Vibration Isolation Control Via Simultaneous Left and Right Eigenvector Assignment

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.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

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

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.

scholarly journals Robust Linear Output Regulation Using Extended State Observer

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Mehran Hosseini-Pishrobat ◽  
Jafar Keighobadi ◽  
Atta Oveisi ◽  
Tamara Nestorović
Keyword(s):  
Disturbance Rejection ◽  
Closed Loop ◽  
State Observer ◽  
Output Regulation ◽  
Loop System ◽  
Extended State Observer ◽  
Dynamical Structure ◽  
Extended State ◽  
Closed Loop System ◽  
Robust Output Regulation

This paper presents a disturbance rejection-based solution to the problem of robust output regulation. The mismatch between the underlying plant and its nominal mathematical model is formulated by two disturbance classes. The first class is assumed to be generated by an autonomous linear system while for the second class no specific dynamical structure is considered. Accordingly, the robustness of the closed-loop system against the first disturbance class is achieved by following the internal model principle. On the other hand, in the framework of disturbance rejection control, an extended state observer (ESO) is designed to approximate and compensate for the second class, i.e., unstructured disturbances. As a result, the proposed output regulation method can deal with a vast range of uncertainties. Finally, the stability of the closed-loop system based on the proposed compound controller is carried out via Lyapunov and center manifold analyses, and some results on the robust output regulation are drawn. A representative simulation example is also presented to show the effectiveness of the control method.

Optimal Eigenvectors Design for Structural Noise Reduction Through Adaptive Sandwich Algorithm

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.

Safety and Performance of the Omnipod®Hybrid Closed-Loop System in Adolescents with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 1376-P
Author(s):  
GREGORY P. FORLENZA ◽  
BRUCE BUCKINGHAM ◽  
JENNIFER SHERR ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions

1066-P: Improvement in Time-in-Range (TIR) with Real-Life Use of Hybrid Closed-Loop System in Patients with Type 1 Diabetes (T1D)

Diabetes ◽  
2019 ◽  
Vol 68 (Supplement 1) ◽  
pp. 1066-P
Author(s):  
HALIS K. AKTURK ◽  
DOMINIQUE A. GIORDANO ◽  
HAL JOSEPH ◽  
SATISH K. GARG ◽  
JANET K. SNELL-BERGEON
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Real Life ◽  
Loop System ◽  
Closed Loop System ◽  
Time In Range

Safety and Performance of the Omnipod® Hybrid Closed-Loop System in Adults with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 207-OR
Author(s):  
BRUCE A. BUCKINGHAM ◽  
JENNIFER SHERR ◽  
GREGORY P. FORLENZA ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions
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