Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Mehdi Tabe Arjmand ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Single Mode ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Model Parameters ◽  
Unstable Periodic Orbits ◽  
Single Mode Approximation

The taping mode Atomic Force Microscopic (T-AFM) can be properly described by a sinusoidal excitation of its base and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In this paper a nonlinear delayed feedback control is proposed to control chaos in a single mode approximation of a T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The effectiveness of the presented methods is numerically verified and the results show the high performance of the controller.

Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Kaveh Merat ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Electrical Circuit ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Parameter Uncertainties ◽  
First Order

In this paper a nonlinear delayed feedback control is proposed to control chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs). Firstly, the system parameters assumed to be known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then the sliding mode scheme of the proposed controller is presented in presence of model parameter uncertainties. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first order periodic orbit and is compared with a typical linear delayed feedback control. Simulation results show the high performance of the methods for chaos elimination in Sprott circuit.

Chaos Control in Continuous Mode of T-AFM Systems Using Nonlinear Delayed Feedback via Sliding Mode Control

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Potential Interaction ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Model Parameters ◽  
Unstable Periodic Orbits ◽  
Nonlinear Potential ◽  
The Galerkin Method

The taping mode Atomic Force Microscopic (T-AFM) can be assumed as a cantilever beam which its base is excited by a sinusoidal force and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In order to modeling, using the galerkin method, the PDE equation is reduced to a single ODE equation which properly describing the continuous beam. In this paper a nonlinear delayed feedback control is proposed to control chaos in T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The numerical results show the high quality and good performance of the proposed method.

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