Vibration suppression by eigenstructure optimization

Volume 1: 21st Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2007

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.

Journal of Vibration and Acoustics, 2010

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 d...

Shock and Vibration, 2009

This paper provides a state-of-the-art review of eigenstructure assignment methods for vibration cancellation. Eigenstructure assignment techniques have been widely used during the past three decades for vibration suppression in structures, especially in large space structures. These methods work similar to mode localization in which global vibrations are managed such that they remain localized within the structure. Such localization would help reducing vibrations more effectively than other methods of vibration cancellation, by virtue of confining the vibrations close to the source of disturbance. The common objective of different methods of eigenstructure assignment is to provide controller design freedom beyond pole placement, and define appropriate shapes for the eigenvectors of the systems. These methods; however, offer a large and complex design space of options that can often overwhelm the control designer. Recent developments in orthogonal eigenstructure control offers a sig...

Journal of Vibration and Acoustics, 1999

A method of simultaneous optimization of structure and control using mixed H2 and H" norms of the transfer function as the objective function is proposed and the modeling and formulation of simultaneous optimization problems associated with this approach are discussed in this paper. Simultaneous optimization is realized by iteratively executing structural optimization and controller optimization. Both serial and parallel approaches to combine structural optimization and controller optimization are investigated. They are applied to the simultaneous optimization of the crosssectional parameters of a spring-supported beam and the parameters of the controller used to actively suppress the vibration of the beam. The performance of both displacement output and control input is improved significantly after simultaneous optimization. The simulation results show the great potential advantages of simultaneous optimization over traditional design methods and the effectiveness of the proposed approach.

Journal of Applied Mechanics, 2010

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 dis...

SPIE Proceedings, 2009

Orthogonal Eigenstructure Control (OEC) is a novel control method that can be used for active vibration cancellation. OEC is an output feedback control method applicable to multiple-input, multiple-output linear systems. In this paper, application of OEC for active vibration cancellation in a plate is presented. A steel plate clamped at four edges is used as a test plate and piezoelectric actuators are used as control actuators. Accelerometers are used for measuring the acceleration and displacement at ten locations on the plate. A tonal disturbance with a frequency of 150 Hz is applied to the plate by an electromagnetic actuator. After identification of the state-space model of the plate, orthogonal eigenstructure control is used to find the control gains that decouple the modes of vibrations and reduce transferring of vibrational energy between them. The results show significant vibration suppression throughout the plate.

Journal of Sound and Vibration, 1999

A quadratic programming algorithm is presented for studying the design tradeoffs of active-passive vibration isolation systems. The novelty of the technique is that the optimal control problem is posed as a quadratic optimization with linear constraints. The quadratic cost function represents the mean square response of the payload acceleration and isolator stroke, and the linear constraints represent asymptotic tracking requirements and peak response constraints. Posing the problem as a quadratic optimization guarantees that a global optimal solution can be found if one exists, and the existence of an optimal solution guarantees that the vibration isolation system satisfies the specified design constraints. The utility of the technique is demonstrated on a comparison of passive vibration isolation and active-passive vibration isolation utilizing relative displacement feedback.

Journal of Vibration and Acoustics, 2004

The underlying principle for vibration confinement is to alter the structural vibration modes so that the corresponding modal components have much smaller amplitude in concerned area than in the remaining part of the structure. In this research, the state-of-the-art in vibration confinement technique is advanced in two correlated ways. First, a new eigenstructure assignment algorithm is developed to more directly suppress vibration in regions of interest. This algorithm is featured by the optimal selection of achievable eigenvectors that minimizes the eigenvector components at concerned region by using the Rayleigh Principle. Second, the active control input is applied through an active-passive hybrid piezoelectric network. With the introduction of circuitry elements, which are much easier to implement than changing or adding mechanical components, the state matrices can be reformed and the design space for eigenstructure assignment can be greatly enlarged. To maximize the system pe...

Procedia Engineering, 2012

This work addresses the solution to the problem of active vibration suppression of a cantilever beam using piezoelectric actuation. For this purpose, we are taking advantage of the effectiveness of the positive position feedback control strategy (PPF) in order to control first mode vibrations of the analyzed beam. This control technique is well-known in the literature as a modal control method for vibration attenuation. The PPF controller accomplishes its best performance if tuned properly to the characteristics of the structure to be controlled. According to this we are going to realize the modal analysis of the cantilever beam utilizing the finite element method in Ansys to determine the structural frequency corresponding to the first mode, which is used as PPF controller frequency. On the other hand, we shall obtain the state-space representation of the cantilever beam using the subspace identification method in frequency domain applying the fast fourier transformation (FFT). Furthermore, we will simulate the discrete-time PPF controller using Matlab/Simulink. Lastly, the simulink designed discrete-time PPF controller will be tested using an xPC Target real-time system.

Exact optimal classical closed-open loop control is not achievable for the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. This has motivated the researchers to develop suboptimal control policies. This study proposes some representative simple methods to obtain the suboptimal passive damping and stiffness parameters from the optimal control gain matrix since it is not possible to add the exact optimal damping and stiffness parameters to the structure in practice [1]. Proposed method is applied to a 3-dimensional tier building structure. For this study, a 3-story steel building designed for the SAC project Los Angeles, California region is considered [2]. This structure is idealized with two translational and a single rotational degree of freedom in each story. The structure is tested under a unidirectional real earthquake excitation. Dynamic equations of motion are derived in matrix form for the three dimensional stru...