scholarly journals Distance function design and Lyapunov techniques for the stability of hybrid trajectories

Automatica ◽  
2016 ◽  
Vol 73 ◽  
pp. 38-46 ◽  
Author(s):  
J.J. Benjamin Biemond ◽  
W.P. Maurice H. Heemels ◽  
Ricardo G. Sanfelice ◽  
Nathan van de Wouw
Keyword(s):  
Distance Function ◽  
Lyapunov Techniques ◽  
Function Design ◽  
The Stability ◽  
Hybrid Trajectories

scholarly journals A Robust Control Scheme for Renewable-Based Distributed Generators Using Artificial Hydrocarbon Networks

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1896 ◽  
Author(s):  
Antonio Rosales ◽  
Pedro Ponce ◽  
Hiram Ponce ◽  
Arturo Molina
Keyword(s):  
Robust Control ◽  
Control Algorithm ◽  
Solar Panels ◽  
Lyapunov Techniques ◽  
Distributed Generators ◽  
Stability Robustness ◽  
Network Controller ◽  
Control Scheme ◽  
Power Regulation ◽  
The Stability

Distributed generators (DGs) based on renewable energy systems such as wind turbines, solar panels, and storage systems, are key in transforming the current electric grid into a green and sustainable network. These DGs are called inverter-interfaced systems because they are integrated into the grid through power converters. However, inverter-interfaced systems lack inertia, deteriorating the stability of the grid as frequency and voltage oscillations emerge. Additionally, when DGs are connected to the grid, its robustness against unbalanced conditions must to be ensured. This paper presents a robust control scheme for power regulation in DGs, which includes inertia and operates under unbalanced conditions. The proposed scheme integrates a robust control algorithm to ensured power regulation, despite unbalanced voltages. The control algorithm is an artificial hydrocarbon network controller, which is a chemically-inspired technique, based on carbon networks, that provides stability, robustness, and accuracy. The robustness and stability of the proposed control scheme are tested using Lyapunov techniques. Simulation, considering one- and three-phase voltage sags, is executed to validate the performance of the control scheme.

scholarly journals Subgeometric Ergodicity under Random-Time State-Dependent Drift Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Stochastic Networks ◽  
Random Time ◽  
Stopping Times ◽  
Lyapunov Techniques ◽  
State Dependent ◽  
Drift Conditions ◽  
The Stability

Motivated by possible applications of Lyapunov techniques in the stability of stochastic networks, subgeometric ergodicity of Markov chains is investigated. In a nutshell, in this study we take a look atf-ergodic general Markov chains, subgeometrically ergodic at rater, when the random-time Foster-Lyapunov drift conditions on a set of stopping times are satisfied.

Regions of asymptotic stability of dynamic systems by the combination of Lyapunov techniques and digital simulation

SIMULATION ◽  
1965 ◽  
Vol 5 (6) ◽  
pp. 384-391 ◽  
Author(s):  
Thomas Z. Fahidy
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Dynamic Systems ◽  
Digital Simulation ◽  
Systematic Search ◽  
Function Technique ◽  
Lyapunov Techniques ◽  
Machine Interference ◽  
The Stability

The usefulness of the combination of the Lyapunov function technique and digital simulation for the stability analysis of dynamic systems is illustrated in two examples where the region of asymptotic sta bility is estimated by the analytical Lyapunov ap proach and established by a systematic search via digital simulation of the Lyapunov function. The ad vantage of the PACTOLUS simulator, with particular regard to man-to-machine interference, is empha sized.

Adaptive control of the TORA system with partial state constraint

2018 ◽  
Vol 41 (4) ◽  
pp. 1172-1177 ◽  
Author(s):  
Xianqing Wu ◽  
Minming Gu
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
State Constraint ◽  
Parameter Uncertainties ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Lyapunov Techniques ◽  
Adaptive Control Strategy ◽  
The Stability ◽  
Rotational Actuator

In this paper, we consider the problem of stabilization of a translational oscillator with a rotational actuator (TORA) system. In practical applications, TORA systems usually suffer from parametric uncertainties. Moreover, existing control methods for TORA systems cannot guarantee the rotational scope of the actuator and often lead to unwanted unwinding behaviour. To handle these issues, we present an adaptive control strategy for TORA systems with uncertain or unknown parameters, which is robust to parameter uncertainties and can guarantee that the rotational actuator rotates in a preset range. Specifically, a Lyapunov function is elegantly constructed on the basis of the nonlinear interaction between the translational oscillator and the eccentric rotational proof mass. Then an adaptive control method, along with an online estimation mechanism, is proposed straightforwardly and the stability of the closed-loop system is proven, invoking Lyapunov techniques and LaSalle’s invariance principle. Simulation results are provided to demonstrate the performance of the presented method.

On Stability of N-Dimensional Dynamical Systems

2009 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Distance Function ◽  
Relative Distance ◽  
Stability Of Equilibrium ◽  
The Stability

This paper presents a theory of the stability of equilibrium in dynamical systems. The measuring function is introduced through a relative distance function. The kth -order, G – functions at the equi-measuring function surface and the increment of the equi-measuring function are introduced. Based on the kth -order, G – functions, a theory for the stability of dynamical system is presented, including the definitions and theorems.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Sign in / Sign up

Export Citation Format

Share Document