Simplified treatment of the transconductance linearization problem employing any number of coupled differential pairs

2020 ◽  
Vol 48 (7) ◽  
pp. 1124-1139
Author(s):  
Lazhar Fekih‐Ahmed
Keyword(s):  
Linearization Problem

On the Pseudo-Linearization Problem for Nonlinear Systems.

1988 ◽  
Author(s):  
Jianliang Wang ◽  
Wilson J. Rugh
Keyword(s):  
Nonlinear Systems ◽  
Linearization Problem

scholarly journals New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1573
Author(s):  
Waleed Mohamed Abd-Elhameed ◽  
Badah Mohamed Badah
Keyword(s):  
Differential Equation ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Tau Method ◽  
Riccati Differential Equation ◽  
Shifted Jacobi Polynomials ◽  
Linearization Problem ◽  
Linearization Coefficients ◽  
New Formula ◽  
Connection Formulas

This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new formula in which the moments of the shifted Jacobi polynomials are expressed in terms of other shifted Jacobi polynomials. The derived moments formula involves a hypergeometric function of the type 4F3(1), which cannot be summed in general, but for special choices of the involved parameters, it can be summed. The reduced moments formulas lead to establishing new linearization formulas of certain parameters of Jacobi polynomials. Another approach for obtaining other linearization formulas of some Jacobi polynomials depends on making use of the connection formulas between two different Jacobi polynomials. In the two suggested approaches, we utilize some standard reduction formulas for certain hypergeometric functions of the unit argument such as Watson’s and Chu-Vandermonde identities. Furthermore, some symbolic algebraic computations such as the algorithms of Zeilberger, Petkovsek and van Hoeij may be utilized for the same purpose. As an application of some of the derived linearization formulas, we propose a numerical algorithm to solve the non-linear Riccati differential equation based on the application of the spectral tau method.

Global Darboux theorems and a linearization problem

1994 ◽  
pp. 37-44
Author(s):  
Eleonora Ciriza
Keyword(s):  
Linearization Problem

scholarly journals A Parametric Solution to the Generalized Bias Linearization Problem

Actuators ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 14 ◽  
Author(s):  
David Meeker ◽  
Eric Maslen
Keyword(s):  
Analytical Solution ◽  
Bias Current ◽  
Magnetic Bearings ◽  
Parametric Solution ◽  
Equal Area ◽  
Analytical Computation ◽  
Linearization Problem

Previously, a generalized bias current linearization was presented for the control of radial magnetic bearings. However, a numerically intensive procedure was required to obtain bias linearization currents. The present work develops an analytical solution to the generalized bias linearization problem in which solutions are indexed by a small number of parameters. The formulation also permits the analytical computation of bias linearization currents for faulted-coil cases. A limitation of the solution presented is that it only applies to stators with an even number of evenly spaces poles of equal area.

An Approximation Algorithm for the Minimum Breakpoint Linearization Problem

2009 ◽  
Vol 6 (3) ◽  
pp. 401-409 ◽  
Author(s):  
Xin Chen ◽  
Yun Cui
Keyword(s):  
Approximation Algorithm ◽  
Linearization Problem

scholarly journals On the Connection and Linearization Problem for Discrete Hypergeometric q-Polynomials

2001 ◽  
Vol 257 (1) ◽  
pp. 52-78 ◽  
Author(s):  
R. Álvarez-Nodarse ◽  
J. Arvesú ◽  
R.J. Yáñez
Keyword(s):  
Linearization Problem

Linearization of High Precision Human Body Temperature Measurement Circuit Based on NTC Thermistor

2015 ◽  
Vol 713-715 ◽  
pp. 381-384
Author(s):  
De Jun Li ◽  
Chi Gang Xing
Keyword(s):  
Body Temperature ◽  
The Body ◽  
Measuring System ◽  
Measurement Circuit ◽  
Actual Measurement ◽  
Thermistor Bridge ◽  
Ntc Thermistor ◽  
Human Body Temperature ◽  
Body Temperature Measurement ◽  
Linearization Problem

In the micro-climate cloth researching, we usually need to accurate measuring the body temperature, in this paper we choose the constant-voltage temperature measuring system based on the NTC thermistor to measure the temperature. Because the resistance of the thermistor and the temperature is not linear, so this will cause the output of the measurement circuit is not linear. In actual measurement we usually require the output of the circuit varies linearly in the required range. This paper mainly research the linearization problem of the NTC thermistor bridge circuit in the required temperature range.

A Non-Negative Representation of the Linearization Coefficients of the Product of Jacobi Polynomials

1981 ◽  
Vol 33 (4) ◽  
pp. 915-928 ◽  
Author(s):  
Mizan Rahman
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Function ◽  
Jacobi Polynomials ◽  
Defining Relation ◽  
Linearization Problem ◽  
Image Position ◽  
Linearization Coefficients ◽  
Negative Representation

The problem of linearizing products of orthogonal polynomials, in general, and of ultraspherical and Jacobi polynomials, in particular, has been studied by several authors in recent years [1, 2, 9, 10, 13-16]. Standard defining relation [7, 18] for the Jacobi polynomials is given in terms of an ordinary hypergeometric function:with Re α > –1, Re β > –1, –1 ≦ x ≦ 1. However, for linearization problems the polynomials Rn(α,β)(x), normalized to unity at x = 1, are more convenient to use:(1.1)Roughly speaking, the linearization problem consists of finding the coefficients g(k, m, n; α,β) in the expansion(1.2)

Modeling and Simulation on Temperature Control System for Hot Pressure Welding

2013 ◽  
Vol 690-693 ◽  
pp. 2589-2593
Author(s):  
Bing Xie ◽  
Fang Hu ◽  
Shi Min Chen
Keyword(s):  
Temperature Control ◽  
Dynamic Performance ◽  
Step Response ◽  
Temperature Control System ◽  
Delay Model ◽  
Pressure Welding ◽  
Steady Stage ◽  
Data Acquisition Card ◽  
Linearization Problem ◽  
Heating Up

Hot pressure welding (HPW) is one of the inner lead bonding process which is widely used in microelectronics manufacturing. This paper presents a practical digital temperature controller for HPW. Based on the step response, an identification method is developed to obtain a nonlinear time-delay model for heating-up control design. The input-output linearization problem is solved by means of second-order Pade approximation and static inverse transform, and an optimal controller is obtained for the welding machine. The experimental equipment on the temperature control is designed based on LabVIEW and data acquisition card. Simulation and experimental results show that the dynamic performance, steady stage error and overshoot satisfy the designed requirements.

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