Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Disturbance response instability theory of rock bursts in coal mines and its application

Aiming at the rock burst prevention in coal mines,this study argue that a rock burst is the instability of the coal mass deformation system with the infinite deformation response subjected to a small disturbance,and the concepts of control,disturbance and response variables of the coal mass deformation system are proposed.The analytical solution of rock bursts of circular roadways is derived,using a mechanical model of the coal mass deformation system of circular roadways,and the stress and energy conditions of the disturbance response instability of a rock burst are also presented.Based on the disturbance response instability theory,this study identifies the factors controlling the occurrence of rock bursts,involving the coal uniaxial compressive strength,coal bursting liability and roadway support stress.The relationship between the critical stress and the critical resistance zone of surrounding rock in roadways,the coal uniaxial compressive strength,roadway support stress,roadway geometric parameters and coal burst liability is revealed,and the critical stress index evaluation method of rock burst risk is proposed.Considering the disturbance and response variables of rockburst occurrence,a monitoring system of rock burst based on stress and energy monitoring is established.Considering managing the disturbance and control variables,regional and local prevention measures of rock burst are proposed from four aspects:destressing in coal mass,avoiding the mutual disturbance between multi-group mining or excavation,reducing the dynamic load disturbance and weakening of the physical properties of the coal mass.Based on the enhancement principle of the roadway support stress on the critical load of rockburst occurrence and the energy absorption effect of the support,an energy absorption and anti-bursting support technology for roadways are proposed.The disturbance response instability theory of rock bursts has formed a technical system from the aspects of mechanism,prediction and prevention to guide the engineering practice for rock burst mitigation.

Effect of local wall temperature on hypersonic boundary layer stability and transition

Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation(DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the eNmethod to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it;local heating always slightly promotes the transition.Finally, recommendations are given for practical engineering applications based on the present results.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

Verification of parabolized stability equations for its application to compressible boundary layers

Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory （LST）, the situation was similar to those for incom- pressible boundary layer.

Stability analysis method considering non-parallelism:EPSE method and its application

The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation （PSE） method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation （DNS）. In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.

Stability Analysis on Speed Control System of Autonomous Underwater Vehicle

The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle（AUV）.The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov＇s direct method is proposed in this paper.After decoupling the six degree-of-freedom（DOF）motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.

Linear stability of plane creeping Couette flow for Burgers fluid

It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simpli- fied perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.

Application of Arnoldi method to boundary layer instability

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.

INSTABILITY OF SOLUTION FOR A CLASS OF THE THIRD ORDER NONLINEAR DIFFERENTIAL EQUATION

In Ref [1] the asymptotic stability of nonlinear slowly changing system has been discussed .In Ref [2] the instability of solution for the order linear differential equaiton with varied coefficient has been discussed .In this paper,we have discussed instability of solution for a class of the third order nonlinear diffeential equation by means of the metod of Refs [1] and [2] .

New results on the robust stability analysis of neural networks with discrete and distributed time delays

Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.

Stability Analysis of Stochastic Swarm Systems

In this paper, we present a model of stochastic swarm system and prove the stability of this kind of systems. We establish the stable aggregating behavior for the group using a coordination control scheme. This individual-based control scheme is a combination of attractive and repulsive interactions among the individuals in the group, which ensures the cohesion of the group and collision avoidance among the individuals. The dynamics of each individual depends on the relative positions between the individuals and the influences of the random disturbances. Under the influences of the noises, this position-based control strategy still generates the stable aggregating behavior harmoniously for the group and the self-organized swarm pattern is formed.

INSTABILITY OF SOLUTION FOR THE FOURTH ORDER LINEAR DIFFERENTIAL EQUATION WITH VARIED COEFFICIENT

In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory （LST）. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded（polytope type） uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.

Convective Instability and Appearance of Structured Flows for Diffusion in Multicomponent Gas Mixtures

The main objective of this article is to investigate the behavior of gaseous systems with two and more independent gradients or thermodynamic forces exhibiting complicated behavior,when the convective flows occur.The existence of structural formations in these systems is shown by the schlieren method and the fast-response transducers.The linear analysis of stability can explain reasons of the appearance of convective instability in multicomponent gas mixtures.

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.

ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA

We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.

Dynamical analysis and anti-synchronization of a new 6D model with self-excited attractors

A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points,stability,Lyapunov exponents,time phase portraits,and circuit implementation.Also,anti-synchronization phenomena were implemented on the new system.Firstly,the error dynamics is found.Then,four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways:linearization and Lyapunov stability theory.In comparison with previous works,the present controllers realize anti-synchronization based on another method/linearization method.Finally,a comparison between the two ways was made.The simulation results show the effectiveness and accuracy of the first analytical strategy.

Overview of Earth-Moon Transfer Trajectory Modeling and Design

TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the construction of the lunar space station,the permanent lunar base,and the Earth-Moon transportation network have been proposed,requiring low-cost,expansive launch windows and a fixed arrival epoch for any launch date within the launch window.The low-energy and low-thrust transfers are promising strategies to satisfy the demands.This review provides a detailed landscape of Earth-Moon transfer trajectory design processes,from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods.Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp thebasic overviewof the current Earth-Moon transfer orbitdesignmethods anda deep academic background is unnecessary for the context understanding.