Adaptive Nonlinear PD Controller of Two-Wheeled Self-Balancing Robot with External Force

This paper proposes an adaptive nonlinear proportional-derivative(ANPD)controller for a two-wheeled self-balancing robot(TWSB)modeled by the Lagrange equation with external forces.The proposed control scheme is designed based on the combination of a nonlinear proportional-derivative(NPD)controller and a genetic algorithm,in which the proportional-derivative(PD)parameters are updated online based on the tracking error and the preset error threshold.In addition,the genetic algorithm is employed to adaptively select initial controller parameters,contributing to system stability and improved control accuracy.The proposed controller is basic in design yet simple to implement.The ANPD controller has the advantage of being computationally lightweight and providing high robustness against external forces.The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov theory,providing theoretical assurance of its robustness.Simulations and experimental results show that the TWSB robot with the proposed ANPD controller achieves quick balance and tracks target values with very small errors,demonstrating the effectiveness and performance of the proposed controller.The proposed ANPD controller demonstrates significant improvements in balancing and tracking performance for two-wheeled self-balancing robots,which has great applicability in the field of robot control systems.This represents a promising solution for applications requiring precise and stable motion control under varying external conditions.

Exact Solutions of Forced Schrödinger Equation and How to Choose the External Forces

Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.

Contribution of external forcing to summer precipitation trends over the Qinghai-Tibet Plateau and Southwest China

在过去的60年中,全球气候经历了快速变暖和短暂的变暖停滞,而中国的区域降水也经历了多样而复杂的变化.本文分析了1961年至2014年外强迫因子对青藏高原和中国西南地区夏季降水趋势的影响.观测数据显示,青藏高原的夏季降水呈增加趋势,而中国西南地区的夏季降水呈减少趋势,这两个相邻地区的夏季降水变化趋势相反.利用CMIP6数据,本文研究了不同外强迫因子对两个区域夏季降水趋势的影响.结果表明,温室气体对青藏高原夏季降水的增加具有显著影响,而气溶胶在中国西南地区夏季降水减少中起主要作用。

Establishment and validation of standardized animal models of spinal cord injury by normal external force-caused fracture dislocation

The duplication of animal models plays a key role in spinal cord injury research; however, there has been limited study into normal, external force-derived fracture dislocation. This study adopted experimental devices, designed in-house, to construct standardized ventral and dorsal spinal cord injury animal models of 6 g and 17 g falling from a height of 2, 4, and 10 cm, and 15, 30 or 50 g transversal compression on the spinal cord. The results showed that gradual increases in the degree of histopathological injury led to decreased Tarlov and Basso, Beattie and Bresnahan scores for the behavioral test, and increased Ashworth scores for the hind limb. Furthermore, there was a gradual decline in the slope test in the rats with dorsal spinal cord injury that correlated to increases in the falling substance weight or falling height. Similar alterations were observed in the ventral spinal cord injured rats, proportional to the increase in compression weight. Our experimental findings indicate that the standardized experimental rat models of dorsal and ventral spinal cord injury are stable, reliable and reproducible.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

Nonstationary Time Series Prediction by Incorporating External Forces

Almost all climate time series have some degree of nonstationarity due to external forces of the observed system. Therefore, these external forces should be taken into account when reconstructing the climate dy- namics. This paper presents a novel technique in predicting nonstationary time series. The main difference of this new technique from some previous methods is that it incorporates the driving forces in the pre- diction model. To appraise its effectiveness, three prediction experiments were carried out using the data generated from some known classical dynamical models and a climate model with multiple external forces. Experimental results indicate that this technique is able to improve the prediction skill effectively.

Analysis of Externality of Rural Labor Force Flow in Central and Western Regions of China and Benefit Compensation

According to the theories of institutional economics and development economics,the positive and negative externality of rural labor force flowing from central and western regions and into eastern regions of China were analyzed,and then it was proposed that it is necessary to positive externality,rather than take"household register"measures to solve the problem simply.

Self-Organization of Charged Particulates in the Presence of External Force

Evolution of spatial distribution of charged particulates under the action of an external force is investigated. It is found that starting from a homogeneous Maxwellian distribution of particulates, clusters can form and aggregate. The evolution process, as well as the asymptotic number and configuration of the clusters formed, depends strongly on the strength of the external force. The particulates in most of the final clusters are in the crystal state, as can also be deduced from the corresponding velocity and auto-correlation functions.

