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

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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Sector stability criteria for a nonlinear axial motion string system

10.22541/au.161944403.39426300/v1 ◽

2021 ◽

Author(s):

Rui Wu ◽

Yi Cheng ◽

Donal O'Regan

Keyword(s):

Exponential Stability ◽

Closed Loop ◽

Semigroup Theory ◽

Nonlinear Partial Differential Equation ◽

Loop System ◽

Closed Loop System ◽

Axially Moving ◽

The Right ◽

Nonlinear Semigroup Theory ◽

Control Criterion

The paper investigates the exponential stability criterion for an axially moving string system driven by a nonlinear partial differential equation with nonlinear boundary feedback.The control criterion based on a sector condition contains a large class of nonlinearities, which is a negative feedback of the velocity at the right boundary of the moving string. By invoking nonlinear semigroup theory, the well-posedness result of the closed-loop system is verified under the sector criteria. Furthermore, a novel energy like function is constructed to establish the exponential stability of the closed-loop system by using a integral-type multiplier method and the generalized Gronwall-type integral inequality.

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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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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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