Optimal Eigenvectors Design for Structural Noise Reduction Through Adaptive Sandwich Algorithm

Volume 15: Sound, Vibration and Design ◽

10.1115/imece2009-12725 ◽

2009 ◽

Author(s):

T. Y. Wu ◽

Y. L. Chung

Keyword(s):

Noise Reduction ◽

Closed Loop ◽

Active Noise Control ◽

Optimal Combination ◽

Loop System ◽

Structural Vibration ◽

Feedback Gain ◽

Structural Noise ◽

Closed Loop System ◽

Left And Right

The purpose of this research is to investigate the feasibility of utilizing the adaptive sandwich algorithm to find the optimal left and right eigenvectors for active structural noise reduction. As depicted in the previous studies, the structural acoustic radiation depends on the structural vibration behavior, which is strongly related to both the left eigenvectors (concept of disturbance rejection capability) and right eigenvectors (concept of mode shape distributions) of the system, respectively. In this research, a novel adaptive sandwich algorithm is developed for determining the optimal combination of left and right eigenvectors of the structural system. The sound suppression performance index (SSPI) is defined by combining the orthogonality index of left eigenvectors and the modal radiation index of right eigenvectors. Through the proposed adaptive sandwich algorithm, both the left and right eigenvectors are adjusted such that the SSPI decreases, and therefore one can find the optimal combination of left and right eigenvectors of the closed-loop system for structural noise reduction purpose. The optimal combination of left-right eigenvectors is then synthesized to determine the feedback gain matrix of the closed-loop system. The result of the active noise control shows that the proposed method can significantly suppress the sound pressure radiated from the vibrating structure.

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Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System

Complexity ◽

10.1155/2020/4986026 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Boumediène Chentouf ◽

Nejib Smaoui

Keyword(s):

Flow Control ◽

Closed Loop ◽

Semigroup Theory ◽

Loop System ◽

Delayed Feedback Control ◽

Feedback Gain ◽

Wave System ◽

Closed Loop System ◽

Decay Of Solutions ◽

Time Delayed Feedback

This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results.

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Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

Complexity ◽

10.1155/2020/1468109 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Walid Hamdi ◽

Wissal Bey ◽

Naceur Benhadj Braiek

Keyword(s):

Closed Loop ◽

Uncertain System ◽

Loop System ◽

Invariant Sets ◽

Feedback Gain ◽

Closed Loop System ◽

Control Laws ◽

Robust Model Predictive Control ◽

Robust Model ◽

Polyhedral Set

An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

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Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

Abstract and Applied Analysis ◽

10.1155/2014/301375 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Hua-Feng He ◽

Guang-Bin Cai ◽

Xiao-Jun Han

Keyword(s):

Assignment Problem ◽

Closed Loop ◽

Sufficient Conditions ◽

Pole Assignment ◽

Loop System ◽

Linear Matrix ◽

Feedback Gain ◽

Matrix Equations ◽

Closed Loop System ◽

Linear Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.

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Polynomial matrix decomposition for the synthesis of non-square control systems

Analysis and data processing systems ◽

10.17212/2782-2001-2021-1-21-38 ◽

2021 ◽

pp. 21-38

Author(s):

Alexander Voevoda ◽

◽

Vladislav Filiushov ◽

Keyword(s):

Closed System ◽

Closed Loop ◽

Single Channel ◽

Polynomial Matrix ◽

Matrix Decomposition ◽

Loop System ◽

Characteristic Matrix ◽

Closed Loop System ◽

Left And Right ◽

The Right

The application of advanced synthesis methods is due to the increasing complexity of control objects. Relatively simple objects are represented as a single-channel system or as a combination of such systems and are calculated separately. More complex systems must be viewed as multi-input and multi-output systems. There are several approaches to this. Within the framework of this paper we will consider the synthesis of a system presented in the form of a polynomial matrix decomposition. It allows us to write a closed loop system in such a way that, by analogy with single-channel systems, it is possible to single out the "numerator" and "denominator" not only of the object and the controller, but of the entire system. For multichannel objects, they will be written in a matrix form allowing you to select the characteristic matrix whose determinant is the characteristic polynomial. In this paper, an emphasis is placed on the derivation of four variants of the polynomial matrix description (PMD) of a closed system. Such a variety of representation of a closed-loop system follows from the equivalent writing of the transfer matrix in the form of left and right PMD of an object or controller. Of the four options for recording the system, two options – left and right – for the characteristic matrix are distinguished. When they are reduced to a diagonal form, the elements on the main diagonal contain the poles of a closed system along the corresponding channel. From the example given at the end of the paper, it can be seen that it is more convenient to use the left characteristic matrix because it has a lower dimension for a non-square object (the number of input and output quantities is not equal), with the number of input actions exceeding the number of output quantities, The right characteristic matrix can also be used to synthesize such a control object, but the resulting solution is more complicated and not obvious. The situation is reversed if we consider an object with fewer inputs than outputs. In this case, the right characteristic matrix will be smaller and more suitable for synthesis. It follows from this that the procedure for synthesizing a control system for non-square objects differs depending on the number of inputs and outputs.

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Vibration Isolation Control Via Simultaneous Left and Right Eigenvector Assignment

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-84824 ◽

2005 ◽

Author(s):

T. Y. Wu ◽

K. W. Wang

Keyword(s):

Disturbance Rejection ◽

Vibration Isolation ◽

Closed Loop ◽

Integrated System ◽

Loop System ◽

Closed Loop System ◽

Left Eigenvector ◽

Assignment Method ◽

Left And Right ◽

New Formulation

The objective of this research is to investigate the feasibility of utilizing the simultaneous left and right eigenvector assignment concept for vibration isolation feedback control design. The purpose of the right eigenvector assignment method is to alter the closed-loop system modes such that the modal components corresponding to the concerned regions (isolation end of an isolator) have relatively small amplitude. Correspondently, the design goal of left eigenvector assignment is to alter the left eigenvectors of the closed-loop system so that they are as closely orthogonal to the system’s forcing vectors as possible. With this approach, one can achieve both disturbance rejection and modal confinement concurrently for the purpose of vibration isolation. In this research, a new formulation is developed so that the desired left eigenvectors of this integrated system are selected through solving a generalized eigenvalue problem, where the orthogonality indices between the forcing vector and the left eigenvectors are minimized. The components of right eigenvectors corresponding to the concerned regions are minimized concurrently. To realistically implement the algorithm, an integrated closed-loop system with state estimator is developed. Numerical simulations are performed to evaluate the effectiveness of the proposed method on concurrent disturbance rejection and modal confinement for a isolator rod design. Frequency responses of the isolator in the selected frequency range are illustrated. It is shown that with the simultaneous left-right eigenvector assignment technique, both disturbance rejection and modal confinement can be achieved, and thus the vibration amplitude in the isolated regions can be suppressed significantly.

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