A Novel Technique for the Stability of Multiple Frequency Resonators

1999 ◽  
Author(s):  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Dimensional Space ◽  
Multiple Delays ◽  
Stability Assessment ◽  
Multiple Frequency ◽  
Novel Technique ◽  
Controlled Systems ◽  
The Stability ◽  
The Given

Abstract A novel stability analysis is presented for feedback controlled systems with multiple unrelated time delays. The concern arises in an effort creating multi-frequency delayed resonators. Despite the broad treatment of single time delay cases there is no mechanism to analyze the stability of systems involving multiple delays. The proposed method is an advancement over the D-subdivision methodology. It reduces the stability based subdivisions and search to a single dimensional space instead of multiple dimensional platform. The method is very simple to implement and it results in the stability assessment of the given system as the number of unstable root pairs present.

scholarly journals Сombined ships stability analysis at the stage of design study

2021 ◽  
pp. 29-35
Author(s):  
Ilya A. Gulyaev Gulyaev ◽  
Evgeniy P. Ronnov
Keyword(s):  
Stability Analysis ◽  
Optimization Problems ◽  
Mutual Influence ◽  
Static Stability ◽  
Wind Effect ◽  
Stability Assessment ◽  
Design Study ◽  
Hull Design ◽  
The Stability ◽  
Russian River

. A method of stability analysis for combined ship (oil carrier/platform ship type) at the stage of design study is presented. It should be noted that not all of ship’s main seaworthiness and operational characteristics are the result of a simple addition of the characteristics of an oil carrier and a platform ship. Their mutual influence takes place, which should be taken into account when analysing the stability in the multivariant optimization problems of internal and external design of such ships. This leads to the requirement to adjust the known methods of stability analysis at the initial stages of ship design, which was the purpose of the present work and its originality. Taking into account the multivariance of the task and the hull design type, the stability assessment will be carried out through the analysis of the metacentric height extreme value on the assumption that the requirements of Russian River Register for admissible heeling angle at static wind effect are met. In order to account for nonlinearity of static stability curve when inclining up to the angles of deck immersion into water and emergence of bilge, it is suggested to apply an approximate method of metacentric radius determination. The proposed method of combined ship stability assessment is recommended to apply at the stage of justification and analysis of ship’s key elements as a limitation in the problems of mathematical modeling of optimization of such type of ships. The method allows to exclude from further consideration at the design study stage the possible options that do not meet the requirements of seaworthiness.

scholarly journals The Stability Analysis of a Multi-Port Single-Phase Solid-State Transformer in the Electromagnetic Timescale

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2250 ◽  
Author(s):  
Rui Wang ◽  
Qiuye Sun ◽  
Qifu Cheng ◽  
Dazhong Ma
Keyword(s):  
Stability Analysis ◽  
Solid State ◽  
Single Phase ◽  
Control Strategies ◽  
Current Source ◽  
Practical Stability ◽  
Stability Assessment ◽  
Solid State Transformer ◽  
The Stability ◽  
Signal Sinusoïdal

This paper proposes an overall practical stability assessment for a multi-port single-phase solid-state transformer (MS3T) in the electromagnetic timescale. When multiple stable subsystems are combined into one MS3T, the newly formed MS3T has a certain possibility to be unstable. Thus, this paper discusses the stability assessment of the MS3T in detail. First and foremost, the structure of the MS3T and its three stage control strategies are proposed. Furthermore, the stability analysis of each of the MS3T’s subsystems is achieved through the closed loop transfer function of each subsystem, respectively, including an AC-DC front-end side converter, dual active bridge (DAB) with a high-frequency (HF) or medium-frequency (MF) transformer, and back-end side incorporating DC-AC and dc-dc converters. Furthermore, the practical impedance stability criterion in the electromagnetic timescale, which only requires two current sensors and one external high-bandwidth small-signal sinusoidal perturbation current source, is proposed by the Gershgorin theorem and Kirchhoff laws. Finally, the overall stability assessment, based on a modified impedance criterion for the MS3T is investigated. The overall practical stability assessment of the MS3T can be validated through extensive simulation and hardware results.

scholarly journals An iterative frequency-sweeping approach for stability analysis of linear systems with multiple delays

2017 ◽  
Vol 36 (2) ◽  
pp. 379-398
Author(s):  
Xu-Guang Li ◽  
Silviu-Iulian Niculescu ◽  
Arben Çela
Keyword(s):  
Stability Analysis ◽  
Asymptotic Behaviour ◽  
Linear Systems ◽  
Invariance Property ◽  
Multiple Delays ◽  
Numerical Examples ◽  
The Stability ◽  
Imaginary Roots ◽  
Frequency Sweeping

