Chongxin Liu

Fast Fixed-time Nonsingular Terminal Sliding Mode Control and its Application to Chaos Suppression in Power System

This brief presents a novel control scheme to achieve fast fixed-time system stabilization. Based on fixed-time stability theory, a novel fixed-time stable system is presented. Using the proposed fixed-time stable system, a fast fixed-time nonsingular terminal sliding mode control method is derived. Our control scheme achieves system stabilization within bounded time independent of the initial condition and has an advantage in convergence rate over the existing result of the fixed-time stable control method. The proposed control strategy is applied to suppress chaotic oscillation in power systems, and its effectiveness as well as superiority is verified through numerical simulation. The proposed control strategy can be applied to address the control and synchronization problem for other complex systems.

EXPERIMENTAL VERIFICATION OF A FOUR-DIMENSIONAL CHUA'S SYSTEM AND ITS FRACTIONAL ORDER CHAOTIC ATTRACTORS

This paper introduces a modified Chuas system which is a smooth four-dimensional continuous-time autonomous chaotic system with a cubic nonlinearity. Some dynamical behaviors of this 4-D Chuas system are further investigated by means of Poincare mapping, parameter phase portraits, equilibrium points, bifurcations and calculated Lyapunov exponents. Moreover, using RC-opamp and analog multiplier we describe a simple electronic circuit for hardware implementation of the 4-D Chuas system which differ from previously reported Chuas circuits. Various attractors of experimental results from this chaotic oscillator are in good agreement with theoretical analysis. In particular, based on the approximation theory of fractional-order operator, a relevant analog circuit diagram of this fractional-order modified Chuas system is designed with α = 0.9. Observation results demonstrate that chaos exists indeed in this fractional-order modified Chuas system with an order as low as 3.6. This fractional-order oscillation circuit, for the first time in the literature, realizes high-dimensional Chuas chaotic system.

Fixed-Time Leader-Following Consensus for Second-Order Multiagent Systems With Input Delay

This paper studies fixed-time leader-following lag consensus problem of second-order multiagent systems with input delay. Using fixed-time distributed observer, we obtain the leaders states for each followers. An extension of the Artsteins reducing transformation is employed to transform the delayed error system into a second-order system without time delay and a novel nonsingular terminal sliding mode protocol is proposed to achieve fixed-time consensus. The presented sliding mode controller can avoid singularity, eliminate chattering, and achieve exact convergence. It is mathematically proved that the presented protocol can achieve exact fixed-time leader-following lag consensus. Moreover, the upper bound of convergence time only depends on observer parameters, controller parameters, network parameters, and delay time, which makes it possible to determine the convergence time offline regardless of initial condition. The presented protocol is applied to coordinated lag tracking control of single-link robotic manipulators and the results validate the effectiveness of the proposed fixed-time protocol.

Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus

In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM). Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.

Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System

A novel nonlinear four-dimensional hyperchaotic system and its fractional-order form are presented. Some dynamical behaviors of this system are further investigated, including Poincare mapping, parameter phase portraits, equilibrium points, bifurcations, and calculated Lyapunov exponents. A simple fourth-channel block circuit diagram is designed for generating strange attractors of this dynamical system. Specifically, a novel network module fractance is introduced to achieve fractional-order circuit diagram for hardware implementation of the fractional attractors of this nonlinear hyperchaotic system with order as low as 0.9. Observation results have been observed by using oscilloscope which demonstrate that the fractional-order nonlinear hyperchaotic attractors exist indeed in this new system.

Chaos suppression for a four-dimensional fundamental power system model using adaptive feedback control

In this paper, the problem of chaos suppression for a four-dimensional fundamental power system (FDFPS) model is considered via the design of a novel adaptive feedback controller. The period doubling bifurcation route to chaos and some dynamical behaviors of the power system are investigated in detail. Based on stability analysis using an energy-type Lyapunov function, a single adaptive feedback controller is derived to suppress chaotic oscillation in four-dimensional fundamental power systems. The proposed controller simplifies the design of power system stabilizer and provides an easy way to implement in practical power system control. In addition, effectiveness of damping out chaotic oscillation and robustness against parameter uncertainty and external disturbance also make the proposed control scheme applicable for industrial application. Simulation results illustrate the effectiveness, the robustness and the superiority of proposed control method.

Drive-Response Synchronization of a Fractional-Order Hyperchaotic System and Its Circuit Implementation

A novel fractional-order hyperchaotic system is proposed; the theoretical analysis and numerical simulation of this system are studied. Based on the stability theory of fractional calculus, we propose a novel drive-response synchronization scheme. In order to achieve this synchronization control, the Adams-Bashforth-Moulton algorithm is studied. And then, a drive-response synchronization controller is designed to realize the synchronization of the drive and response system, and the simulation results are given. At last, the fractional oscillator circuit of the new fractional-order hyperchaotic system is designed based on the EWB software, and it is verified that the simulation results of the fractional-order oscillator circuit are consistent with the numerical simulation results through circuit simulation.

Chattering-Free Time Scale Separation Sliding Mode Control Design with Application to Power System Chaos Suppression

This paper presents a novel chattering-free sliding mode control method for a class of disturbed nonlinear systems, which achieves fast and exact disturbance estimation, eliminates chattering, and recovers the performance of nominal system and nominal control input. The proposed approach combines time scale separation design and sliding mode control. Different from the existing disturbance estimation based sliding mode control methods, the proposed scheme achieves fast and exact disturbance estimation through time scale separation and eliminates discontinuous switching term, thereby achieving good chattering alleviation effect and providing good transient response. The proposed control method is applied to suppress chaos in power system and simulation results confirm the effectiveness and robustness of proposed control scheme and highlight the advantages of the proposed control scheme over the existing disturbance estimation based sliding mode control methods in terms of chattering alleviation effect and transient response.

NONLINEAR STATE OBSERVER DESIGN FOR PROJECTIVE SYNCHRONIZATION OF FRACTIONAL-ORDER PERMANENT MAGNET SYNCHRONOUS MOTOR

In this paper, a nonlinear state observer control strategy is developed for projective self-synchronization of the fractional-order chaotic attractors of a permanent magnet synchronous motor (PMSM) system. The mathematical model of PMSM system in a smooth fractional-order form is derived by using the fractional derivative theory. A state observer control design can achieve the full-state projective synchronization of the fractional-order PMSM (FO-PMSM) system without the limitation of partial-linearity. Global stability and asymptotic synchronization between the outputs of drive system and response system can be obtained. Simulation results are provided to demonstrate the effectiveness of the approach.

Fixed-Time Disturbance Observer Design for Brunovsky Systems

This brief presents a fixed-time disturbance observer for Brunovsky systems. The proposed disturbance observer is composed of a uniform convergent part and a finite time convergent part. The uniform convergent part first drives the estimation error trajectories into a compact set containing the origin and then the finite time convergent part achieves exact disturbance estimation. The proposed disturbance observer can achieve exact disturbance estimation within finite time upper bounded by a constant independent of initial estimation error. In addition, the upper bound of the estimation time can be calculated theoretically. Numerical simulations are provided to demonstrate the effectiveness of the proposed disturbance observer and verify the declared fixed-time property.