scholarly journals Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

2021 ◽  
Author(s):  
Giuseppe Habib
Keyword(s):  
Iterative Procedure ◽  
System Parameter ◽  
Basin Of Attraction ◽  
Mechanical Systems ◽  
Industrial Applications ◽  
Viable Alternative ◽  
Integrity Assessment ◽  
Stable Equilibria ◽  
Short Time ◽  
The Basin Of Attraction

AbstractA new algorithm for the estimation of the robustness of a dynamical system’s equilibrium is presented. Unlike standard approaches, the algorithm does not aim to identify the entire basin of attraction of the solution. Instead, it iteratively estimates the so-called local integrity measure, that is, the radius of the largest hypersphere entirely included in the basin of attraction of a solution and centred in the solution. The procedure completely overlooks intermingled and fractal regions of the basin of attraction, enabling it to provide a significant engineering quantity in a very short time. The algorithm is tested on four different mechanical systems of increasing dimension, from 2 to 8. For each system, the variation of the integrity measure with respect to a system parameter is evaluated, proving the engineering relevance of the results provided. Despite some limitations, the algorithm proved to be a viable alternative to more complex and computationally demanding methods, making it a potentially appealing tool for industrial applications.

scholarly journals Adaptive multimode signal reconstruction from time–frequency representations

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150205 ◽  
Author(s):  
Sylvain Meignen ◽  
Thomas Oberlin ◽  
Philippe Depalle ◽  
Patrick Flandrin ◽  
Stephen McLaughlin
Keyword(s):  
Signal Reconstruction ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Alternative View ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Fm Signals ◽  
Adaptive Reconstruction ◽  
Short Time ◽  
The Basin Of Attraction

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM–FM signals by their time–frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM–FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges . An alternative view is to consider a mode as a particular TF domain termed a basin of attraction . Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

scholarly journals Experimental investigation on a novel approach for laser surface hardening modelling

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
L. Orazi ◽  
A. Rota ◽  
B. Reggiani
Keyword(s):  
Surface Hardening ◽  
Carbon Diffusion ◽  
Industrial Applications ◽  
Laser Surface ◽  
Simplified Approach ◽  
Laser Surface Hardening ◽  
Novel Approach ◽  
Laser Treatments ◽  
High Flexibility ◽  
Short Time

AbstractLaser surface hardening is rapidly growing in industrial applications due to its high flexibility, accuracy, cleanness and energy efficiency. However, the experimental process optimization can be a tricky task due to the number of involved parameters, thus suggesting for alternative approaches such as reliable numerical simulations. Conventional laser hardening models compute the achieved hardness on the basis of microstructure predictions due to carbon diffusion during the process heat thermal cycle. Nevertheless, this approach is very time consuming and not allows to simulate real complex products during laser treatments. To overcome this limitation, a novel simplified approach for laser surface hardening modelling is presented and discussed. The basic assumption consists in neglecting the austenite homogenization due to the short time and the insufficient carbon diffusion during the heating phase of the process. In the present work, this assumption is experimentally verified through nano-hardness measurements on C45 carbon steel samples both laser and oven treated by means of atomic force microscopy (AFM) technique.

scholarly journals Optimization and Stability of Heat Engines: The Role of Entropy Evolution

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 865 ◽  
Author(s):  
Julian Gonzalez-Ayala ◽  
Moises Santillán ◽  
Maria Santos ◽  
Antonio Calvo Hernández ◽  
José Mateos Roco
Keyword(s):  
Local Stability ◽  
Production Efficiency ◽  
Basin Of Attraction ◽  
Heat Engine ◽  
Time Constraints ◽  
Thermal Gradients ◽  
Heat Engines ◽  
Low Dissipation ◽  
The Basin Of Attraction

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed.

scholarly journals Time Delay and Feedback Control of an Inverted Pendulum With Stick Slip Friction

2007 ◽  
Author(s):  
Sue Ann Campbell ◽  
Stephanie Crawford ◽  
Kirsten Morris
Keyword(s):  
Time Delay ◽  
Basin Of Attraction ◽  
Critical Time ◽  
Viscous Friction ◽  
Experimental System ◽  
Friction Model ◽  
Stable Equilibrium Point ◽  
Feedback Controllers ◽  
Stick Slip ◽  
The Basin Of Attraction

