Discrete-Time Models and Stability of Distributed Parameter Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 327-333 ◽  
Author(s):  
D. C. Garvey ◽  
A. F. D’Souza
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Time Model ◽  
Closed Loop Systems ◽  
Distributed Parameters ◽  
Analysis And Synthesis ◽  
The Stability ◽  
Linear And Nonlinear Systems

The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of closed loop systems, the transcendental transfer functions have to be approximated in a suitable manner. In this paper, discrete-time model of distributed parameter systems is obtained. The model employs a sample and hold circuit in the loop. The response of the model system is compared with the response obtained by approximating the transcendental transfer function by root factor and other approximations. The stability of linear and nonlinear systems with distributed parameters is investigated by employing the Mikhailov stability criterion.

Feedback Control of Parabolic Distributed Parameter Systems

2013 ◽  
Vol 455 ◽  
pp. 337-343
Author(s):  
Hai Long Xing ◽  
Wen Shan Cui
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Closed Loop Systems ◽  
Uniformly Convergent ◽  
System States ◽  
The Stability ◽  
Parabolic Distributed Parameter Systems

In this paper, the feedback control problem is considered for a class of parabolic distributed parameter systems (DPS). By employing a new Lyapunov-Krasovskii functional as well as the linear matrix inequality (LMI), a novel feedback controller is developed, which can guarantee the closed-loop system states uniformly convergent to zero. The stability conditions for closed-loop systems can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. At last, a numerical example shows the effectiveness of the presented LMI-based methods.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

On the Control of Discrete-Time Distributed Parameter Systems

1972 ◽  
Vol 10 (2) ◽  
pp. 361-376 ◽  
Author(s):  
Kwang Yun Lee ◽  
Shui-Nee Chow ◽  
Robert O. Barr
Keyword(s):  
Discrete Time ◽  
Distributed Parameter Systems ◽  
Distributed Parameter

Engineering Methods and Software Support for Modeling and Design of Discrete-time Control of Distributed Parameter Systems

2009 ◽  
Vol 15 (3-4) ◽  
pp. 407-417 ◽  
Author(s):  
G. Hulkó ◽  
C. Belavý ◽  
A. Mészáros ◽  
P. Bucek ◽  
K. Ondrejkovic ◽  
...  
Keyword(s):  
Discrete Time ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Software Support ◽  
Time Control

Discrete-time Inversion Model Control of a Double-damper System with Uncertain Parameters

2017 ◽  
Vol 6 (3) ◽  
pp. 168
Author(s):  
Marwa Hannachi ◽  
Ikbel Bencheikh Ahmed ◽  
Dhaou Soudani
Keyword(s):  
Discrete Time ◽  
Algebraic Approach ◽  
Building Blocks ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Inversion ◽  
Time Model ◽  
Model Control ◽  
The Stability

<span>This paper addresses the control at discrete time of physical complex systems multi-inputs multi-outputs with variables parameters. Classified among the robust control laws the Internal Model Control (IMC) is adopted in this work to ensure the desired performances adjacent to the complexities of the system. However, the application of this control strategy requires that these different building blocks be open loop stable, which invites us, on the one hand, to apply the algebraic approach of Kharitinov for delimiting the summits stability domain’s system. On the other case, the Linear Matrix Inequalities (LMI) approach is applied to determine the corrector’s stability conditions obtained by a specific inversion of the chosen model. It is in this sense that we contribute by this work to execute the command by inversion the discrete-time model in order to ensure the stability and to maintain the performances the stability conditions of required for the double damper system with variable parameters.</span>

A Discrete-Time Adaptive Filter for Stochastic Distributed Parameter Systems

1981 ◽  
Vol 103 (3) ◽  
pp. 266-278 ◽  
Author(s):  
K. Watanabe ◽  
T. Yoshimura ◽  
T. Soeda
Keyword(s):  
Discrete Time ◽  
Adaptive Filter ◽  
Adaptive Estimation ◽  
Gaussian White Noise ◽  
Numerical Procedure ◽  
Linear Partial Differential Equation ◽  
Distributed Parameter Systems ◽  
Complete Orthonormal System ◽  
Distributed Parameter ◽  
Nonlinear Part

A discrete-time adaptive filter is derived for a distributed system described by a linear partial differential equation with some unknown random constants whose a priori probabilities are known. The system concerned contains the Gaussian white noise in time, and its measurement system is treated as a so-called pointwise observation in which the measurement is taken at the finite discrete subdomains in the coordinate spaces. The use is conceptually made of an adaptive technique based on the Bayesian method and it is shown that the optimal distributed filter proposed here can be partitioned into two parts, a linear nonadaptive part that consists of a bank of distributed Kalman-Bucy type filters and a nonlinear part that incorporates the learning nature of the estimator. For the derivation of each “elemental filter”, the discrete-time innovation theory is utilized. The eigenfunction expanding method in a complete orthonormal system is applied for the numerical procedure of the proposed filter. From the simulation of the estimation problem for the neutron flux distribution in a slab type nuclear reactor, the proposed adaptive filter is shown to have attractive characteristics and therefore can be recommended for practical online adaptive estimation of distributed parameter systems.

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