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chaos-control
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Prediction and Control of Chaos in Permanent Magnet Synchronous Machines
, M.Sc. Thesis Sharif University of Technology ; Tavazoei, Mohammad Saleh (Supervisor)
Abstract
Synchronous machines is one of the most popular machines in industry and in power plants. Because the dynamic of this machine is nonlinear, it can exhibit complex behaviors. In this project we have studied a special case in Permanent Magnet Synchronous Machines. A case in which speed of rotor, frequency, currents amplitude and voltages amplitude change in an irregular manner. This special case is called chaos. Chaos occurs for some specific values of parameters and inputs. In this study in the first step, we have tried to find the chaotic area of parameters of system (Prediction of chaos). Then in the next step, we have designed some controllers which can eliminate chaos in the system. The...
Stabilization of unstable fixed points of fractional-order systems by fractional-order linear controllers and its applications in suppression of chaotic oscillations
, Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 132, Issue 2 , 2010 , Pages 1-7 ; 00220434 (ISSN) ; Haeri, M ; Sharif University of Technology
2010
Abstract
In this paper, two fractional-order linear controllers are proposed to stabilize unstable equilibrium points of a chaotic fractional-order system. The first controller is based on the dynamic output feedback control idea and requires detectability of the linearized model of the fractional-order system on the equilibrium point. The second controller is a dynamic state feedback controller and requires observability of the linearized model. In both considered cases, the stabilizability of the model is assumed. The number of inner states in the second controller is one and therefore its structure is much simpler than the first controller. To illustrate the applicability, these controllers are...
Delayed feedback control of chaotic spinning disk via minimum entropy approach
, Article Nonlinear Analysis, Theory, Methods and Applications ; Volume 69, Issue 10 , 2008 , Pages 3273-3280 ; 0362546X (ISSN) ; Alasty, A ; Sharif University of Technology
2008
Abstract
Chaos control of a spinning disk model via delayed feedback method is presented. The feedback gain is obtained and adapted according to a minimum entropy (ME) algorithm. In this method, stabilizing an unstable fixed point of the system Poincare map is achieved by minimizing the entropy of point distribution on the Poincare section. Simulation results show the feasibility of the proposed method in applying the delayed feedback technique for chaos control of spinning disks. © 2007 Elsevier Ltd. All rights reserved
Chaos Control in Delayed phase Space Constructed by the Takens' Embedding Theory
, M.Sc. Thesis Sharif University of Technology ; Salarieh, Hassan (Supervisor) ; Alasty, Aria (Supervisor)
Abstract
One of the most surprising lessons of dynamical systems theory is that the phase spaces of simple nonlinear systems may contain strange attractors. For certain simple systems, such as pendulum, direct observations of the phase space and finding strange attractors are possible. But physical systems in which all the relevant dynamical variables can be simultaneously monitored are relatively scarce. Takens’ theory shows how a time-series of measurements of a single observable state can be often used to reconstruct qualitative features of the phase space of the system. In this research, using the time-series of one measurable state, an algorithm is proposed to control chaos. The approach...
Chaos control in uncertain dynamical systems using nonlinear delayed feedback
, Article Chaos, Solitons and Fractals ; Volume 41, Issue 1 , 2009 , Pages 67-71 ; 09600779 (ISSN) ; Alasty, A ; Sharif University of Technology
2009
Abstract
In this paper based on the sliding mode concept, a nonlinear delayed feedback control is proposed for stabilizing the unstable periodic orbits (UPOs) of chaotic systems. It is assumed that the period of the desired UPO is known, but its time series and the initial conditions generated the UPO are not available. The ability of the proposed control method in stabilizing the UPO of the chaotic systems is analytically proved and the effectiveness of the method is numerically examined by applying it to the chaotic Duffing system. © 2007 Elsevier Ltd. All rights reserved
Chaos control via a simple fractional-order controller
, Article Physics Letters, Section A: General, Atomic and Solid State Physics ; Volume 372, Issue 6 , 2008 , Pages 798-807 ; 03759601 (ISSN) ; Haeri, M ; Sharif University of Technology
Elsevier
2008
Abstract
In this Letter, we propose a fractional-order controller to stabilize the unstable fixed points of an unstable open-loop system. Also, we show that this controller has strong ability to eliminate chaotic oscillations or reduce them to regular oscillations in the chaotic systems. This controller has simple structure and is designed very easily. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of uncertain chaotic systems. © 2007 Elsevier B.V. All rights reserved
Stabilization of unstable fixed points of chaotic fractional order systems by a state fractional PI controller
, Article European Journal of Control ; Volume 14, Issue 3 , 2008 , Pages 247-257 ; 09473580 (ISSN) ; Haeri, M ; Sharif University of Technology
Lavoisier
2008
Abstract
This paper presents a new method to control chaos in fractional order systems based on the fractional control theory. The proposed controller is a fractional P1 (PIα) controller and can locally stabilize unstable equilibrium points of a class of chaotic fractional order systems. Using the ideas available in the chaos control methods such as On-Grebogi-Yorke (OGY), this local stabilization can be extended to the global stabilization. The controller has simple structure and its parameters can be determined by pole placement technique. To illustrate its capability, the proposed controller is applied to control chaos in the fractional order unified system. Numerical simulations confirm the...
