Model reduction of unstable systems based on balanced truncation algorithm

Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms

Weak Lefschetz property of graded Gorenstein algebras associated to the Apéry set of a numerical semigroup

It has been conjectured that all graded Artinian Gorenstein algebras of codimension three have the weak Lefschetz property over a field of characteristic zero. In this paper, we study the weak Lefschetz property of associated graded algebras A of the Apéry set of M-pure symmetric numerical semigroups generated by four natural numbers. These algebras are graded Artinian Gorenstein algebras of codimension three

Application of model reduction for robust control of self-balancing two-wheeled bicycle

In recent years, balance control of two-wheeled bicycle has received more attention of scientists. One difficulty of this problem is the control object is unstable and constantly impacted by noise. To solve this problem, the authors often use robust control algorithms. However, robust controller of self-balancing two-wheeled bicycle are often complex and higher order so affect to quality during real controlling. The article introduces the stochastic balanced truncation algorithm based on Schur analysis and applies this algorithm to reduce order higher order robust controller in control balancing two-wheeled bicycle problem. The simulation results show that the reduced 4th and 5th order controller arcoording to the stochastic balanced truncation algorithm based on Schur analysis can control the two-wheeled bicycle model. The reduced 3rd order controller cannot control the balance of the two-wheeled bicycle model. The reduced 4th and 5th order controller can replace the original controller while the performance of the control system is ensured. Using reduced 5th, 4th order controller will make the program code simpler, reducing the calculation time of the self-balancing two-wheel control system. The simulation results show the correctness of the model reduction algorithm and the robust control algorithm of two-wheeled self-balancing two-wheeled bicycle

Some algorithms related to consistent decision table

Rough set theory is useful mathematical tool developed to deal with vagueness and uncertainty. As an important concept of rough set theory, an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table. Rough set theory is also the most popular for generating decision rules from decision table. In this paper, we propose an algorithm finding object reduct of consistent decsion table. On the other hand, we also show an algorithm to find some attribute reducts and the correctness of our algorithms is proof-theoretically. These our algorithms have polynomial time complexity. Our finding object reduct helps other algorithms of finding attribute reducts become more effectively, especially as working with huge consistent decision table

Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System

The electrical system's problem stabilizes the electrical system with three primary parameters: rotor angle stability, frequency stability, and voltage stability. This paper focuses on the problem of designing a low-order stable optimal controller for the generator rotor angle (load angle) stabilization system with minor disturbances. These minor disturbances are caused by lack of damping torque, change in load, or change in a generator during operation. Using the RH∞optimal robust design method for the Power System Stabilizer (PSS) to stabilize the generator’s load angle will help the PSS system work sustainably under disturbance. However, this technique's disadvantage is that the controller often has a high order, causing many difficulties in practical application. To overcome this disadvantage, we propose to reduce the order of the higher-order optimal robust controller. There are two solutions to reduce order for high-order optimal robust controller: optimal order reduction according to the given controller structure and order reduction according to model order reduction algorithms. This study selects the order reduction of the controller according to the model order reduction algorithms. In order to choose the most suitable low-order optimal robust controller that can replace the high-order optimal robust controller, we have compared and evaluated the order-reducing controllers according to many model order reduction algorithms. Using robust low-order controllers to control the generator’s rotor angle completely meets the stabilization requirements. The research results of the paper show the correctness of the controller order reduction solution according to the model order reduction algorithms and open the possibility of application in practice. Doi: 10.28991/esj-2021-01299 Full Text: PD

Effectiveness of fluid viscous damper for steel frame building subjected to earthquake load

Since the appearance of the first modern multistories buildings, besides the demand of ensuring the bearing capacity, one of the urgent problems facing the engineer is to do how to design structure to ensure the requirements of normal use such as displacement, motion acceleration within permissible limits. There exist many methods to reduce these response of structure under lateral load. Among these, using fluid viscous damper (FVD) is one of the most applied equipment because of its simplicity. This paper presents the examination of eight-story steel frame structure subjected to seismic load. The FVD system is defined in Etabs with link properties. In each story, four dampers are located in each direction of plan, with two on each side of the center of stiffness of the story. The time history analysis was conducted to study the structure subjected to seimic load collected from the function library of program Etabs. The effect of FVD system was determined by the dynamic response of the building and displacement indexes such as maximum displacement of roof, story drift ratio. The results show that, all the dynamic response characters of structure were decreased significantly when providing the FVD to it

