Dual Variable Inertial Accelerated Algorithm for Split System of Null Point Equality Problems

Author(s):  
Anteneh Getachew Gebrie
Author(s):  
Xiaohua Zeng ◽  
Zhenwei Wang ◽  
Dafeng Song ◽  
Dongpo Yang

The coordination control of a transmission system has gradually attracted more attention with the development of hybrid electric vehicles. However, nonlinear coupling of multiple power sources, superposition of different dynamic characteristics in multiple components, and withdrawal and intervention for a power-split powertrain with a two-speed automated manual transmission (AMT) gearbox can cause jerk and vibration of the transmission system during the shift, which has higher requirements and challenges for the overall performance improvement of the system. This paper designs a novel, robust, augmented H∞ shift control strategy for a power-split system with a two-speed AMT gearbox of a heavy commercial vehicle and verifies the strategy’s effectiveness with simulations and experiments. First, the dynamic plant model and kinetic equations are established, and the shift is divided into five stages to clearly reveal the jerk and vibration problem. Based on augmented theory, a robust H∞ shift control strategy is proposed. Shift coordination is transformed into a speed tracking problem, and state variable and disturbance are reconstructed to obtain a new augmented system. Simulation and hardware-in-the-loop test are carried out to verify the effectiveness of the strategy, which mainly includes simulation of pneumatic actuator and H∞ control strategy. Results show that the proposed H∞ control strategy can greatly reduce the jerk of the transmission system. The jerk produced by the proposed strategy is decreased from 20.4 to 4.07 m/s3, leading to a substantial improvement of 80%. Therefore, the proposed strategy may offer a theoretical reference for the actual vehicle controller during the shift.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.


Author(s):  
Arata Yamamoto

Abstract We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.


Author(s):  
John Locker ◽  
P. M. Prenter

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.


2012 ◽  
Vol 496 ◽  
pp. 50-53
Author(s):  
Zhan Shun Yin ◽  
Yong Wei Han ◽  
Xi Chun Cai

Based on the CAE analysis. The dual variable gear shaft of the transmission for domestic ZL50 wheel loader was redesigned and the processing technology was optimized. The problem of the hardness of the spline which connects the dual variable gear shaft and the working hydraulic pump can not meet the requirements after heat treatment caused by unreasonable design was solved. The problem of the low geometric tolerance and early wear of the spline were solved. After practical application, the market feedback shows that the failure rate, service life and reliability greatly of new designed shaft were enhanced


1998 ◽  
Vol 59 (3) ◽  
pp. 537-541 ◽  
Author(s):  
MANUEL NÚÑEZ

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.


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