In this paper,local stability and performance analysis of fractional-order linear systems with saturating elements are shown,which lead to less conservative information and data on the region of stability and the dist...In this paper,local stability and performance analysis of fractional-order linear systems with saturating elements are shown,which lead to less conservative information and data on the region of stability and the disturbance rejection.Then,a standard performance analysis and global stability by using Lyapunov’s second method are addressed,and the introduction of Lyapunov’s function candidate whose sub-level set provide stability region and performance with a restricted state space origin is also addressed.The results include both single and multiple saturation elements and can be extended to fractional-order linear systems with any nonlinear elements and nonlinear noise that satisfy Lipschitz condition.A noticeable application of these techniques is analysis of control fractional-order linear systems with saturation control inputs.展开更多
Purpose-The purpose of this paper is to address the problem of control in a typical chaotic power system.Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not ...Purpose-The purpose of this paper is to address the problem of control in a typical chaotic power system.Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers.So,the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties.Closed-loop stability is proved using the Lyapunov stability theory.The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system,eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures.Design/methodology/approach-The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties.Closed-loop stability is proved using the Lyapunov stability theory.Findings-Closed-loop stability is proved using the Lyapunov stability theory.The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system,eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures.Originality/value-Main contributions of the paper are as follows:the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed;designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time;while the generator speed is constant,the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time;stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory;simulation of the proposed controller shows that the chattering is low control signal.展开更多
In this paper,a fractional-order adaptive sliding mode controller is designed to synchronise a fractional-order chaotic gyroscope with fractional dynamics.To this end,the error dynamic is defined first and then the ad...In this paper,a fractional-order adaptive sliding mode controller is designed to synchronise a fractional-order chaotic gyroscope with fractional dynamics.To this end,the error dynamic is defined first and then the adaptive slidingmodesynchroniser is designed using through defining a proper sliding surface and estimating uncertainty parameters of the master and slave system and its stability is proved using the Lyapunov theorem.The important point is the efficiency of the controller against input disturbance and uncertainty.Finally,the proposed controller is simulated in MATLAB and the results indicate that the introduced fractional-order chaotic system using an adaptive sliding mode controller is able to synchronise the fractional-order chaotic gyroscope.展开更多
文摘In this paper,local stability and performance analysis of fractional-order linear systems with saturating elements are shown,which lead to less conservative information and data on the region of stability and the disturbance rejection.Then,a standard performance analysis and global stability by using Lyapunov’s second method are addressed,and the introduction of Lyapunov’s function candidate whose sub-level set provide stability region and performance with a restricted state space origin is also addressed.The results include both single and multiple saturation elements and can be extended to fractional-order linear systems with any nonlinear elements and nonlinear noise that satisfy Lipschitz condition.A noticeable application of these techniques is analysis of control fractional-order linear systems with saturation control inputs.
文摘Purpose-The purpose of this paper is to address the problem of control in a typical chaotic power system.Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers.So,the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties.Closed-loop stability is proved using the Lyapunov stability theory.The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system,eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures.Design/methodology/approach-The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties.Closed-loop stability is proved using the Lyapunov stability theory.Findings-Closed-loop stability is proved using the Lyapunov stability theory.The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system,eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures.Originality/value-Main contributions of the paper are as follows:the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed;designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time;while the generator speed is constant,the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time;stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory;simulation of the proposed controller shows that the chattering is low control signal.
文摘In this paper,a fractional-order adaptive sliding mode controller is designed to synchronise a fractional-order chaotic gyroscope with fractional dynamics.To this end,the error dynamic is defined first and then the adaptive slidingmodesynchroniser is designed using through defining a proper sliding surface and estimating uncertainty parameters of the master and slave system and its stability is proved using the Lyapunov theorem.The important point is the efficiency of the controller against input disturbance and uncertainty.Finally,the proposed controller is simulated in MATLAB and the results indicate that the introduced fractional-order chaotic system using an adaptive sliding mode controller is able to synchronise the fractional-order chaotic gyroscope.
