This paper investigates the ${H_{\infty}}$ dynamic composite nonlinear output feedback control of the inductive coupled power transfer (ICPT) system with load resistance variation, coil structural perturbation, and energy-bounded external disturbance under event-triggering mechanism. A small-signal model is first developed to characterize the dynamic behavior of the ICPT system under S/S resonance, wherein the system mismatch is considered as a type of stochastic process and described as a Markov jump model. In view of the difficulties in measuring system state, poor transient performance, limited controller computation and communication capabilities, an event-triggered dynamic composite nonlinear output feedback controller is designed, and sufficient conditions are presented to guarantee the mean square stability and ${H_{\infty}}$ performance of the ICPT system. The controller gains can be obtained by solving a set of linear matrix inequalities. Finally, the effectiveness and reliability of the proposed control method is verified through simulation examples.

Over the past few years, many scholars began to study averaging principles for fractional stochastic differential equations since they can provide an approximate analytical method to reduce such systems. However, in the most previous studies, there is a misunderstanding of the standard form of fractional stochastic differential equations, which consequently causes the wrong estimation of the convergence rate. In this note, we take fractional stochastic differential equations with Lévy noise as an example to clarify these two issues. The corrections herein have no effect on the main proofs except the two points mentioned above. The innovation of this paper lies in three aspects: (i) the standard form of the fractional stochastic differential equations is derived under natural time scale; (ii) it is first proved that the convergence interval and rate are related to the fractional order; and (iii) the presented results contain and improve some well known research achievements.

Aero-engine rotor system contains a variety of connectors such as bolts and bearings. However, the dynamic behaviors of the connection are complex in actual engineering. In this paper, the dynamic behavior of the rotor-bearing system with bolted joints and the influence of the parameters of the joints on it are clarified. The parameters include the bearing clearance and the deflection caused by the uneven bolt preload. A rotor-bearing model with bolted joints is established by using Lagrange equations. The bifurcation diagram is solved to explore the tendency of vibration of the system at different speeds by considering the Hertz contact force. Furthermore, the phase diagram, Poincaré map, time-domain steady-state response curve, and spectrum diagram are used to discuss the dynamic behaviors of the system specifically. The influence of the bearing clearance change and uneven bolt preload on the dynamic behaviors is investigated by using the bifurcation diagram. The result shows that the motion of the system is extremely complex, which includes chaotic motion. The Lyapunov exponent is then calculated to verify whether the system enters chaos. The correctness of the model is verified by comparing the result in this work with those in the literature. The model can clarify the dynamic behaviors of the system well and has high accuracy, which can provide the theoretical guidance for the design of rotor-bearing systems with bolted joints.

This paper investigates the event-triggered model predictive control (MPC) for the series–series (SS) resonant inductive coupling power transfer (ICPT) system in electric vehicles (EVs). Different from most existing literature in ICPT systems, a data-driven modeling approach based on input–output data is proposed to describe the system dynamics and achieve constant voltage output in the presence of load variations. In the traditional MPC control strategies, the optimal control input should be calculated at each time instant to achieve the desired output voltage, which causes great computational burden. To tackle this issue, an event-triggered MPC mechanism is therefore developed to effectively alleviate the computational burden, which will generate the optimal control input only when the norm of the state error exceeds a predefined threshold. The effectiveness and reliability of the proposed event-triggered MPC control strategy are successfully verified by the experimental results.

Based on the layered and porous characteristics of functionally graded materials and the finite deformation assumption of solids, the fractal nonlinear propagation equation of longitudinal waves in a functionally graded rod is derived. A large number of exact displacement gradient traveling wave solutions of the fractal equation are obtained by using an equivalent simplified extended (G′/G) expansion method. Three sets of existing and different displacement gradient solutions are obtained by analyzing these exact solutions, and then three corresponding fractal dimension strain waves are derived. The results of numerical simulation of the evolution of these three strain waves with fractal dimension show that when the strain wave propagates in the rod, the smaller the fractal dimension or, the larger the radius of the rod, the higher the tensile strength of the material.

This paper explores the stochastic dynamics in a Rijke tube model. Dynamical model is established to identify the bifurcation properties of the Rijke tube model. We gain the analytical expression of the local Hopf bifurcation and global saddle-node bifurcation of the limit cycle in the deterministic case. The stationary probability density function (PDF) of the model is attained base on the method of stochastic average in the case of stochasticity. The investigations indicate that the stationary PDF switches from unimodal shape to bimodal one, and then, from bimodal shape to unimodal one again, when noise intensity, fractional order, time delay monotonically increase which is the typical feature of stochastic P-bifurcation. Further, we conclude that the stochastic P-bifurcation can be induced or suppressed by modulating the time delay, the noise intensity, or the fractional order. These findings of the study will be helpful to the theoretical study of thermoacoustic instability and the preliminary design of thermoacoustic devices where thermoacoustic instability is a concern. (C) 2021 Elsevier Ltd. All rights reserved.

In this paper, the impact of parameters on bifurcation and birhythmicity is studied theoretically and numerically in a fractional-order birhythmic Van der Pol oscillator coupled with delayed feedback and noise. By implementing the multiple-scale expansion approach and stochastic averaging method, deterministic bifurcation and the comprehensive evolution details of stochastic bifurcation are explored respectively. Then, the birhythmicity of the birhythmic oscillator is discussed both under the deterministic and stochastic cases. This investigation may be conducive to understanding the underlying mechanisms which control the biorhythms of the cell cycle in certain biological systems.

This paper is concerned with a novel stochastic bifurcation and its discrimination of stochastic dynamical system. A new kind of stochastic response—called extremely possible response and a novel stochastic bifurcation—called stochastic extremum bifurcation is defined for the first time. An entirely new method for discriminating stochastic bifurcation is proposed based on the new definition mentioned above. In addition, the classical Van der Pol oscillator is used as the illustrative example to demonstrate the validity of the proposed method. Worthy of note is that the new stochastic extremum bifurcation defined in this paper is mathematically equivalent to the stochastic P-bifurcation defined by Arnold and the new proposed method for discriminating stochastic bifurcation is more convenient than the “traditional” method.

The continuous electrocoagulation (EC) with bipolar electrode was modeled and simulated. The generation and mass transfer of coagulants and hydroxide flocs were simulated. The electrocoagulation with bipolar electrode (B-EC) was compared with the electrocoagulation with monopolar electrode (M-EC). During B-EC, the flocs are uniformly generated and distributed in the channel. During M-EC, the flocs are generated in the extremely narrow area, which is located in the middle of EC channel. This concentration distribution is suitable for the formation of hydroxide flocs. Also another advantage should be mentioned is that the concentration of produced H+ and OH-is much lower in B-EC. The lower concentration of H+ and OH- is suitable for the formation of Al hydrate flocs. Thus, the bipolar electrode structure improves the mass transfer of generated coagulants, when compared with the monopolar electrode. Under the same total current, the B-EC has much higher flocs production than that of M-EC. The edge effects of bipolar electrode in B-EC were modeled and studied. The edge effects were discussed with the consideration of mass transfer. In the edge areas, the concentration of cation and anion hydroxide species is not negligible. The electro-migration in the direction perpendicular to the streamline will also make the ionic hydroxide species transfer into the bulk channel. Thus, in edge area, the electro-migration could also contribute to the mixture of the ions. The edge effect of bipolar electrode in EC process could be neglected.

The adaptive neuron control of the hydraulic turbine set speed regulating system was studied. The closed-loop stability of this system was analyzed. The semiphysical dynamic real-time simulation and the industrial field use test were carried out. The results show that the adaptive neuron control has good performance.