A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

Experiments and Simulation of Thermal Behaviors of the Dual-drive Servo Feed System

The machine tool equipped with the dual-drive servo feed system could realize high feed speed as well as sharp precision. Currently, there is no report about the thermal behaviors of the dual-drive machine, and the current research of the thermal characteristics of machines mainly focuses on steady simulation. To explore the influence of thermal characterizations on the precision of a jib boring machine assembled dual-drive feed system, the thermal equilibrium tests and the research on thermal-mechanical transient behaviors are carried out. A laser interferometer, infrared thermography and a temperature-displacement acquisition system are applied to measure the temperature distribution and thermal deformation at different feed speeds. Subsequently, the finite element method （FEM） is used to analyze the transient thermal behaviors of the boring machine. The complex boundary conditions, such as heat sources and convective heat transfer coefficient, are calculated. Finally, transient variances in temperatures and deformations are compared with the measured values, and the errors between the measurement and the simulation of the temperature and the thermal error are 2 ~C and 2.5 pm, respectively. The researching results demonstrate that the FEM model can predict the thermal error and temperature distribution very well under specified operating condition. Moreover, the uneven temperature gradient is due to the asynchronous dual-drive structure that results in thermal deformation. Additionally, the positioning accuracy decreases as the measured point became further away from the motor, and the thermal error and equilibrium period both increase with feed speeds. The research proposes a systematical method to measure and simulate the boring machine transient thermal behaviors.

Design of a control system for a macro-micro dual-drive high acceleration high precision positioning stage for IC packaging

A macro-micro dual-drive positioning system showing good potential for high acceleration and high precision positioning required in IC packaging applications is devised in this paper. The dual-drive positioning stage uses a VCM (voice coil motor) driven macro positioning stage and a PZT piezo-electric driven micro positioning stage. The coupling characteristics of the system are analyzed to produce a control structure with a micro positioning stage that can dynamically compensate for the positioning error produced by the macro positioning stage. Models of the two positioning stages are described. The models cover both the mechanism and the actuator. For the macro positioning stage, friction characteristics are taken into account, and a controller with an LQG (linear-quadratic-Gaussian) control algorithm combining a feed-forward compensation algorithm is derived. A PID controller is used to control the micro positioning stage. Detailed designs are derived for the proposed approach, and the performance is validated by simulation.

Anti-synchronization of Four-wing Chaotic Systems via Sliding Mode Control

Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.

A New Four-Wing Chaotic System and Its Unified Generalized Projective Synchronization

In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria displaying graceful symmetry with respect to the origin and coordinate planes,and the stability of them are discussed.Then detailed bifurcation analysis is given to demonstrate the evolution processes of the system.Numerical simulations show that the system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.We design a new scheme of generalized projective synchronization,so-called unified generalized projective synchronization,whose response signal synchronizes with the linear combination of drive signal.The design has the advantages of containing complete synchronization,anti-synchronization and disorder synchronization over the usual generalized projective synchronization,such that it can provide greater security in secure communication.Based on Lyapunov stability theorem,some sufficient conditions for the new synchronization are inferred.Numerical simulations demonstrate the effectiveness and feasibility of the method by employing the four-wing chaotic system.

Adaptive Kalman filter and dynamic recurrent neural networks-based control design of macro-micro manipulator

In this paper, a composite control scheme for macro-micro dual-drive positioning stage with high accel- eration and high precision is proposed. The objective of control is to improve the precision by reducing the influence of system vibration and external noise. The positioning stage is composed of voice coil motor （VCM） as macro driver and piezoelectric actuator （PEA） as micro driver. The precision of the macro drive positioning stage is improved by the com- bined PID control with adaptive Kalman filter （AKF）. AKF is used to compensate VCM vibration （as the virtual noise） and the external noise. The control scheme of the micro drive positioning stage is presented as the integrated one with PID and intelligent adaptive inverse control approach to compensate the positioning error caused by macro drive positioning stage. A dynamic recurrent neural networks （DRNN） based inverse control approach is proposed to offset the hysteresis nonlinearity of PEA. Simulations show the positioning precision of macro-micro dual-drive stage is clearly improved via the proposed control scheme.