Chaos Control in Continuous Time Systems Using Delayed Phase Space Constructed by Takens’ Embedding Theory
, M.Sc. Thesis Sharif University of Technology ; Salarieh, Hassan (Supervisor)
Abstract
This research has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states. There are many chaotic systems with these features occurring in many biological, economical and mechanical systems. The usual chaos control methods do not have the ability to present a systematic control method for these kinds of systems. To fulfill these strict conditions we have employed Takens embedding theory which guarantees the preservation of topological characteristics of the chaotic attractor under an embedding named "Takens transformation". Takens transformation just needs time series of one of the measurable states. This transformation...
Studying Synchronization Control in Complex Systems
, M.Sc. Thesis Sharif University of Technology ; Rahimi Tabar, Mohammad Reza (Supervisor)
Abstract
In this thesis, we review recent advances on controlling of complex systems. We provide in details, the concepts of synchronizability and synchronization controllability.Then we will investigate synchronization controllability under different pinning schemes, and propose a new pinning strategy to increase controllability and consequently decrease the number of required pinned nodes (known as driver nodes) to assure a stable synchronized state. We also study the network characteristics of resulted sequence of driver nodes. Finally, we will employ our proposed schemes to study the controllability of complex networks of chaotic Rossler oscillators
Minimum entropy control of chaos via online particle swarm optimization method
, Article Applied Mathematical Modelling ; Vol. 36, Issue. 8 , 2012 , pp. 3931-3940 ; ISSN: 0307904X ; Salarieh, H ; Alasty, A ; Sharif University of Technology
Abstract
One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation...
Chaos control in lateral oscillations of spinning disk via linear optimal control of discrete systems
, Article JVC/Journal of Vibration and Control ; Volume 23, Issue 1 , 2017 , Pages 103-110 ; 10775463 (ISSN) ; Ali Nojoumian, M ; Merat, K ; Salarieh, H ; Sharif University of Technology
SAGE Publications Inc
2017
Abstract
Chaos control of a spinning disk having transverse vibration is considered in this article by stabilizing the system on its corresponding unstable periodic orbit (UPO). At the first step, the system continuous-time dynamic equations are quantized by utilizing a proper Poincare map. Then, using the regression method a linear description from the obtained cross points is achieved around the corresponding fixed point of the target UPO. Finally, through solving the Riccati equation, an optimal controller is introduced which stabilizes the system on its unstable fixed point. At the end, the effectiveness of the proposed control method is examined through numerical simulations. © SAGE Publications...
On the control of unknown continuous time chaotic systems by applying takens embedding theory
, Article Chaos, Solitons and Fractals ; Volume 109 , April , 2018 , Pages 53-57 ; 09600779 (ISSN) ; Salarieh, H ; Hajiloo, R ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of...
Taming single input chaotic systems by fractional differentiator-based controller: theoretical and experimental study
, Article Circuits, Systems, and Signal Processing ; Volume 28, Issue 5 , 2009 , Pages 625-647 ; 0278081X (ISSN) ; Haeri, M ; Jafari, S ; Sharif University of Technology
2009
Abstract
A simple fractional differentiator-based controller is proposed to suppress chaos in a 3D single input chaotic system by stabilizing some of the fixed points. The tuning procedure for the proposed controller is based on the stability concepts in the incommensurate fractional order systems. To show the efficiency of the controller, some numerical simulations are given. Also, to evaluate the practical capability of the proposed controller, we experimentally apply it to control chaos in a chaotic circuit. Moreover, some mathematical analyses are presented to show the applicability of the proposed controller, when its structure is not exactly implementable. © Birkhäuser Boston 2009
Control of continuous time chaotic systems with unknown dynamics and limitation on state measurement
, Article Journal of Computational and Nonlinear Dynamics ; Volume 14, Issue 1 , 2019 ; 15551415 (ISSN) ; Salarieh, H ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2019
Abstract
This paper has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states. There are many chaotic systems with these features occurring in many biological, economical and mechanical systems. The usual chaos control methods do not have the ability to present a systematic control method for these kinds of systems. To fulfill these strict conditions, we have employed Takens embedding theorem which guarantees the preservation of topological characteristics of the chaotic attractor under an embedding named "Takens transformation." Takens transformation just needs time series of one of the measurable states. This transformation...