Ultra high Performance Fiber Reinforced Concrete Panel Subjected to Severe Blast Loading

Experimental studies play a crucial role in shedding light on the dynamic behaviour of structures under blast loading. However, high costs and complicated technical requirements, particularly for full-scale structures, are still huge disadvantages to conduct such a series of tests. Hence, the finite element method is much needed to provide supplementary information to previous experiments and to enable further parametric studies without testing. This article presents a numerical investigation carried out to understand the behaviour of ultra high performance fiber reinforced concrete (UHPFRC) panels under severe blast loading. The authors designed a subroutine with eight numbers of solution-dependent state variables, 32 mechanical constants, integrated with the Abaqus program to analyze the dynamic behaviour of UHPFRC against multiple blast impacts, using the Johnson-Holmquist 2 damage model incorporating both the damage and residual strength of the material. The subroutine was validated by comparing the simulation results with test results. For the purpose of estimating the structural response of the UHPFRC panel subjected to blast loading, other studying scenarios were considered by varying input parameters, including the thickness of the panel, stand-off distance, and steel reinforcement bar volume. The variations in deflection, strain, and damage of the UHPFRC panel, as well as the steel reinforcement strain, were also evaluated. Through important obtained results, the UHPFRC panel is strongly recommended for a protective barrier installed in the vicinity of critical infrastructure against severe blast loadin

Condensation Heat Transfer of R410A Inside Multiport Minichannels with Different Cross-sectional Geometry

Condensation heat transfer of R410a in a multiport mini-channels tubes with different cross-sectional geometry is experimentally investigated. Three tubes with aspect ratio of 0.395, 0.385 and 0.446, and hydraulic diameters of 1.147 mm, 1.135 mm and 0.846 mm with number of channels (7, 11 and 18) are tested in this study. The experimented range of heat flux is from 3 to 15 kW/m2, mass flux from 50 to 500 kg/m2s. The data show that the heat transfer coefficient increases with heat flux, mass flux and vapor quality. A performance comparison was conducted among the 3 tested tubes and it was found out that the number of channels increases heat transfer coefficient significantly at low heat flux and mass flux, while this effect is damped at higher heat/mass flux condition. In addition, it was found that heat transfer in small hydraulic diameter and high aspect ratio channels deteriorated. Possible mechanism to this deterioration is proposed. Finally, a new correlation is developed to predict the heat transfer coefficient of R410a in a multiport mini-channels tube

The lasting effects of innovation on firm profitability: panel evidence from a transitional economy

This study is the first to study the lasting effects of innovation on firm profitability in Vietnam. Using a unique panel dataset for the period 2005–2015, our results show that innovators achieve higher profit in comparison with non-innovating firms. The positive effects of innovation on firm profitability are observed not only in the short term but also in the longer term. The benefits of innovation for firm profitability can be seen in higher export probability, better productivity, better access to formal credit, and the ability to secure government support, but only after innovation

EXTRACURRICULAR SPORTS: POPULAR CONTENTS AND FORMS AMONG STUDENTS IN THE DORMITORY OF VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY

This article is written to provide thorough information about popular contents and forms of extracurricular sports performed by university students at a dormitory of Vietnam National University Ho Chi Minh City (VNUHCMC). The study uses document references, surveys, and statistical mathematics to investigate what extracurricular sports are favored by the students and how they organize their practices. The results indicate that the majority of students choose to practice football, volleyball, badminton, athletics, and martial arts. They play with themselves and/or in teams, without instructors, from 30 minutes to 02 hours in the afternoon after school time and/or in the morning, at the dormitory and/or sports centers.  Article visualizations