Stereographic Visualization of 5-Dimensional Regular Polytopes

Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional (n≥4) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs (n>5)

The Active Fractional Order Control for Maglev Suspension System

Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller

Error Estimates for the Heterogeneous Multiscale Finite Volume Method of Convection-Diffusion-Reaction Problem

Based on the heterogeneous multiscale method, this paper presents a finite volume method to solve multiscale convection-diffusion-reaction problem. The paper constructs an algorithm of the optimal order convergence rate in H1-norm under periodic medias

Design of a Maglev Vibration Test Platform for the Research of Maglev Vehicle-girder Coupled Vibration Problem

The maglev vehicle-girder coupled vibration problem has been encountered in many maglev test or commercial lines, which significantly degrade the performance of the maglev train. In previous research on the principle of the coupled vibration problem, it has been discovered that the fundamental model of the maglev girder can be simplified as a series of mass-spring resonators of different but related resonance frequencies, and that the stability of the vehicle-girder coupled system can be investigated by separately examining the stability of each mass-spring resonator – electromagnet coupled system. Based on this conclusion, a maglev test platform, which includes a single electromagnetic suspension control system, is built for experimental study of the coupled vibration problem. The guideway of the test platform is supported by a number of springs so as to change its flexibility. The mass of the guideway can also be changed by adjusting extra weights attached to it. By changing the flexibility and mass of the guideway, the rules of the maglev vehicle-girder coupled vibration problem are to be examined through experiments, and related theory on the vehicle-girder self-excited vibration proposed in previous research is also testified

Design of a Maglev Vibration Test Platform for the Research of Maglev Vehicle-girder Coupled Vibration Problem

The maglev vehicle-girder coupled vibration problem has been encountered in many maglev test or commercial lines, which significantly degrade the performance of the maglev train. In previous research on the principle of the coupled vibration problem, it has been discovered that the fundamental model of the maglev girder can be simplified as a series of mass-spring resonators of different but related resonance frequencies, and that the stability of the vehicle-girder coupled system can be investigated by separately examining the stability of each mass-spring resonator – electromagnet coupled system. Based on this conclusion, a maglev test platform, which includes a single electromagnetic suspension control system, is built for experimental study of the coupled vibration problem. The guideway of the test platform is supported by a number of springs so as to change its flexibility. The mass of the guideway can also be changed by adjusting extra weights attached to it. By changing the flexibility and mass of the guideway, the rules of the maglev vehicle-girder coupled vibration problem are to be examined through experiments, and related theory on the vehicle-girder self-excited vibration proposed in previous research is also testified

Fractal Tilings Based on Successive Adjacent Substitution Rule

A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. f-tilings have complicated structures and strong visual appeal. However, so far, the discovered f-tilings are very limited since constructing such f-tilings needs special talent. Based on the idea of hierarchically subdividing adjacent tiles, this paper presents a general method to generate f-tilings. Penrose tilings are utilized as illustrators to show how to achieve it in detail. This method can be extended to treat a large number of tilings that can be constructed by substitution rule (such as chair and sphinx tilings and Amman tilings). Thus, the proposed method can be used to create a great many of f-tilings

Aesthetic Patterns with Symmetries of the Regular Polyhedron

A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra

Decoupling Control for Module Suspension System of Maglev Train Based on Feedback Linearization and Extended State Observer

The suspension gap of the electromagnetic suspension maglev train is around 8 mm. In practice, it is found that the system gap fluctuations are amplified due to the inner coupling of the suspension module system in the maglev train. In addition, maglev trains are affected by load disturbances and parameter perturbations during operation. These uncertainties reduce the ride comfort. Therefore, it is necessary to propose a novel control strategy to suppress inner coupling while reducing the influence of uncertainties on the system. In this paper, a control strategy based on feedback linearization and extended state observer (ESO) is proposed to address this challenge. Firstly, the suspension module system model is established with parameter uncertainties and external disturbances. Additionally, the inner coupling of the suspension module is represented in this model. Subsequently, the feedback linearization method based on differential geometry theory is applied to reduce the effect of inner coupling. Meanwhile, the system uncertainties are transformed into equivalent disturbances by this method. Afterward, a linear ESO is designed to estimate the equivalent disturbances. Finally, a state feedback controller is used to achieve stable suspension and compensate for the disturbances. Simulation and experimental results show that the proposed decoupled control strategy significantly suppresses the influence of inner coupling and uncertainties on the system compared with the traditional PID control strategy