A Closed Form Solution for Wave Propagation in a Rectangular Waveguide Filled with Time-Varying Media

2014 ◽  
Vol 900 ◽  
pp. 110-115
Author(s):  
Bing Kang Chen ◽  
Feng Guo
Keyword(s):  
Closed Form ◽  
Rectangular Waveguide ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Varying ◽  
Propagation Characteristics ◽  
Te Mode ◽  
Accurate Expression ◽  
The Waves

In this paper, the solution and some propagation characteristics of waves inside a rectangular waveguide in the time-varying media are presented. The separation of variables method is used to get a closed form solution i.e. accurate expression for TE mode when the permittivity of media changes with respect to time. It is clearly shown that both the amplitude and frequency of the waves in rectangular waveguide change with respect to time in time-varying permittivity.

Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

2018 ◽  
Vol 18 (07) ◽  
pp. 1850098 ◽  
Author(s):  
Kai Zhou ◽  
Jinpeng Su ◽  
Hongxing Hua
Keyword(s):  
Closed Form ◽  
Orthotropic Plate ◽  
Acoustic Analysis ◽  
Thermal Environment ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Thermal Loads ◽  
Orthotropic Plates ◽  
Heated Plates

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment.

An Adaptive Nonlinear Trajectory Tracking Design for Mobile Robots and it’s Practical Implementation

2013 ◽  
Vol 284-287 ◽  
pp. 1744-1748
Author(s):  
Yung Hsiang Chen ◽  
Tzuu Hseng S. Li ◽  
Yung Yue Chen
Keyword(s):  
Mobile Robot ◽  
Closed Form ◽  
Trajectory Tracking ◽  
Tracking System ◽  
Closed Form Solution ◽  
Form Solution ◽  
Practical Implementation ◽  
Time Varying ◽  
Nonlinear Controller ◽  
Reference Trajectories

An adaptive nonlinear trajectory tracking design for mobile robot and its practical implementation are presented in this paper. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, based on the property of the trajectory tracking system of the nonholonomic mobile robot, the adaptive H2 trajectory tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and S type reference trajectories are used for performance verification.

scholarly journals Control Design of a Swarm of Intelligent Robots: A Closed-Form H2 Nonlinear Control Approach

2020 ◽  
Vol 10 (3) ◽  
pp. 1055
Author(s):  
Yung-Hsiang Chen ◽  
Shi-Jer Lou
Keyword(s):  
Nonlinear Control ◽  
Closed Form ◽  
Trajectory Tracking ◽  
Control Method ◽  
Tracking Error ◽  
Closed Form Solution ◽  
Form Solution ◽  
Practical Implementation ◽  
Time Varying ◽  
Tracking Problem

A closed-form H2 approach of a nonlinear trajectory tracking design and practical implementation of a swarm of wheeled mobile robots (WMRs) is presented in this paper. For the nonlinear trajectory tracking problem of a swarm of WMRs, the design purpose is to point out a closed-form H2 nonlinear control method that analytically fulfills the H2 control performance index. The key and primary contribution of this research is a closed-form solution with a simple control structure for the trajectory tracking design of a swarm of WMRs is an absolute achievement and practical implementation. Generally, it is challenging to solve and find out the closed-form solution for this nonlinear trajectory tracking problem of a swarm of WMRs. Fortunately, through a sequence of mathematical operations for the trajectory tracking error dynamics between the control of a swarm of WMRs and desired trajectories, this H2 trajectory tracking problem is equal to solve the nonlinear time-varying Riccati-like equation. Additionally, the closed-form solution of this nonlinear time-varying Riccati-like equation will be acquired with a straightforward form. Finally, for simulation-controlled performance of this H2 proposed method, two testing scenarios, circular and S type reference trajectories, were applied to performance verification.

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