scholarly journals A variable structure algorithm using the (3,2)-scheme and the Fehlberg method

2015 ◽  
pp. 446-455
Author(s):  
Е.А. Новиков
Keyword(s):  
Stability Criterion ◽  
Jacobi Matrix ◽  
Variable Structure ◽  
Stability Control ◽  
Accuracy Control ◽  
Stable Method ◽  
Third Order ◽  
Structure Algorithm ◽  
The Stability ◽  
Embedded Method

Построен (3,2)-метод третьего порядка с замораживанием матрицы Якоби, в котором $L$-устойчивыми являются основная и промежуточные численные схемы. Получено неравенство для контроля точности вычислений с использованием вложенного метода второго порядка. Предложено неравенство для контроля устойчивости явного трехстадийного метода Рунге-Кутта-Фельберга третьего порядка. Сформулирован алгоритм переменной структуры, в котором на каждом шаге явный или $L$-устойчивый метод выбираются по критерию устойчивости. Приведены результаты расчетов. A third-order (3,2)-method allowing freezing the Jacobi matrix is constructed. Its main and intermediate numerical schemes are $L$-stable. An accuracy control inequality is obtained using an embedded method of second order. A stability control inequality for the explicit three-stage Runge-Kutta-Fehlberg method of third order is proposed. A variable structure algorithm is formulated. An explicit or $L$-stable method is chosen according to the stability criterion at each step. Numerical results are discussed.

scholarly journals Dynamic Imbalance Analysis and Stability Control of Galloping Gait for a Passive Quadruped Robot

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Chunlei Wang ◽  
Ting Zhang ◽  
Xiaohui Wei ◽  
Yongjun Long ◽  
Shigang Wang
Keyword(s):  
Stability Criterion ◽  
Center Of Mass ◽  
Zero Point ◽  
Stability Control ◽  
Quadruped Robot ◽  
Peak Time ◽  
Flight Phase ◽  
Trunk Posture ◽  
The Stability ◽  
Necessary And Sufficient

Some imbalance and balance postures of a passive quadruped robot with a simplified mathematical model are studied. Through analyzing the influence of the touchdown angle of the rear leg on the posture of the trunk during the flight phase, the stability criterion is concluded: the closer are the two moments which are the zero time of the pitching angle and the peak time of the center of mass, the better is the stability of the trunk posture during the flight phase. Additionally, the validity of the stability criterion is verified for the cat, greyhound, lion, racehorse, basset hound, and giraffe. Furthermore, the stability criterion is also applicable when the center of the mass of body is shifted. Based on the stability criterion, the necessary and sufficient condition of the galloping stability for the quadruped robot is proposed to attain a controlled thrust. The control strategy is designed by an optimization dichotomy algorithm for seeking the zero point of the balance condition. Through the control results, it is demonstrated that the imbalance posture of the trunk could be stabilized by adjusting the stiffness of four legs.

Duffing Chaotic System Stability Control Based on Sliding Mode Control

2012 ◽  
Vol 605-607 ◽  
pp. 1639-1642
Author(s):  
Ding Ma
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability Control ◽  
System Stability ◽  
Terminal Sliding Mode ◽  
Sliding Mode Variable Structure ◽  
The Stability ◽  
And Control

Considering the Duffing chaotic system, the problem of stability control based on the terminal sliding mode variable structure is studied. A new terminal sliding mode surface and control law are designed. On this basis, the stability of closed-loop system is analyzed. Simulation results show the effectiveness of the control method.

scholarly journals Stability Control for Electric Vehicles with Four In-Wheel-Motors Based on Sideslip Angle

2021 ◽  
Vol 12 (1) ◽  
pp. 42
Author(s):  
Kun Yang ◽  
Danxiu Dong ◽  
Chao Ma ◽  
Zhaoxian Tian ◽  
Yile Chang ◽  
...  
Keyword(s):  
Electric Vehicles ◽  
Control Method ◽  
Sliding Mode ◽  
Stability Control ◽  
Torque Control ◽  
Wheel Load ◽  
Sideslip Angle ◽  
Distribution Method ◽  
Load Rate ◽  
The Stability

Tire longitudinal forces of electrics vehicle with four in-wheel-motors can be adjusted independently. This provides advantages for its stability control. In this paper, an electric vehicle with four in-wheel-motors is taken as the research object. Considering key factors such as vehicle velocity and road adhesion coefficient, the criterion of vehicle stability is studied, based on phase plane of sideslip angle and sideslip-angle rate. To solve the problem that the sideslip angle of vehicles is difficult to measure, an algorithm for estimating the sideslip angle based on extended Kalman filter is designed. The control method for vehicle yaw moment based on sliding-mode control and the distribution method for wheel driving/braking torque are proposed. The distribution method takes the minimum sum of the square for wheel load rate as the optimization objective. Based on Matlab/Simulink and Carsim, a cosimulation model for the stability control of electric vehicles with four in-wheel-motors is built. The accuracy of the proposed stability criterion, the algorithm for estimating the sideslip angle and the wheel torque control method are verified. The relevant research can provide some reference for the development of the stability control for electric vehicles with four in-wheel-motors.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

The flow of a micropolar liquid layer down an inclined plane

1968 ◽  
Vol 64 (2) ◽  
pp. 513-526 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Thin Films ◽  
Steady State ◽  
Liquid Layer ◽  
Stability Criterion ◽  
Long Waves ◽  
Inclined Plane ◽  
The Stability ◽  
Micropolar Liquid

AbstractConsideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

2016 ◽  
Vol 24 (01) ◽  
pp. 1550021 ◽  
Author(s):  
Heekyu Woo ◽  
Young S. Shin
Keyword(s):  
Order Approximation ◽  
Stable Model ◽  
Approximation Model ◽  
Third Order ◽  
Acoustic Structure ◽  
Structure Interaction ◽  
Proposed Model ◽  
The Stability ◽  
Third Order Approximation ◽  
Interaction Problem

In this paper, a new third-order approximation model for an acoustic-structure interaction problem is introduced. The new approximation model is designed to be an accurate and a stable model for predicting the response of a submerged structure. The proposed model is obtained by combining two lower order approximation models instead of using an operator matching method. The stability of this model is checked by a modal analysis. Finally, the approximation model is coupled to the spherical shell structure, and its performance is checked by a shock analysis.

