Robust Stabilization of a Class of Uncertain Fractional-order Chaotic Systems via a Novel Sliding Mode Control Scheme

Xiaomin Tian,Shumin Fei,Lin Chai 보안공학연구지원센터 2014 International Journal of Hybrid Information Techno Vol.7 No.6

This paper proposes a novel sliding mode control (SMC) scheme to stabilize a class of fractional-order chaotic systems. Through constructing two sliding mode variables, the control problem of n-dimensional system can be transformed to the equivalent stabilizing problem of a reduced-order system. Subsequently, on the basis of second-order sliding mode (SOSM) technique, a robust control law is designed, which strongly attenuates the chattering phenomenon inherent in traditional sliding mode controller, and guarantees the existence of sliding motion in a finite time. The stability of two sliding mode variables to the origin is proved by conventional and fractional Lyapunov theories, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Thermoelastic deformation properties of non-localized and axially moving viscoelastic Zener nanobeams

Ahmed E. Abouelregal,Badahi Ould Mohamed,Hamid M. Sedighi Techno-Press 2024 Advances in nano research Vol.16 No.2

This study aims to develop explicit models to investigate thermo-mechanical interactions in moving nanobeams. These models aim to capture the small-scale effects that arise in continuous mechanical systems. Assumptions are made based on the Euler-Bernoulli beam concept and the fractional Zener beam-matter model. The viscoelastic material law can be formulated using the fractional Caputo derivative. The non-local Eringen model and the two-phase delayed heat transfer theory are also taken into account. By comparing the numerical results to those obtained using conventional heat transfer models, it becomes evident that non-localization, fractional derivatives and dual-phase delays influence the magnitude of thermally induced physical fields. The results validate the significant role of the damping coefficient in the system's stability, which is further dependent on the values of relaxation stiffness and fractional order.

Optimized Fuzzy Fractional-order Controller for a Nonlinear Chaos System With Period-doubling Bifurcation Analysis

Eman Moustafa,Belal Abou-Zalam,Abdel-Azem Sobaih,Essam Nabil,Amged Sayed 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.10

Chaos study and control is one of the dynamic fields of research nowadays. The non-linear dynamic behavior such as fast scale bifurcation results in an unpredictable chaos action so it is essential to eliminate this behavior. So, the main objective of this paper is to propose an optimized fuzzy fractional PID controller to suppress the chaos action and stabilize a nonlinear chaotic. The cuckoo search optimization (CSO) technique’s optimal solution is used to optimize the fractional order controller parameters while considering integral time absolute error as the objective function and the FLC will adapt the controller parameters so that it provides a good performance. Here, the boost converter for permanent magnet DC motor is selected as a chaotic system as case study. The dynamic characteristic of the system is analysed by waveform, phase portrait, and Fillipov theory. Then, the proposed controller is compared with three additional controllers, such as controlling saltation matrix, optimized-PID, and optimizedFractional PID. The proposed technique enhances the performance of the system and stabilized the response of the output and suppress the bifurcation behavior for nonlinear system. Finally, the effectiveness of the proposed technique has justified by simulation results on the PMDC drive system in a specified interval with variation the load to emphasize its superiority over all other controllers.

Static analysis of the FGM plate with porosities

R. Benferhat,T. Hassaine Daouadji,L. Hadji,M. Said Mansour 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.21 No.1

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

Bending analysis of an imperfect advanced composite plates resting on the elastic foundations

Daouadji, Tahar Hassaine,Benferhat, Rabia,Adim, Belkacem Techno-Press 2016 Coupled systems mechanics Vol.5 No.3

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

EVALUATION OF A VEHICLE DIRECTIONAL CONTROL WITH A FRACTIONAL ORDER PDμ CONTROLLER

Dejun Zhuang,F. Yu,Y. Lin 한국자동차공학회 2008 International journal of automotive technology Vol.9 No.6