AbstractIn this article, we study the stability of linear systems with multiple (incommensurate) delays, by extending a recently proposed frequency-sweeping approach. First, we consider the case where only one delay parameter is free while the others are fixed. The complete stability w.r.t. the free delay parameter can be systematically investigated by proving an appropriate invariance property. Next, we propose an iterative frequency-sweeping approach to study the stability under any given multiple delays. Moreover, we may effectively analyse the asymptotic behaviour of the critical imaginary roots (if any) w.r.t. each delay parameter, which provides a possibility for stabilizing the system through adjusting the delay parameters. The approach is simple (graphical test) and can be applied systematically to the stability analysis of linear systems including multiple delays. A deeper discussion on its implementation is also proposed. Finally, various numerical examples complete the presentation.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

scholarly journals Effect of Frequency Coupling on Stability Analysis of a Grid-Connected Modular Multilevel Converter System

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6580
Author(s):  
Yixing Wang ◽  
Qianming Xu ◽  
Josep M. Guerrero
Keyword(s):  
Stability Analysis ◽  
Coupling Effect ◽  
Modular Multilevel Converter ◽  
Stability Assessment ◽  
Analysis Method ◽  
Multilevel Converter ◽  
Single Input Single Output ◽  
Impedance Model ◽  
Frequency Coupling ◽  
The Stability

Due to the internal dynamics of the modular multilevel converter (MMC), the coupling between the positive and negative sequences in impedance, which is defined as frequency coupling, inherently exists in MMC. Ignoring the frequency coupling of the MMC impedance model may lead to inaccurate stability assessment, and thus the multi-input multi-output (MIMO) impedance model has been developed to consider the frequency coupling effect. However, the generalized Nyquist criterion (GNC), which is used for the stability analysis of an MIMO model, is more complicated than the stability analysis method applied on single-input-single-output (SISO) models. Meanwhile, it is not always the case that the SISO model fails in the stability assessment. Therefore, the conditions when the MIMO impedance model needs to be considered in the stability analysis of an MMC system should be analyzed. This paper quantitatively analyzes the effect of frequency coupling on the stability analysis of grid-connected MMC, and clarifies the frequency range and grid conditions that the coupling effect required to be considered in the stability analysis. Based on the quantitative relations between the frequency coupling and the stability analysis of the grid-connected MMC system, a simple and accurate stability analysis method for the grid-connected MMC system is proposed, where the MIMO impedance model is applied when the frequency coupling has a significant effect and the SISO impedance model is used if the frequency coupling is insignificant.

Stability analysis of three-dimensional (3-D) systems using a wave advanced model (WAM)

2015 ◽  
Vol 39 (6) ◽  
pp. 898-906
Author(s):  
SaeedReza Tofighi ◽  
Masoud Shafiee ◽  
Sayyid Mehdi Alavinia
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Wave Model ◽  
System Stability ◽  
The Stability ◽  
Representation Scheme ◽  
The Given ◽  
Advanced Model ◽  
New Criteria ◽  
D Wave

In this paper, the problem of three-dimensional (3-D) system stability is studied. In order to investigate the stability of 3-D systems, a new representation scheme is introduced based on the local state model proposed by Givone–Roesser for 3-D systems. This representation is obtained from the extended expression of the 1-D wave model proposed by Porter–Aravena. Then, according to the obtained model a new criteria for the stability of 3-D systems is stated. This criteria provides a simpler way to investigate asymptotic stability. Furthermore, an algorithm is performed to illustrate the procedure of analysing stability. Finally, some examples are performed and verified using numerical simulations in order to illustrate the given criteria for the stability.

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

2015 ◽  
Vol 25 (05) ◽  
pp. 1550074 ◽  
Author(s):  
Lingling Zhang ◽  
Jianhua Huang ◽  
Lihong Huang ◽  
Zhizhou Zhang
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Delayed Feedback Control ◽  
Multiple Delays ◽  
Maglev System ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory ◽  
Time Delayed Feedback

This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.

A New Approach to Popov Criterion for Stability Analysis of Nonlinear Control Systems

2012 ◽  
Vol 463-464 ◽  
pp. 1549-1552
Author(s):  
Ivan Svarc
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Nonlinear Control Systems ◽  
Engineering Practice ◽  
The Stability ◽  
The Given

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

Sign in / Sign up

Export Citation Format

Share Document