DYNAMIC MODEL OF CROP GROWTH SYSTEM AND NUMERICAL SIMULATION OF CROP GROWTH PROCESS UNDER THE MULTI-ENVIRONMENT EXTERNAL FORCE ACTION

According to the biomechanic theory and method, the dynamic mechanism of crop growth under the external force action of multi_environment factors (light, temperature,soil and nutrients etc.) was comprehensively explored.Continuous_time Markov(CTM) approach was adopted to build the dynamic model of the crop growth system and the simulated numerical method. The growth rate responses to the variation of the external force and the change of biomass saturation value were studied. The crop grew in the semiarid area was taken as an example to carry out the numerical simulation analysis, therefore the results provide the quantity basis for the field management. Comparing the dynamic model with the other plant growth model, the superiority of the former is that it displays multi_dimension of resource utilization by means of combining macroscopic with microcosmic and reveals the process of resource transition. The simulation method of crop growth system is advanced and manipulated. A real simulation result is well identical with field observational results.

External grind-hardening experiments and its grinding force

The grind-hardening method suitable for external grinding is proposed in this paper and the experiments are carried out on M1432B grinding machine. The hardened layer of the workpiece with cut depth 0.3 mm and speed 0.2 m/min is analyzed. The result indicates the metallurgical structure of the hardened layer is martensite and the top hardness value is 754 HV （about 62.3 HRC）. At the same time, the grinding force, one of the most important factors of external grind-hardening process is modeled, and the measurement method is provided with elastic core clampers. The measurement result shows that the values of both the tangential force and the normal force increase when the cut depth increases, and the top value is 146 N and 656 N with the cut depth value of 0.4 mm. The increment speed and the value of the normal force are larger than the tangential force.

EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE

In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp（-p｜x - v｜^2）, which has infinite mass and energy.

PARTITION RATIO AT SOLID-LIQUID INTERFACE UNDER INFLUENCE OF TEMPERATURE GRADIENT AND EXTERNAL FORCE FIELD

The relationship between the partition ratio at a solid-liquid interface and the temperature gradient or the external force field has been theoretically analysed.It is shown that under the influence of a temperature gradient or an external force field,the partition ratio at a solid-liquid interface will deviate from the equilibrium value.

BIFURCATION IN A NONLINEAR DUFFING SYSTEM WITHMULTI-FREQUENCY EXTERNAL PERIODIC FORCES

By introducing nonlinear frequency, using Floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitations as well as the possible ways to chaos are studied in this paper.

Numerical Quantification Model and Experiment of External Force on Roller Hemming of Curved Edge Aluminium Alloy with Adhesive

Accurate quantification of external force is the key to improve the high-precision hemming of autobody closure panels.However,the mechanism of external force on forming quality of complex contour sheet metal with adhesive is not clear subjected to geometric curvature and materials.In the present study,taking the curved edge aluminum sheet as the research object,SPH(smooth particle hydrodynamics)is introduced to simulate the viscous adhesive,and the SPH-FEM(Finite element method)coupling model of adhesive and panels considering the viscosity-pressure effect is established.The numerical simulation of the roller hemming process is carried out,then the validity and reliability of the proposed method are verified by measuring the external force in real time using triaxial force sensor.The multi-step forming process and the effect of external force on the roll in/out,surface wave and plastic strain of aluminum alloy sheet under the viscosity-pressure effect are studied,and the relationship between process parameters and external force is discussed.Results show that the coupling SPH-FEM model can well reflect the hemming process of curved edge structure.The normal force is about 2–3 times of the tangential force in the pre and final hemming process.Compared with the case without adhesive,the surface wave of flange part of the hemming with adhesive is slightly larger.The normal force and the tangential force increase about 90 N and 30 N respectively,when the height increases by 1 mm.It provides an important basis for the accurate control of hemming trajectory and the improvement of manufacturing quality of autobody closure panels.

Oscillating Propagation of Kink in Nondissipative Frenkel-Kontorova Chain Due to External DC Force

We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink ＆ transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.

Long-time evolution of charged grains in plasma under harmonic external force and after being withdrawn

Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dynamics simulation.Under an external force and a grain–grain interaction force,initially homogeneously distributed grains can reach a quasistationary state in the form of a disk crystal.After the external force is withdrawn,the disk moves initially with its size and shape nearly unchanged until it rapidly stops moving,and eventually the disk grain rotates like a vortex.The time needed to reach the final state increases with the strength of the initial external force increasing.

