scholarly journals Neural Network Based Semi-Empirical Models for Dynamical Systems Represented by Differential-Algebraic Equations of Index 2

2018 ◽  
Vol 123 ◽  
pp. 252-257 ◽  
Author(s):  
Dmitry S. Kozlov ◽  
Yury V. Tiumentsev
Keyword(s):  
Neural Network ◽  
Dynamical Systems ◽  
Differential Algebraic Equations ◽  
Empirical Models ◽  
Algebraic Equations ◽  
Index 2 ◽  
Semi Empirical

scholarly journals Biodiesel Production by Reactive Flash: A Numerical Simulation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Alejandro Regalado-Méndez ◽  
Sigurd Skogestad ◽  
Reyna Natividad ◽  
Rubí Romero
Keyword(s):  
Numerical Simulation ◽  
Differential Algebraic Equations ◽  
Biodiesel Production ◽  
Algebraic Equations ◽  
Flow Ratio ◽  
Bubble Point ◽  
Biodiesel Quality ◽  
Index 2 ◽  
Globally Stable ◽  
System Approaches

Reactive flash (RF) in biodiesel production has been studied in order to investigate steady-state multiplicities, singularities, and effect of biodiesel quality when the RF system approaches to bubble point. The RF was modeled by an index-2 system of differential algebraic equations, the vapor split (ϕ) was computed by modified Rachford-Rice equation and modified Raoult’s law computed bubble point, and the continuation analysis was tracked on MATCONT. Results of this study show the existence of turning points, leading to a unique bubble point manifold,(xBiodiesel,T)=(0.46,478.41 K), which is a globally stable flashing operation. Also, the results of the simulation in MATLAB® of the dynamic behavior of the RF show that conversion of triglycerides reaches 97% for a residence time of 5.8 minutes and a methanol to triglyceride molar flow ratio of 5 : 1.

An implicit class of continuous dynamical system with data-sample outputs: a robust approach

2019 ◽  
Vol 37 (2) ◽  
pp. 589-606
Author(s):  
Raymundo Juarez ◽  
Vadim Azhmyakov ◽  
A Tadeo Espinoza ◽  
Francisco G Salas
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Models ◽  
Differential Algebraic Equations ◽  
Linear Feedback ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Nonlinear Dynamical ◽  
Ellipsoid Method ◽  
Invariant Ellipsoid

Abstract This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

scholarly journals On Asymptotics in Case of Linear Index-2 Differential-Algebraic Equations

1998 ◽  
Vol 35 (4) ◽  
pp. 1326-1346 ◽  
Author(s):  
Michael Hanke ◽  
Ebroul Izquierdo Macana ◽  
Roswitha März
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Index ◽  
Index 2

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

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