The Stability Control of Soft Soil Foundations of Urban Roads According to the Surface Subsidence Monitoring Data

2013 ◽  
Vol 859 ◽  
pp. 222-227
Author(s):  
Hong Jun Liu ◽  
Jin Hua Tan ◽  
Xue Wen Su ◽  
Hao Wu
Keyword(s):  
Soft Soil ◽  
Stability Control ◽  
Surface Subsidence ◽  
Monitoring Data ◽  
Research Results ◽  
The Road ◽  
Future Design ◽  
Left And Right ◽  
Soil Foundation ◽  
The Stability

Two typical monitoring sections are selected for obtaining the change law of the surface subsidence and the settlement after construction of soft soil foundations, and determining the reasonable unloading time. The research results show that the surface settlement rate is large during the filling stage, the rate decreases after the loading and gradually stabilized. The embankment midline settlement is larger than the settlement of the road shoulder which is concluded from the fact that the subsidence of the middle settlement plate is larger than those of the left and right plate. The surface subsidence rate is less than 5mm per month during the two month before unloading according to the data in the tables. The settlement after construction presumed from the middle plate is more significantly larger than that of left and right sides, hence, as the unloading basis of preloading drainage method in soft soil foundation treatment the settlement after construction which is calculated from the midline monitoring data of the road is appropriate. After 6 months the calculated post-construction settlements of the two sections are in the scope of the design requirement since they decrease with preloading time. The reliable basis is provided for the future design and construction of soft foundation in this area through the research results.

Vibration and Stability Control of Spinning Flexible Shaft via Integration of Smart Materials Technology

2000 ◽  
Author(s):  
Ohseop Song ◽  
Liviu Librescu ◽  
Nam-Heui Jeong
Keyword(s):  
Smart Materials ◽  
Stability Control ◽  
Rotational Axis ◽  
Rotating Shaft ◽  
Nonconservative System ◽  
Gyroscopic Forces ◽  
Points Of View ◽  
The Stability ◽  
Spinning Speed ◽  
Static Character

Abstract Within this paper problems related with the vibration and stability control of circular flexible shafts spinning about their rotational axis are addressed. Due to the occurrence, as a result of the spinning speed, of gyroscopic forces in the system, the rotating shaft can experience, in some conditions, instabilities of the same nature as any nonconservative system, namely divergence and flutter instabilities. Whereas the former instability is of a static character, the latter one is of dynamic character and the results of its occurrence are catastrophic. By including collocated sending and actuating capabilities via integration in the system of piezoelectric devices and of a feedback control law, it is shown that a dramatic enhancement of both the free dynamic response and of the stability behavior from both the divergence and flutter points of view can be achieved. This implies that via the implementation of this technology an increase of the spinning speed can be achieved without the occurrence of these instabilities. Numerical simulations documenting these findings are provided and pertinent conclusions are outlined. It is also worthy to mention that the shaft is modeled as a thin-walled cylinder made of an anisotropic material and incorporating a number of non-classical features.

scholarly journals Study of the Stability Control of the Rock Surrounding Double-Key Strata Recovery Roadways in Shallow Seams

2019 ◽  
Vol 2019 ◽  
pp. 1-21 ◽  
Author(s):  
Cheng Zhu ◽  
Yong Yuan ◽  
Zhongshun Chen ◽  
Zhiheng Liu ◽  
Chaofeng Yuan
Keyword(s):  
Engineering Application ◽  
Stability Control ◽  
Surrounding Rock ◽  
Control Effect ◽  
Pressure Relief ◽  
Support Design ◽  
Key Strata ◽  
Fracture Development ◽  
Surrounding Rock Control ◽  
The Stability

The stability control of the rock surrounding recovery roadways guarantees the safety of the extraction of equipment. Roof falling and support crushing are prone to occur in double-key strata (DKS) faces in shallow seams during the extraction of equipment. Therefore, this paper focuses on the stability control of the rock surrounding DKS recovery roadways by combining field observations, theoretical analysis, and numerical simulations. First, pressure relief technology, which can effectively release the accumulated rock pressure in the roof, is introduced according to the periodic weighting characteristics of DKS roofs. A reasonable application scope and the applicable conditions for pressure relief technology are given. Considering the influence of the eroded area on the roof structure, two roof mechanics models of DKS are established. The calculation results show that the yield load of the support in the eroded area is low. A scheme for strengthening the support with individual hydraulic props is proposed, and then, the support design of the recovery roadway is improved based on the time effects of fracture development. The width of the recovery roadway and supporting parameters is redesigned according to engineering experience. Finally, constitutive models of the support and compacted rock mass in the gob are developed with FLAC3D software to simulate the failure characteristics of the surrounding rock during pressure relief and equipment extraction. The surrounding rock control effects of two support designs and three extraction schemes are comprehensively evaluated. The results show that the surrounding rock control effect of Scheme 1, which combines improved support design and the bidirectional extraction of equipment, is the best. Engineering application results show that Scheme 1 realizes the safe extraction of equipment. The research results can provide a reference and experience for use in the stability control of rock surrounding recovery roadways in shallow seams.

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