Preliminary experimental study on applicability of Lorentz force velocimetry in an external magnetic field

Lorentz force velocimetry(LFV) is a noncontact technique for measuring electrically conducting fluids based on the principle of electromagnetic induction. This work aims to answer the open and essential question of whether LFV can work properly under a surrounding external magnetic field(ExMF). Two types of Ex MFs with different magnetic intensities were examined: a magnetic field with a typical order of 0.4 T generated by a permanent magnet(PM) and another generated by an electromagnet(EM) on the order of 2 T. Two forces, including the magnetostatic force between the Ex MF and PM in the LFV, and the Lorentz force generated by the PM in LFV were measured and analyzed in the experiment. In addition,Ex MFs of varying strengths were added to the LFV, and the location of the LFV device in the iron cores of the EM was considered. The experimental outcomes demonstrate that it is possible for a LFV device to operate normally under a moderate Ex MF. However, the magnetostatic force will account for a high proportion of the measured force,thus inhibiting the normal LFV operation, if the Ex MF is too high.

Dynamic analysis of double-layer and pre-stressed multi-limb six-axis force sensor

In order to adapt to the specific task, the six-axis dynamic contact force between end-effectors of intelligent robots and working condition needs to be perceived. Therefore, the dynamic property of six-axis force sensor which is installed on the end-effectors of intelligent robots will have influence on the veracity of detection and judgment to working environment contact force by intelligent robots directly. In this paper, dynamic analysis to double-layer and pre-stressed multi-limb six-axis force sensor is conducted. First, the structure of the sensor is introduced, and the limb number is confirmed by introducing the related definitions of convex analysis. Then, based on vibration of multiple-degree-of-freedom system, a mechanical vibration simplified model of double-layer and pre-stressed multiple limb six-axis force sensor is set up. After that, movement differential equations of sensor and the response of analytical expression are deduced, and the movement differential equations is solved. Finally, taking the double-layer and pre-stressed seven limb six-axis force sensor as an example, numerical calculation and simulation of deriving result is conducted, which verify the correctness and feasibility of the theoretical analysis.

Rolling Force and Rolling Moment in Spline Cold Rolling Using Slip-line Field Method

Rolling force and rolling moment are prime process parameter of external spline cold rolling. However, the precise theoretical formulae of rolling force and rolling moment are still very fewer, and the determination of them depends on experience. In the present study, the mathematical models of rolling force and rolling moment are established based on stress field theory of slip-line. And the isotropic hardening is used to improve the yield criterion. Based on MATLAB program language environment, calculation program is developed according to mathematical models established. The rolling force and rolling moment could be predicted quickly via the calculation program, and then the reliability of the models is validated by FEM. Within the range of module of spline m=0.5-1.5 mm, pressure angle of reference circle α=30.0°-45.0°, and number of spline teeth Z=19-54, the rolling force and rolling moment in rolling process （finishing rolling is excluded） are researched by means of virtualizing orthogonal experiment design. The results of the present study indicate that： the influences of module and number of spline teeth on the maximum rolling force and rolling moment in the process are remarkable; in the case of pressure angle of reference circle is little, module of spline is great, and number of spline teeth is little, the peak value of rolling force in rolling process may appear in the midst of the process; the peak value of rolling moment in rolling process appears in the midst of the process, and then oscillator weaken to a stable value. The results of the present study may provide guidelines for the determination of power of the motor and the design of hydraulic system of special machine, and provide basis for the farther researches on the precise forming process of external spline cold rolling.

Study of Slope Reinforcement Force Based on FLAC

A slope will slide if the unbalanced force does not tend to zero when the stability of the slope is analyzed with the help of FLAC. Thus the ultimate reason of slope sliding is the unbalanced force determined by FLAC. The slope will remain stable if the unbalanced force is counterbalanced by a reinforcement force which is produced by a suitable reinforcement method. In this paper, the stability of the slope was analyzed by using FLAC, and the unbalanced force of the slope was obtained through the FISH function in FLAC. According to the equilibrium conditions, the relationship between the reinforcement force and unbalanced force was derived and accordingly the reinforcement force was determined. The reinforcement design was adopted by using pre-stressed anchor bars on the basis of the reinforcement force. An example is used to show that the effect of slope reinforcement based on the reinforcement force is safe and economical. The method doesn＇t need to suppose a sliding surface to obtain the reinforcement force, and it is also clear in physical meaning. So this method realized the organic unification of the stability analysis and the slope reinforcement.