Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed ...Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.展开更多
For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the p...For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the power transmission system displays chaotic oscillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.展开更多
In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned ...In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned power system by means of modern nonlinear theory (Bifurcation and Chaos). Our model is based on a three bus power system that consists of multi generators containing both dynamic and static loads. They are considered to be in the form of an induction motor in parallel with a capacitor, as well as a combination of constant power along with load impedance, PQ. We consider the load reactive power as the control parameter. At this stage, after changing the control parameter, the study showed that the system is experiencing a subcritical Hopf bifurcation point. This leads to a chaos within the system period doubling path. We then discuss the system controllability and present that the all chaotic oscillations fade away through the linear controller that we impose on the system.展开更多
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different ...This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.展开更多
基金Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51521065)
文摘Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.
文摘For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the power transmission system displays chaotic oscillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.
文摘In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned power system by means of modern nonlinear theory (Bifurcation and Chaos). Our model is based on a three bus power system that consists of multi generators containing both dynamic and static loads. They are considered to be in the form of an induction motor in parallel with a capacitor, as well as a combination of constant power along with load impedance, PQ. We consider the load reactive power as the control parameter. At this stage, after changing the control parameter, the study showed that the system is experiencing a subcritical Hopf bifurcation point. This leads to a chaos within the system period doubling path. We then discuss the system controllability and present that the all chaotic oscillations fade away through the linear controller that we impose on the system.
文摘This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