We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart which can move in one dimension. There is stick slip friction between the cart and the track on which it moves. Using two different models for this friction we design feedback controllers to stabilize the pendulum in the upright position. We show that controllers based on either friction model give better performance than one based on a simple viscous friction model. We then study the effect of time delay in this controller, by calculating the critical time delay where the system loses stability and comparing the calculated value with experimental data. Both models lead to controllers with similar robustness with respect to delay. Using numerical simulations, we show that the effective critical time delay of the experiment is much less than the calculated theoretical value because the basin of attraction of the stable equilibrium point is very small.

Retrogression and Re-aging Heat Treatment: AA7XXX Aluminum Alloys

2019 ◽  
Author(s):  
V. Anil Kumar ◽  
S. Arjun ◽  
R.K. Gupta ◽  
P.V. Venkitakrishnan
Keyword(s):  
Heat Treatment ◽  
Aluminum Alloys ◽  
Industrial Applications ◽  
Age Hardening ◽  
Large Cross Section ◽  
Structural Applications ◽  
The Matrix ◽  
Peak Aged ◽  
Aged Temper ◽  
Short Time

Retrogression and re-aging (RRA) treatment was introduced to increase the stress corrosion cracking (SCC) resistance while retaining the strength attainable in T6 (peak aged) temper. Retrogression is a short-term heat treatment at an elevated temperature wherein a partial dissolution of metastable precipitates occurs, which are responsible for the hardening. During the next step, the material is re-aged in the regime of typical age hardening parameters to restore the strength with improved ductility. Response of RRA treatment has been reported on AA7XXX series Aluminum alloys such as AA7075, AA7050, AA7150, AA7049, and AA7010. Studies have been done on the effect of RRA on microstructure, mechanical properties such as tensile and hardness, corrosion, exfoliation corrosion, and SCC resistance by various researchers. The key characteristic of RRA is retrogression, which makes the re-precipitation in the matrix and coarsening of grain boundary precipitates such as MgZn2, η′. The retrogression treatment however requires high temperature and a short time, which limits the industrial application of RRA, especially in the heat treatment of the components with large cross section, due to the inherent thermal conductivity limitations. Hence, further work needs to be done in this area to apply this specialized heat treatment for industrial applications. This article brings out a comprehension of the changes in microstructure, tensile properties, and corrosion resistance of the various commonly used AA7XXX Aluminum alloys in structural applications with RRA heat treatment. The future scope of the work in RRA heat treatment is also discussed in this article.

Stable running of a planar underactuated biped robot

Robotica ◽  
2010 ◽  
Vol 29 (5) ◽  
pp. 657-665 ◽  
Author(s):  
Yong Hu ◽  
Gangfeng Yan ◽  
Zhiyun Lin
Keyword(s):  
Limit Cycle ◽  
Stance Phase ◽  
Control Strategies ◽  
Basin Of Attraction ◽  
Biped Robot ◽  
State Spaces ◽  
Continuous State ◽  
Event Based ◽  
Telescopic Legs ◽  
The Basin Of Attraction

SUMMARYThis paper investigates the stable-running problem of a planar underactuated biped robot, which has two springy telescopic legs and one actuated joint in the hip. After modeling the robot as a hybrid system with multiple continuous state spaces, a natural passive limit cycle, which preserves the system energy at touchdown, is found using the method of Poincaré shooting. It is then checked that the passive limit cycle is not stable. To stabilize the passive limit cycle, an event-based feedback control law is proposed, and also to enlarge the basin of attraction, an additive passivity-based control term is introduced only in the stance phase. The validity of our control strategies is illustrated by a series of numerical simulations.

Basin of Attraction of the Simplest Walking Model

2001 ◽  
Author(s):  
A. L. Schwab ◽  
M. Wisse
Keyword(s):  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Mapping Method ◽  
Walking Robots ◽  
Natural Energy ◽  
Walking Motion ◽  
The Stability ◽  
The Basin Of Attraction ◽  
General Method ◽  
Small Disturbances

Abstract Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

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