On a novel non-smooth output feedback controller for the attitude control of a small float satellite antenna

A novel non-smooth controller of the second order double integrator system with a bounded disturbance is proposed,which stability is proved and which disturbance rejection capability is analyzed by MATLAB simulation experiments. The novel non-smooth output feedback controller and tracking differentiator are applied to control the azimuth servo systemof the small floating satellite antenna. The MATLAB simulation and hardware in the loop simulation experiments are conducted. The experiment results validate that the non-smooth output feedback controller with stronger surge and sudden disturbance rejection capability can realize the stable azimuth servo control of the small floating antenna to ensure the communication between the target satellite and the antenna with high quality.

Design Principles of the Non-smooth Surface of Bionic Plow Moldboard

The diverse non-smooth body surfaces to reduce soil adhesion are the evolutional results for the soil animals to fit the adhesive and wet environment and can be used as a biological basis for the design of bionic plow moldboard. The model surfaces for bionic simulation should be taken from soil animal digging organs, on which the soil motion is similar to what is on the surface of moldboard. By analyzing the distribution of non-smooth units on the body surface of the ground beetle jaw and the soil moving stresses, the design principles of the bionic moldboard for the local and the whole moldboard were presented respectively. As well, the effect of soil moving speed on reducing adhesion, the dimensions relationship between soil particles and non-smooth convexes, the relationship between the enveloping surface of non-smooth convexes and the initial smooth surface of the plow body, and the convex types of the sphere coronal and the pangolin scales,etc.were discussed.

Friction and Wear Study on Friction Pairs with a Biomimetic Non-smooth Surface of 316L Relative to CF/PEEK under a Seawater Lubricated Condition

Current studies of a seawater axial piston pump mainly solve the problems of corrosion and wear in a slipper pair by selecting materials with corrosion resistance, self-lubrication, and wear resistance. In addition, an appropriate biomimetic non-smooth surface design for the slipper pair can further improve the tribological behavior. In this paper, 316 L stainless steel and CF/PEEK were selected to process the upper and bottom specimens, and the biomimetic non-smooth surface was introduced into the interface between the friction pair. The friction and wear tests were performed on a MMD-5 A tester at a rotation speed of 1000 r/min and load of 200 N under seawater lubricated condition. The results indicate that the main friction form of the smooth surface friction pair corresponds to abrasive wear and adhesive wear and that it exhibits a friction coe cient of 0.05–0.07, a specimen temperature of 56 ℃, a high wear rate, and surface roughness. Pits on the non-smooth surface friction pairs produced hydrodynamic lubrication and reduced abrasive wear, and thus the plowing e ect is their main friction form. The non-smooth surface friction pairs exhibit a friction coe cient of 0.03–0.04, a specimen temperature of 48 ℃, a low wear rate, and surface roughness. The study has important theoretical significance for enriching the lubrication, friction, and wear theory of a seawater axial piston pump, and economic significance and military significance for promoting the marine development and the national defense military.

A METHOD FOR THE ANALYSIS OF DYNAMIC RESPONSE OF STRUCTURE CONTAINING NON-SMOOTH CONTACTABLE INTERFACES

A novel single-step method is proposed for the analysis of dynamicresponse of visco-elastic structures containing non-smooth contactable interfaces.Inthe method,a two-level algorithm is employed for dealing with a nonlinear boundarycondition caused by the dynamic contact of interfaces.At the first level,an explicitmethod is adopted to calculate nodal displacements of global viscoelastic system with-out considering the effect of dynamic contact of interfaces and at the second level,by introducing contact conditions of interfaces,a group of equations of lower orderis derived to calculate dynamic contact normal and shear forces on the interlaces.The method is convenient and efficient for the analysis of problems of dynamic cou-tact.The accuracy of the method is of the second order and the numerical stabilitycondition is wider than that of other explicit methods.

Non-smooth environment modeling and global path planning for mobile robots

An Approximate Voronoi Boundary Network is constructed as the environmental model by way of enlar-ging the obstacle raster. The connectivity of the path network under complex environment is ensured through build-ing the second order Approximate Voronoi Boundary Network after adding virtual obstacles at joint-close grids. Thismethod embodies the network structure of the free area of environment with less nodes, so the complexity of pathplanning problem is reduced largely. An optimized path for mobile robot under complex environment is obtainedthrough the Genetic Algorithm based on the elitist rule and re-optimized by using the path-tightening method. Sincethe elitist one has the only authority of crossover, the management of one group becomes simple, which makes forobtaining the optimized path quickly. The Approximate Voronoi Boundary Network has a good tolerance to the im-precise a priori information and the noises of sensors under complex environment. Especially it is robust in dealingwith the local or partial changes, so a small quantity of dynamic obstacles is difficult to alter the overall character ofits connectivity, which means that it can also be adopted in dynamic environment by fusing the local path planning.

