Analysis of Longitudinally Inhomogeneous Waveguides using Taylor's Series Expansion

2006 ◽  
Vol 20 (8) ◽  
pp. 1093-1100 ◽  
Author(s):  
M. Khalaj-Amirhosseini
Keyword(s):  
Series Expansion ◽  
Taylor’S Series

THE EVALUATION OF CONTROLLER TRACKING PERFORMANCE BASED ON TAYLOR’S SERIES EXPANSION MODEL

2015 ◽  
Vol 74 (9) ◽  
Author(s):  
Maziyah Mat Noh ◽  
M. R. Arshad ◽  
Rosmiwati Mohd-Mokhtar
Keyword(s):  
Series Expansion ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Linear Quadratic Regulator ◽  
Tracking Performance ◽  
Convergence Time ◽  
Linear Quadratic ◽  
Glide Path ◽  
Expansion Model ◽  
Taylor’S Series

This paper presents the controller tracking performance of Underwater Glider. The controllers are designed based on linearised model. The equations of motion are restricted to longitudinal plane. The controllers are designed and tested for the glide path moving from 45° to 30° downward and upward. The model is linearised using Taylor’s series expansion linearisation method. The controller developed here is Sliding Mode Control (SMC), and Linear Quadratic Regulator (LQR). The performance of both controllers are compared and analysed. The simulations show SMC produce better performance with about over 30% faster than LQR based its convergence time.

Modeling of unsteady aerodynamic characteristics at high angles of attack

2018 ◽  
Vol 233 (6) ◽  
pp. 2291-2301 ◽  
Author(s):  
Dong Hao ◽  
Lin Zhang ◽  
Jing Yu ◽  
Daiyong Mao
Keyword(s):  
State Space ◽  
Series Expansion ◽  
Angular Rate ◽  
Minimum Mean Square Error ◽  
Aerodynamic Characteristics ◽  
Unsteady Aerodynamic ◽  
Aerodynamic Model ◽  
Constant Pitch ◽  
High Angles Of Attack ◽  
Taylor’S Series

An improved model to express the unsteady aerodynamic characteristics at high angles of attack is presented in this paper. The proposed aerodynamic model is expressed on the basis of a progressive state-space representation and Taylor’s series expansion. The state-space expression is a first-order differential equation in which the power item of the angular rate of attack is introduced. The unsteady aerodynamic coefficients are described by Taylor’s series expansion in terms of input variables. The approach of minimum mean square error criterion is utilized to identify the unknown parameters of the proposed model by nonlinear least square method from the tunnel data. The given modeling method is experimentally demonstrated by the wind tunnel measurements of NACA 0015 airfoil with constant rate to high angles of attack, F18 aircraft with constant pitch rate ramp motion, and F18 HARV (high alpha research vehicle) configuration with large-amplitude harmonic oscillatory. The results show that it is possible to analyze more complex unsteady aerodynamic problems for an aircraft within the framework of the proposed aerodynamic model and the represented model is directly amenable to the simulation and control system design.

Asymptotic Expansion Technique for Evaluating the Uncertainty of Moist-Air Density Formula

2019 ◽  
Author(s):  
Sejong Chun
Keyword(s):  
Asymptotic Expansion ◽  
Measurement Uncertainty ◽  
Series Expansion ◽  
Moist Air ◽  
Air Density ◽  
Expansion Technique ◽  
Commercial Instrument ◽  
Output Quantity ◽  
Measurement Uncertainty Evaluation ◽  
Taylor’S Series

Abstract Asymptotic expansion technique can evaluate the measurement uncertainty by classifying an output quantity into a measured value and its correction values. The asymptotic expansion technique combines simultaneous observations of input quantities into the output measured value. The asymptotic expansion technique is useful in evaluating a multi-variate output quantity such as the moist-air density formula (CIPM-2007), in which covariances among input quantities could complicate the evaluation of measurement uncertainty. This study demonstrates that both the Taylor’s series expansion and the chain rule of differentiation are enough to calculate the sensitivity coefficients for the CIPM-2007 air density formula. The measurement uncertainty is found to be greater than the original CIPM-2007 formula by two orders of magnitude. It is because the uncertainty of correction values come from a commercial instrument for monitoring laboratory environments. Nevertheless, the asymptotic expansion technique is useful for measurement uncertainty evaluation to avoid subtle problems of ignoring covariance of input quantities in the literature.

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