scholarly journals The State-space Model of Micro-chaos

2021 ◽  
Vol 15 ◽  
pp. 184-189
Author(s):  
Gabor Csernak ◽  
Gabor Stepan
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
State Space Model ◽  
Unstable State ◽  
Considerable Influence ◽  
Chaotic Oscillations ◽  
Controlled System ◽  
Space Model ◽  
Digitally Controlled

Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.

Determination of state-space model uncertainty using bootstrap techniques

2006 ◽  
Vol 16 (7) ◽  
pp. 685-692 ◽  
Author(s):  
Vitor V. Lopes ◽  
Carla C. Pinheiro ◽  
Jose C. Menezes
Keyword(s):  
State Space ◽  
Model Uncertainty ◽  
State Space Model ◽  
Space Model ◽  
Bootstrap Techniques

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

Multivariable modeling and control of an activated sludge process

1998 ◽  
Vol 37 (12) ◽  
pp. 149-156 ◽  
Author(s):  
Carl-Fredrik Lindberg
Keyword(s):  
Activated Sludge ◽  
Nitrate Concentration ◽  
State Space Model ◽  
Activated Sludge Process ◽  
Invariant State ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Space Model ◽  
And Control ◽  
Time Invariant

This paper contains two contributions. First it is shown, in a simulation study using the IAWQ model, that a linear multivariable time-invariant state-space model can be used to predict the ammonium and nitrate concentration in the last aerated zone in a pre-denitrifying activated sludge process. Secondly, using the estimated linear model, a multivariable linear quadratic (LQ) controller is designed and used to control the ammonium and nitrate concentration.

Development of L1-norm sliding mode observer for sensor fault diagnosis of an industrial gas turbine

2021 ◽  
pp. 095965182199617
Author(s):  
Mahyar Akbari ◽  
Abdol Majid Khoshnood ◽  
Saied Irani
Keyword(s):  
Fault Detection ◽  
State Space ◽  
Gas Turbine ◽  
Sliding Mode ◽  
State Space Model ◽  
Sensor Fault ◽  
Space Model ◽  
Decision Logic ◽  
Sensor Fault Detection ◽  
Industrial Gas Turbine

In this article, a novel approach for model-based sensor fault detection and estimation of gas turbine is presented. The proposed method includes driving a state-space model of gas turbine, designing a novel L1-norm Lyapunov-based observer, and a decision logic which is based on bank of observers. The novel observer is designed using multiple Lyapunov functions based on L1-norm, reducing the estimation noise while increasing the accuracy. The L1-norm observer is similar to sliding mode observer in switching time. The proposed observer also acts as a low-pass filter, subsequently reducing estimation chattering. Since a bank of observers is required in model-based sensor fault detection, a bank of L1-norm observers is designed in this article. Corresponding to the use of the bank of observers, a two-step fault detection decision logic is developed. Furthermore, the proposed state-space model is a hybrid data-driven model which is divided into two models for steady-state and transient conditions, according to the nature of the gas turbine. The model is developed by applying a subspace algorithm to the real field data of SGT-600 (an industrial gas turbine). The proposed model was validated by applying to two other similar gas turbines with different ambient and operational conditions. The results of the proposed approach implementation demonstrate precise gas turbine sensor fault detection and estimation.

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