IMPULSIVE CONTROL IN MICROORGANISMS CONTINUOUS FERMENTATION

2012 ◽  
Vol 05 (02) ◽  
pp. 1250013 ◽  
Author(s):  
LIJUAN SHEN ◽  
ENMIN FENG ◽  
QIDI WU
Keyword(s):  
Dynamical System ◽  
Continuous Culture ◽  
Upper Bound ◽  
Impulsive Control ◽  
Continuous Fermentation ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Nonlinear Dynamical ◽  
Control Scheme ◽  
Comparison Technique

This work presents the nonlinear dynamical system of continuous fermentation from glycerol to 1,3-propanediol. The impulsive control scheme of continuous culture is introduced. By employing impulsive control, Lyapunov's method and comparison technique, sufficient conditions are established for the asymptotical stability and synchronization of the dynamical system of continuous fermentation. The upper bound of the impulse interval is also estimated. An example will illustrate the effectiveness of the results in Sec. 4.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

scholarly journals Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1794
Author(s):  
Hilmy Awad ◽  
Ehab H. E. Bayoumi ◽  
Hisham M. Soliman ◽  
Michele De Santis
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Dynamical ◽  
Load Variations ◽  
Invariant Ellipsoid ◽  
Steady State Responses ◽  
Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

DYNAMICAL ESTIMATION OF CALENDAR EFFECTS

2006 ◽  
Vol 06 (01) ◽  
pp. L7-L15
Author(s):  
ALEXANDROS LEONTITSIS
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Noise Level ◽  
Nonlinear Dynamical System ◽  
Main Tool ◽  
Experimental Results ◽  
Accurate Estimation ◽  
Nonlinear Dynamical ◽  
Correlation Integral ◽  
Calendar Effects

The paper introduces a method for estimation and reduction of calendar effects from time series, which their fluctuations are governed by a nonlinear dynamical system and additive normal noise. Calendar effects can be considered deviations of the distribution(s) of particular group(s) of observations that have a common characteristic related to the calendar. The concept of this method is the following: since the calendar effects are not related to the dynamics of the time series, the accurate estimation and reduction will result a time series with a smaller amount of noise level (i.e. more accurate dynamics). The main tool of this method is the correlation integral, due to its inherit capability of modeling both the dynamics and the additive normal noise. Experimental results are presented on the Nasdaq Cmp. index.

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