Influence of Bionic Non-smooth Surface on Water Flow in Antiskid Tire Tread Pattern

Inspired by the idea that bionic non-smooth surfaces(BNSS)can reduce water flow resistance,the application of BNSS resistance reduction method in grooves surface of antiskid tire tread pattern has been investigated for increasing hydroplaning velocity of tire by using computational fluid dynamics(CFD)simulation.Three kinds of BNSS(riblet,convex dome,and dimple concave)are arranged in tire tread grooves to study the water flow resistance effects in grooves with non-smooth characteristics.A tire-water coupled model is established and CFD technique is applied to simulating hydroplaning.The simulation results show that BNSS grooves can reduce water flow resistance and increase mean flow rate by disturbing the eddy movement in boundary layers.The drag forces of riblet and dimple surface are lower and drainage capacity is higher than those of smooth surface under the same void space on tread pattern,but it is not in dome.BNSS is a good way to promote antiskid performance without increasing additional groove space;extra tire-road noise production is therefore avoided due to groove space enlargement.

Computer simulation of rolling wear on bionic non-smooth convex surfaces

The study of bionics has found that the skins of many burrow animals which live in soil and stone conditions have an anti wear function, and which is related to their body surfaces’non-smooth morphology. In the present study, bionic non-smooth surfaces are used in roll surface design, and roll models with convex non-smooth surfaces are developed. The rolling wear of non-smooth roll in steel rolling is simulated by the FEM software-ANSYS. The equivalent stress, the node friction stress, and the node contact pressure between the roll and the rolling piece are calculated; and the anti-wear mechanism is analyzed.

Research on semi-active control method of a building structure based on non-smooth control

This study investigates the effectiveness of the non-smooth semi-active control algorithm on suppressing the vibration performance of a building structure subjected to seismic waves. According to the Lyapunov stability theory, it has bene proven that the non-smooth semi-active control algorithm can achieve a finite-time stability of the vibration relative to the isolation layer of a building structure. Through numerical simulation of two buildings with different parameters subjected to the input of a seismic wave, the vibration conditions of passive control, LQR semi-active control and non-smooth semiactive control are compared and analyzed. The simulation results show that the non-smooth semi-active control algorithm has a better robustness and effectiveness in restraining the impact of earthquakes on the structure.

An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface

A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.

Wettability of a Biomimetic Non-smooth Coating by Water

Through the evolution of hundreds of millions of years,the living creature have superior structure and function such as the structure of non-smooth surfaces have a well water-repellent,drag reduction,adhesion reduction functions.This study chose a kind of widely used material gray cast iron as substrate,which the metal and nano-ceramic nanocomposite coatings by electrodepositon on gray cast iron surface were prepared.The 2-D and 3-D surface morphologies of composite coating were observed and the result indicated that 2-D and 3-D had a typical geometrical non-smooth character.Furthermore,the contact angles of coating were measured.The relation between coating morphology and wettability was analysed.Therefore,the water-repellent of the composite coating surface was due to the characteristic microstructure and content of coating.

Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

Non-smooth dynamic modeling and simulation of an unmannedbicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground.According to the Carvallo-Whipple configuration,the unmanned bicycle is reduced to four rigid bodies,namely,rear wheel,rear frame,front fork,and front wheel,which are connected by perfect revolute joints.The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point,and these forces are described by the Hunt-Crossley contact force model and the Lu Gre friction force model,respectively.According to the characteristics of flat and curved pavements,calculation methods for contact forces and their generalized forces are presented.The dynamics of the system is modeled by the Lagrange equations of the first kind,a numerical solution algorithm of the dynamic equations is presented,and the Baumgarte stabilization method is used to restrict the drift of the constraints.The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies.The feasibility of the proposed model is demonstrated by simulations under different motion states.

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces,making it challenging to carry out the research of this category of complex systems with non-smooth characteristics.To address this problem,by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation,a modified conducting process has proposed.Taking the multiple nonlinear parameters,the non-smooth parameters,and the external excitation frequency into consideration,the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed.It can be found that the system parameters can make the system stability topology change.The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo(MC)simulation.Consequently,the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Some new advance on the research of stochastic non-smooth systems

Due to the extensive applicability in real life, the non-smooth system with random factors attracted much attention in past two decades. A lot of methods and techniques have been proposed to research these systems by scholars. In this paper, we will summarize some new research advance on the stochastic non-smooth systems. The existing results about the stochastic vibro-impact system, the stochastic friction system, and the stochastic hysteretic system are introduced respectively. Some conclusions and outlook are given at the end.

Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Let T_1 be a singular integral with non-smooth kernel or ± I, let T_2 and T_4 be the linear operators and let T_3= ±I. Denote the Toeplitz type operator by T^b= T_1M^bI_αT_2+T_3I_αM^bT_4,where M^bf=bf, and I_α is the fractional integral operator. In this paper, we investigate the boundedness of the operator T^b on the weighted Morrey space when b belongs to the weighted BMO space.

Local Discontinuous Galerkin Methods with Novel Basis for Fractional Diffusion Equations with Non-smooth Solutions

In this paper,we develop novel local discontinuous Galerkin(LDG)methods for fractional diffusion equations with non-smooth solutions.We consider such problems,for which the solutions are not smooth at boundary,and therefore the traditional LDG methods with piecewise polynomial solutions suffer accuracy degeneracy.The novel LDG methods utilize a solution information enriched basis,simulate the problem on a paired special mesh,and achieve optimal order of accuracy.We analyze the L2 stability and optimal error estimate in L2-norm.Finally,numerical examples are presented for validating the theoretical conclusions.

The Non-Smooth Problem of Wheel Motion

Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its solution is determined by an absolutely continuous function having a discontinuous first derivative. For this reason, a collision problem describing abrupt changes of velocity has been formulated next to the equations of motion specifying the acceleration. The non-idealness of constraints means that the constraint reaction force includes also a component resulting from the friction between the wheel and the constraints. Differential equations specifying acceleration of the wheel making contact with the constraints and algebraic equations for determining the changes in the wheel’s velocity at the moment of collision have been formulated in the paper. The principal task in these formulations is to determine the reaction forces of the considered constraints. This task is specified by the relationships between acceleration and the constraint reaction force components. In the description of the collision, these relations refer to the post-collision velocities and reaction force impulses. For determining an approximate solution of the formulated wheel motion problem, an original numerical method and a computer program for wheel motion simulation have been developed. Selected results illustrating the changes in displacements and velocity have been presented.

Bifurcations and Sequences of Elements in Non-Smooth Systems Cycles

This article describes the implementation of a novel method for detection and continuation of bifurcations in non-smooth complex dynamic systems. The method is an alternative to existing ones for the follow-up of associated phenomena, precisely in the circumstances in which the traditional ones have limitations (simultaneous impact, Filippov and first derivative discontinuities and multiple discontinuous boundaries). The topology of cycles in non-smooth systems is determined by a group of ordered segments and points of different regions and their boundaries. In this article, we compare the limit cycles of non-smooth systems against the sequences of elements, in order to find patterns. To achieve this goal, a method was used, which characterizes and records the elements comprising the cycles in the order that they appear during the integration process. The characterization discriminates: a) types of points and segments;b) direction of sliding segments;and c) regions or discontinuity boundaries to which each element belongs. When a change takes place in the value of a parameter of a system, our comparison method is an alternative to determine topological changes and hence bifurcations and associated phenomena. This comparison has been tested in systems with discontinuities of three types: 1) impact;2) Filippov and 3) first derivative discontinuities. By coding well-known cycles as sequences of elements, an initial comparison database was built. Our comparison method offers a convenient approach for large systems with more than two regions and more than two sliding segments.

ABOUT THE FOURIER TRANSFORMS OF NON-SMOOTH MEASURES ON HYPERSPHERES

If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.

Effects of Methanol on Wettability of the Non-Smooth Surface on Butterfly Wing

The contact angles of distilled water and methanol solution on the wings of butterflies were determined by a visual contact angle measuring system.The scale structures of the wings were observed using scanning electron microscopy,The influence of the scale micro-and ultra-structure on the wettability was investigated.Results show that the contact angle of distilled water on the wing surfaces varies from 134.0° to 159.2°.High hydrophobicity is found in six species with contact angles greater than 150°.The wing surfaces of some species are not only hydrophobic but also resist the wetting by methanol solution with 55% concentration.Only two species in Parnassius can not resist the wetting because the micro-structure(spindle-like shape) and ultra-structure(pinnule-like shape) of the wing scales are remarkably different from that of other species.The concentration of methanol solution for the occurrence of spreading/wetting on the wing surfaces of different species varies from 70% to 95%.After wetting by methanol solution for 10 min,the distilled water contact angle on the wing surface increases by 0.8°-2.1°,showing the promotion of capacity against wetting by distilled water.