scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

Energy harvesting for actuators and sensors using free-floating flaps

2016 ◽  
Vol 28 (2) ◽  
pp. 163-177 ◽  
Author(s):  
Lars O Bernhammer ◽  
Roeland De Breuker ◽  
Moti Karpel
Keyword(s):  
Limit Cycle ◽  
Vibrational Energy ◽  
Stable Limit Cycle ◽  
Electric Circuit ◽  
Electronic System ◽  
Rotational Axis ◽  
Stable Limit ◽  
Limit Cycle Oscillations ◽  
Trailing Edge ◽  
The Stability

A novel configuration of an energy harvester for local actuation and sensing devices using limit cycle oscillations has been modeled, designed and tested. A wing section has been designed with two trailing-edge free-floating flaps. A free-floating flap is a flap that can freely rotate around a hinge axis and is driven by trailing edge tabs. In the rotational axis of each flap a generator is mounted that converts the vibrational energy into electricity. It has been demonstrated numerically how a simple electronic system can be used to keep such a system at stable limit cycle oscillations by varying the resistance in the electric circuit. Additionally, it was shown that the stability of the system is coupled to the charge level of the battery, with increasing charge level leading to a less stable system. The system has been manufactured and tested in the Open Jet Wind Tunnel Facility of the Technical University Delft. The numerical results could be validated successfully and voltage generation could be demonstrated at cost of a decrease in lift of 2%.

scholarly journals An analysis of instabilities and limit cycles in glacier-dammed reservoirs

2019 ◽  
Author(s):  
Christian Schoof
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Water Storage ◽  
Drainage System ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Outburst Floods ◽  
The World ◽  
The Stability ◽  
Glacial Hazards

Abstract. Glacier lake outburst floods are common glacial hazards around the world. How big such floods can become (either in terms of peak discharge or in terms of total volume released) depends on how they are initiated: what causes the runaway enlargement of a subglacial or other conduit to start, and how big can the lake get before that point is reached? Here we investigate how the spontaneous channelization of a linked-cavity drainage system controls the onset of floods. In agreement with previous work, we show that floods only occur in a band of water throughput rates, and identify stabilizing mechanisms that allow steady drainage of an ice-dammed reservoir. We also show how stable limit cycle solutions emerge from the instability, a show how and why the stability properties of a drainage system with spatially spread-out water storage differ from those where storage is localized in a single reservoir or lake.

Inducing sustained oscillations in a class of nonlinear discrete time systems

2016 ◽  
Vol 24 (6) ◽  
pp. 1162-1170 ◽  
Author(s):  
AR Hakimi ◽  
T Binazadeh
Keyword(s):  
Limit Cycle ◽  
Discrete Time ◽  
Stable Limit Cycle ◽  
Domain Of Attraction ◽  
Stable Limit ◽  
Discrete Time System ◽  
Sustained Oscillations ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Inducing sustained oscillations in a class of nonlinear discrete time systems is studied in this paper. The novelty of this paper is based on the proposed approach in generating stable oscillations according to limit cycle control. The limit cycle control is not formulated for nonlinear discrete time systems of any order and this paper concentrates on this issue. Considering the stable limit cycle as a positive limit set for the dynamical system, a nonlinear control law is designed to create the considered limit cycle in the phase trajectories of the closed-loop nonlinear discrete time system to achieve oscillations with the desirable amplitude and frequency. For this purpose, firstly, the limit cycle control is proposed for second-order nonlinear discrete time systems. The stability analysis of the generated limit cycle is done via a suitable Lyapunov function. Also, the domain of attraction of the created limit cycle is calculated. The proposed method is then extended for nonlinear discrete time systems of any order via the backstepping technique. Finally, computer simulations are performed for a practical example to demonstrate the ability of the designed controller in generating stable oscillations.

