Summary It has been a common brief that the principle for generating multi‐wing attractor from a Lorenz‐like chaotic system is to construct an even symmetric function for the system. In this pursuit, research effort on exploring the possibility of using non‐even symmetric function is scant, if any. This paper attempts to reveal the intrinsic relation between such a system function and its generated multi‐wing attractor in a chaotic system. It will be shown that a rather simple asymmetric function applying to the Shimizu–Morioka system can indeed generate a multi‐wing butterfly chaotic attractor. Then, some basic properties, compound structure, bifurcation diagram, Lyapunov exponent spectrum, and dynamical analysis of the new chaotic system are investigated in detail. Finally, an electronic circuit is designed and its experimental results are presented, which well match the numerical simulation results, thereby verifying the feasibility of the new method. Copyright © 2017 John Wiley & Sons, Ltd.
A nanoscale memristor can replace the nonlinear part of a chaotic system, which can greatly reduce the physical size of the chaotic system. More importantly, it can enhance the complexity of the chaotic system and the randomness of signals. In this paper, a new memristor-based chaotic system is designed based on a new three-dimensional autonomous chaotic system. In order to study the complex dynamic characteristics of the memristive system, the chaotic system is investigated by the theoretical derivation, numerical simulation, stabilization of equilibrium points, and Lyapunov exponent spectrum. The influences of different parameters on the phase diagram and the stability of equilibrium point of this system are also discussed in detail. It is interesting that when system parameters a and c take different values, the location and stability of the equilibrium point of the system will be changed, then two scrolls of the system will be overturned at a different angle, and it will produce a different degree of aliasing between the two scrolls. Parameter b has a large variable range, when it is changed, and the system will transform into three kinds of classical chaotic systems defined by Vaněček and Celikovsk. These indicate that the memristor-based chaotic system has a lot of valuable dynamic behaviors, so it has applications in the field of secure communication, information processing etc. Field programmable gate array (FPGA) technology has a large capacity and high reliability, which is widely used in modern digital signal processing. And with the development of FPGA technology, applying FPGA technology to realizing the chaotic systems has gradually become a hot topic. Moreover, the improved Newton iteration method is used to design a square root operator of memristor in this paper by using verilog hardware description language (verilog HDL) which only needs three times iteration to reach the required accuracy. The results of FPGA hardware are consistent with the numerical simulation results. It breaks through the previous bottleneck that the chaotic system based on titanium dioxide memristor can only be simulated in computer, which is of great significance for further studing of memristor, and provides a reference for further research on the memristor-based chaotic system and applications in secure communication and information processing.
This paper proposes a novel variable gain switching exact differential observer (SEDO) to deal with the state estimation of mechanical servo system with unknown backlash. In order to compensate unknown non-linear backlash accurately, a switching backlash torque mathematic model is constructed to describe the input-output relationships of backlash. Then, based on the switching backlash torque mathematic model, a novel SEDO with variable gain strategy is implemented to compensate the influence of backlash and estimate system states accurately in terms of the change of real operation conditions . Moreover, the designed controller further alleviates the computational burden by conducting a feedforward compensation strategy, part of which is shared by the observer. It is proven that all the signals in the closed-loop system are bounded, observation error and tracking error are convergent to a small compact set of the origin. Two simulations and two different motor servo test rigs are established to further illustrate the effectiveness of the proposed approach.
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