Control of continuous time chaotic systems with unknown dynamics and limitation on state measurement
, Article Journal of Computational and Nonlinear Dynamics ; Volume 14, Issue 1 , 2019 ; 15551415 (ISSN) ; Salarieh, H ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2019
Abstract
This paper has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states. There are many chaotic systems with these features occurring in many biological, economical and mechanical systems. The usual chaos control methods do not have the ability to present a systematic control method for these kinds of systems. To fulfill these strict conditions, we have employed Takens embedding theorem which guarantees the preservation of topological characteristics of the chaotic attractor under an embedding named "Takens transformation." Takens transformation just needs time series of one of the measurable states. This transformation...
Control of Chaotic Waves in Hard Disk Drives
, M.Sc. Thesis Sharif University of Technology ; Jalali, Mir Abbas (Supervisor)
Abstract
Hard disk drives are the main component of computers for permanent data storage. The security of the stored data is related closely to the air gap between the read-write head and the surface of disk. This gap which is created by the aerodynamic force between head and the disk is altered continually by lateral oscillations of disk. In the extreme condition of zero gap and contact between the protective coating layer and subsequently the magnetic material of the disk with the head, the disk will be scratched and damaged. Therefore, the active or passive control of these vibrations has a particular importance in the technology of manufacturing of hard disks. The first step in active control...
Controlling chaos in tapping mode atomic force microscopes using improved minimum entropy control
, Article Applied Mathematical Modelling ; Vol. 37, Issue 3 , 2013 , pp. 1599-1606 ; ISSN: 0307904X ; Salarieh, H ; Alasty, A ; Sharif University of Technology
Abstract
Minimum entropy control technique, an approach for controlling chaos without using the dynamical model of the system, can be improved by being combined with a nature-based optimization technique. In this paper, an ACO-based optimization algorithm is employed to minimize the entropy function of the chaotic system. The feedback gain of a delayed feedback controller is adjusted in the ACO algorithm. The effectiveness of the idea is investigated on suppressing chaos in the tapping-mode atomic force microscope equations. Results show a good performance. The PSO-based version of the minimum entropy control technique is also used to control the chaotic behavior of the AFM, and corresponding results...
variable control of chaos using PSO-based minimum entropy control
, Article Communications in Nonlinear Science and Numerical Simulation ; Vol. 16, Issue. 6 , 2011 , pp. 2397-2404 ; ISSN: 10075704 ; Salarieh, H ; Vossoughi, G ; Alasty, A ; Sharif University of Technology
Abstract
The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback...
On the fuzzy minimum entropy control to stabilize the unstable fixed points of chaotic maps
, Article Applied Mathematical Modelling ; Vol. 35, issue. 3 , 2011 , pp. 1016-1023 ; ISSN: 0307904X ; Merat, K ; Salarieh, H ; Alasty, A ; Sharif University of Technology
Abstract
This paper presents a fuzzy algorithm for controlling chaos in nonlinear systems via minimum entropy approach. The proposed fuzzy logic algorithm is used to minimize the Shannon entropy of a chaotic dynamics. The fuzzy laws are determined in such a way that the entropy function descends until the chaotic trajectory of the system is replaced by a regular one. The Logistic and the Henon maps as two discrete chaotic systems, and the Duffing equation as a continuous one are used to validate the proposed scheme and show the effectiveness of the control method in chaotic dynamical systems
Stabilizing chaotic system on periodic orbits using multi-interval and modern optimal control strategies
, Article Communications in Nonlinear Science and Numerical Simulation ; Volume 17, Issue 10 , 2012 , Pages 3832-3842 ; 10075704 (ISSN) ; Vatankhah, R ; Assadian, N ; Sharif University of Technology
Elsevier
2012
Abstract
In this paper, optimal approaches for controlling chaos is studied. The unstable periodic orbits (UPOs) of chaotic system are selected as desired trajectories, which the optimal control strategy should keep the system states on it. Classical gradient-based optimal control methods as well as modern optimization algorithm Particle Swarm Optimization (PSO) are utilized to force the chaotic system to follow the desired UPOs. For better performance, gradient-based is applied in multi-intervals and the results are promising. The Duffing system is selected for examining the proposed approaches. Multi-interval gradient-based approach can put the states on UPOs very fast and keep tracking UPOs with...