An Analysis of Micro Aeroelastic Energy Harvesting Devices

2009 ◽  
Author(s):  
Daniel G. Cole ◽  
Lisa M. Weiland
Keyword(s):  
Power Generation ◽  
Renewable Energy ◽  
Energy Harvesting ◽  
Limit Cycle ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Energy Harvesters ◽  
The Stability ◽  
Energy Harvesting Devices ◽  
Multi Mode

New micro renewable energy harvesting devices are being developed using the stable limit cycle response of aeroelastic systems to drive energy conversion. This paper analyzes such devices. This paper investigates devices that use two types of aeroelastic instability: galloping and multi-mode flutter. Since the generation of power can be stabilizing, resulting in no power generation at all, the analysis begins by analyzing the stability of such devices from the perspective of power generation. Next, the level of power generation is discussed, and peak levels of performance are found. The analysis suggests that with proper tuning the power generation of micro aeroelastic energy harvesters operating at representative speeds (∼4.5 m/s (10 mph)) can produce power on the order of 10 mW.

scholarly journals On stability Conditions of Burr X Autoregressive model

2019 ◽  
Vol 24 (5) ◽  
pp. 91
Author(s):  
Zena. S. Khalaf ◽  
, Azher. A. Mohammad
Keyword(s):  
Limit Cycle ◽  
Autoregressive Model ◽  
Cumulative Distribution Function ◽  
Linearization Method ◽  
Cumulative Distribution ◽  
Stability Conditions ◽  
Proposed Model ◽  
Nonlinear Autoregressive Model ◽  
Nonlinear Autoregressive ◽  
Local Linearization Method

This article deals with proposed nonlinear autoregressive model based on Burr X cumulative distribution function known as Burr X AR (p), we demonstrate stability conditions of the proposed model in terms of its parameters by using dynamical approach known as local linearization method to find stability conditions of a nonzero fixed point of the proposed model, in addition the study demonstrate stability condition of a limit cycle if Burr X AR (1) model have a limit cycle of period greater than one.   http://dx.doi.org/10.25130/tjps.24.2019.096

Bouncing Mode Electrostatically Actuated Scanning Micromirror for Laser Display Applications

2004 ◽  
Author(s):  
Viacheslav Krylov ◽  
Daniel I. Barnea
Keyword(s):  
Limit Cycle ◽  
Actuation Voltage ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Operational Mode ◽  
Electrostatically Actuated ◽  
Laser Display ◽  
Voltage Dependent ◽  
Operational Frequency ◽  
The Stability

In laser display applications, the necessity to create images free of distortions imposes specific requirements on the motion of scanning devices. We present an approach of a scanning micromirror operation that is aimed to fulfill the requirements of motion linearity, high operational frequency and low actuation voltages. The operational mode incorporates a contact event between the mirror and an elastic constraint followed by a bouncing event and a subsequent inversion of motion. A stable limit cycle with voltage-dependent frequency and triangular response signal is obtained by the application of an actuation voltage which is piecewise constant in time. Approximate expressions relating the frequency and amplitude of the response with the actuating voltage are obtained by energy balance method. The influence of contact losses on the response as well as the stability of the limit cycle are studied numerically.

Stability of a relay dynamic system with non-linear speed sensor and delay under constant disturbance

2020 ◽  
Author(s):  
R.P. Simonyants ◽  
B.R. Khudaybergenov
Keyword(s):  
Dynamic System ◽  
Limit Cycle ◽  
Initial Conditions ◽  
Stable Limit Cycle ◽  
Approximate Determination ◽  
Cycle Phase ◽  
Stable Limit ◽  
Speed Sensor ◽  
Unstable Limit Cycle ◽  
The Stability

The paper considers the joint effect of the control delay and speed sensor output signal limiting on the stability of the relay dynamic system under the constant disturbance. It is shown that in this case a new property is detected in the system – the appearance of the unstable limit cycle. Phase trajectories are drawn to a stable limit cycle only from the area of initial conditions where their boundaries are determined by the trajectory of an unstable limit cycle. Using the method of Poincare mappings, the parameters of fixed points defining the unstable limit cycle as the boundary of the stability region are found. A simplified method for approximate determination of simple limit cycles and stability in the “large” is proposed based on the property of dynamic symmetry of the system. The method allows the study of the problem under consideration to be limited to applying shift and symmetry mappings to the switching lines.

Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response

2016 ◽  
Vol 26 (02) ◽  
pp. 1650034 ◽  
Author(s):  
Jicai Huang ◽  
Xiaojing Xia ◽  
Xinan Zhang ◽  
Shigui Ruan
Keyword(s):  
Functional Response ◽  
Limit Cycle ◽  
Stable Limit Cycle ◽  
Positive Equilibrium ◽  
Stable Limit ◽  
Homoclinic Loop ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Stable Equilibria

It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

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