In this paper, a novel controller, the fractional order PDμ controller, is designed to improve the performance of the driver-vehicle system. First, fractional calculus and fractional order PIλDμ controller are introduced. A control algorithm for vehicle directional control using the fractional order PDμ controller is then presented. Based on preview-follower theory, the on-line tuning method of the fractional order PDμ controller is designed. By comparing simulated and experimental results, the validity and robustness of the proposed fractional order PDμ controller in the closed loop system are verified. Finally, comprehensive evaluations are performed between the systems with the fractional order PDμ controller and with an integer PD controller. The results demonstrate that the use of the fractional order controller leads to an improvement of the performance of the driver-vehicle system. In this paper, a novel controller, the fractional order PDμ controller, is designed to improve the performance of the driver-vehicle system. First, fractional calculus and fractional order PIλDμ controller are introduced. A control algorithm for vehicle directional control using the fractional order PDμ controller is then presented. Based on preview-follower theory, the on-line tuning method of the fractional order PDμ controller is designed. By comparing simulated and experimental results, the validity and robustness of the proposed fractional order PDμ controller in the closed loop system are verified. Finally, comprehensive evaluations are performed between the systems with the fractional order PDμ controller and with an integer PD controller. The results demonstrate that the use of the fractional order controller leads to an improvement of the performance of the driver-vehicle system.

Fractional Order IMC Controller Design for Two-input-two-output Fractional Order System

Dazi Li,Xingyu He,Tianheng Song,Qibing Jin 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.4

Research on the fractional order system is becoming more and more popular. Most of the fractional ordercontroller design methods focus on single-input-single-output processes. In this paper, a fractional order internalmodel controller with inverted decoupling is proposed to handle non-integer order two-input-two-output systemswith time delay. The fractional order two-input-two-output (FO-TITO) process is decoupled by inverted decouplingmethod. The fractional order internal model control (IMC) is then used to simplify the tuning process. Because ofthe complexity of multiple time delay, the condition of FO-TITO process with time delay is discussed. In order toensure the robustness of the system, a Maximum sensitivity function is used to tune the parameters. Then Lyapunovstability theory is applied to verify the stability of the system. The proposed controller provides ideal performancefor both set point-tracking and disturbance rejection and is robust to process gain variations. Numerical resultsshow the performance of the proposed method.

Variable properties thermopiezoelectric problem under fractional thermoelasticity

Yongbin Ma,Liuchan Cao,Tianhu He 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.21 No.2

The dynamic response of a finite length thermo-piezoelectric rod with variable material properties is investigated in the context of the fractional order theory of thermoelasticity. The rod is subjected to a moving heat source and fixed at both ends. The governing equations are formulated and then solved by means of Laplace transform together with its numerical inversion. The results of the non-dimensional temperature, displacement and stress in the rod are obtained and illustrated graphically. Meanwhile, the effects of the fractional order parameter, the velocity of heat source and the variable material properties on the variations of the considered variables are presented, and the results show that they significantly influence the variations of the considered variables.

EXISTENCE AND CONTROLLABILITY OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL SYSTEMS WITH STATE-DEPENDENT DELAY IN BANACH SPACES

SUBRAMANIAN KAILASAVALLI,SELVARAJ SUGANYA,MANI MALLIKA ARJUNAN 한국산업응용수학회 2016 Journal of the Korean Society for Industrial and A Vol.20 No.1

In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with statedependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.

Variable properties thermopiezoelectric problem under fractional thermoelasticity

Ma, Yongbin,Cao, Liuchan,He, Tianhu Techno-Press 2018 Smart Structures and Systems, An International Jou Vol.21 No.2

The dynamic response of a finite length thermo-piezoelectric rod with variable material properties is investigated in the context of the fractional order theory of thermoelasticity. The rod is subjected to a moving heat source and fixed at both ends. The governing equations are formulated and then solved by means of Laplace transform together with its numerical inversion. The results of the non-dimensional temperature, displacement and stress in the rod are obtained and illustrated graphically. Meanwhile, the effects of the fractional order parameter, the velocity of heat source and the variable material properties on the variations of the considered variables are presented, and the results show that they significantly influence the variations of the considered variables.