric configurations. Although the edge elements will tend to reduce the maximum possible open-loop damping of one (or a few) vibration mode, open-loop damping of the other higher order modes could actually be increased. Moreover, the modal damping reduction in the open-loop system can generally be compensated by the significant increase of the closed-loop damping. In other words, the closed-loop EACL system damping over a wide frequency range can be significant, which makes it attractive for broadband vibration and noise suppression.

Accounting for Out-of-Bandwidth Modes in the Assumed Modes Approach: Implications on Colocated Output Feedback Control

1997 ◽  
Vol 119 (3) ◽  
pp. 390-395 ◽  
Author(s):  
R. L. Clark
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Open Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Open Loop System ◽  
Low Frequencies ◽  
Poles And Zeros ◽  
Admissible Functions

Colocated, output feedback is commonly used in the control of reverberant systems. More often than not, the system to be controlled displays high modal density at a moderate frequency, and thus the compliance of the out-of-bandwidth modes significantly influences the performance of the closed-loop system at low frequencies. In the assumed modes approach, the inclusion principle is used to demonstrate that the poles of the dynamic system converge from above when additional admissible functions are used to expand the solution. However, one can also interpret the convergence of the poles in terms of the zeros of the open-loop system. Since colocated inputs and outputs are known to have interlaced poles and zeros, the effect of a modification to the structural impedance locally serves to couple the modes of the system through feedback. The poles of the modified system follow loci defined by the relative location of the open-loop poles and zeros. Thus, as the number of admissible functions used in the series expansion is increased, the interlaced zeros of the colocated plant tend toward the open-loop poles, causing the closed-loop poles to converge from above as predicted by the inclusion principle. The analysis and results presented in this work indicate that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed-loop system.

scholarly journals A Complete Parametric Solutions of Eigenstructure Assignment by State-Derivative Feedback for Linear Control Systems

10.14311/778 ◽  
2005 ◽  
Vol 45 (6) ◽  
Author(s):  
T. H. S. Abdelaziz ◽  
M. Valášek
Keyword(s):  
Degrees Of Freedom ◽  
Open Loop ◽  
Loop System ◽  
Linear Control Systems ◽  
Feedback Gain ◽  
Eigenstructure Assignment ◽  
System Matrix ◽  
Parametric Solutions ◽  
Gain Matrix ◽  
Controllable Systems

In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach. 

scholarly journals Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Multi-Stage System Identification of a Gas Turbine

2017 ◽  
Author(s):  
Amit Pandey ◽  
Maurício de Oliveira ◽  
Chad M. Holcomb
Keyword(s):  
Gas Turbine ◽  
Closed Loop ◽  
Open Loop ◽  
Loop System ◽  
Closed Loop Control ◽  
Input Output ◽  
Open Loop System ◽  
Loop Control ◽  
Multi Stage ◽  
Identification Techniques

Several techniques have recently been proposed to identify open-loop system models from input-output data obtained while the plant is operating under closed-loop control. So called multi-stage identification techniques are particularly useful in industrial applications where obtaining input-output information in the absence of closed-loop control is often difficult. These open-loop system models can then be employed in the design of more sophisticated closed-loop controllers. This paper introduces a methodology to identify linear open-loop models of gas turbine engines using a multi-stage identification procedure. The procedure utilizes closed-loop data to identify a closed-loop sensitivity function in the first stage and extracts the open-loop plant model in the second stage. The closed-loop data can be obtained by any sufficiently informative experiment from a plant in operation or simulation. We present simulation results here. This is the logical process to follow since using experimentation is often prohibitively expensive and unpractical. Both identification stages use standard open-loop identification techniques. We then propose a series of techniques to validate the accuracy of the identified models against first principles simulations in both the time and frequency domains. Finally, the potential to use these models for control design is discussed.

scholarly journals Controlling the Chaotic Motions of an Airfoil with a Nonlinear Stiffness Using Closed-Loop Harmonic Parametric Excitation

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 165
Author(s):  
Robert Bruce Alstrom
Keyword(s):  
Parametric Excitation ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Preliminary Investigation ◽  
Random Excitation ◽  
Loop System ◽  
Nonlinear Stiffness ◽  
Resonance Capture ◽  
Closed Loop System ◽  
Chaotic Motions

The purpose of this research is to conduct a preliminary investigation into the possibility of suppressing the flutter and post-flutter (chaotic) responses of a two-dimensional self-excited airfoil with a cubic nonlinear stiffness (in torsion) and linear viscous damping via closed-loop harmonic parametric excitation. It was found that the initial configuration of the proposed control scheme caused the torsional/pitch dynamics to act as a nonlinear energy sink; as a result, it was identified that the mechanisms of vibration suppression are the resonance capture cascade and the short duration or isolated resonance capture. It is the isolated resonance capture that is responsible for the second-order-like damping and full vibration suppression of the aeroelastic system. The unforced and closed-loop system was subjected to random excitation to simulate aerodynamic turbulence. It was found that the random excitation suppresses the phase-coherent chaotic response, and the closed-loop system is susceptible to random excitation.

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