scholarly journals Design and implementation of dual-core MIPS processor for LU decomposition based on FPGA

2021 ◽  
Vol 11 (2) ◽  
pp. 1476
Author(s):  
Rusul Khalil Saad ◽  
Safaa S. Omran
Keyword(s):  
Control Systems ◽  
Communication Systems ◽  
Triangular Matrix ◽  
Good Alternative ◽  
Matrix Inversion ◽  
Lu Decomposition ◽  
Lower Triangular Matrix ◽  
Upper Triangular Matrix ◽  
Time Required ◽  
Dual Core

Many systems like the control systems and in communication systems, there is usually a demand for matrix inversion solution. This solution requires many operations, which makes it not possible or very hard to meet the needs for real-time constraints. Methods were exists to solve this kind of problems, one of these methods by using the LU decomposition of matrix which is a good alternative to matrix inversion. The LU matrices are two matrices, the L matrix, which is a lower triangular matrix, and the U matrix, which is an upper triangular matrix. In this paper, a design of dual-core processor is used as the hardware of the work and certain software was written to enable the two cores of the dual-core processor to work simultaneously in computing the value of the L matrix and U matrix. The result of this work are compared with other works that using single-core processor, and the results found that the time required in the cores of the dual-core is more less than using single-core. The designed dual-core processor is invoked using the VHDL language.

scholarly journals Transformation Matrix for Time Discretization Based on Tustin’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yiming Jiang ◽  
Xiaodong Hu ◽  
Sen Wu
Keyword(s):  
Transfer Functions ◽  
Triangular Matrix ◽  
Time Discretization ◽  
Transformation Matrix ◽  
Automatic Design ◽  
Lower Triangular Matrix ◽  
Upper Triangular Matrix ◽  
Lower Triangular ◽  
Theoretical Results ◽  
Bilinear Transform

This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method) is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degreen, the corresponding transformation matrix of ordernexists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.

scholarly journals A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS

2013 ◽  
Vol 23 (04) ◽  
pp. 763-778 ◽  
Author(s):  
NANTEL BERGERON ◽  
NATHANIEL THIEM
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Triangular Matrix ◽  
Lower Triangular Matrix ◽  
Transition Matrices ◽  
Triangular Matrices ◽  
Power Sum ◽  
Upper Triangular Matrices ◽  
Upper Triangular Matrix ◽  
Lower Triangular

We give an LU-decomposition of the supercharacter table of the group of n × n unipotent upper triangular matrices over 𝔽q, into a lower-triangular matrix with entries in ℤ[q] and an upper-triangular matrix with entries in ℤ[q-1]. To this end, we introduce a q deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommuting variables. The decomposition is obtained from the transition matrices between the supercharacter basis, the q-power-sum basis and the superclass basis. This is similar to the decomposition of the character table of the symmetric group Sn given by the transition matrices between Schur functions, monomials and power-sums. We deduce some combinatorial results associated to this decomposition. In particular, we compute the determinant of the supercharacter table.

Use of LU Decomposition of Modal Flexibility in Structural Damage Detection: Numerical Validation

2013 ◽  
Vol 569-570 ◽  
pp. 986-993
Author(s):  
Yong Hui An ◽  
Jin Ping Ou
Keyword(s):  
Structural Damage ◽  
Numerical Study ◽  
Damage Index ◽  
Triangular Matrix ◽  
Mathematical Tool ◽  
Lu Decomposition ◽  
Flexibility Matrix ◽  
Modal Flexibility ◽  
The Matrix ◽  
Upper Triangular Matrix

The flexibility can be approximately synthesized with the first several measured modal parameters, i.e. the so called modal flexibility. The modal flexibility matrix will change with damage in a structure, and the change of modal flexibility should contain the information of damage. It is important to find a damage index that can pick up damage from the change of modal flexibility. To address this issue, the mathematical tool LU decomposition is introduced to deal with the modal flexibility matrix in order to find damage clearly. After decomposition, the modal flexibility is decomposed into a lower triangular matrix L and an upper triangular matrix U. Numerical results of both single and multiple damage cases under white noise excitation indicate that the matrix U has enough information of damage; and the proposed new technique can be utilized to locate the damage accurately. The present numerical study will lay a foundation for the application of real-time structural health monitoring in experiments and engineering.

scholarly journals Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 61
Author(s):  
Oscar Danilo Montoya ◽  
Juan S. Giraldo ◽  
Luis Fernando Grisales-Noreña ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios
Keyword(s):  
Power Flow ◽  
Triangular Matrix ◽  
Distribution Networks ◽  
Flow Method ◽  
Processing Times ◽  
Three Phase ◽  
Derivative Free ◽  
Upper Triangular Matrix ◽  
Power Flow Problem ◽  
Power Flow Method

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.

scholarly journals The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

2021 ◽  
Vol 11 (4) ◽  
pp. 1618
Author(s):  
Ping-Nan Chen ◽  
Yung-Te Chen ◽  
Hsin Hsiu ◽  
Ruei-Jia Chen
Keyword(s):  
Control Systems ◽  
Force Feedback ◽  
Training System ◽  
Considerable Time ◽  
Virtual Training ◽  
Control Gain ◽  
Negative Damping ◽  
The Stability ◽  
Time Required ◽  
Stable Control

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

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