scholarly journals A Gallery of Root Locus of Fractional Systems

2013 ◽  
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Stability Analysis ◽  
Transfer Functions ◽  
Numerical Procedure ◽  
Root Locus ◽  
Closed Loop System ◽  
Fractional Systems ◽  
Finite Precision ◽  
Know How ◽  
The Stability ◽  
Fractional Orders

The root locus (RL) is a classical tool for the stability analysis of integer order linear systems, but its application in the fractional counterpart poses some difficulties. Therefore, researchers have mainly preferred to adopt frequency based methods. Nevertheless, recently the RL was considered for the stability analysis of fractional systems. One first method is by tacking advantage of commensurable expressions that occur when truncating fractional orders up to a finite precision. The second method consists of searching the complex plane for solutions of the characteristic equation using a numerical procedure. The resulting charts are insightful about the characteristics of the closed-loop system that outperform the frequency response methods. Given the limited know how in this particular topic and the shortage of literature, this study explores several types of fractional-order transfer functions and presents the corresponding RL.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Another Note on Stability of Sliding Mode Dynamics in Suppression of Fractional Chaotic Systems

2015 ◽  
Vol 743 ◽  
pp. 303-306
Author(s):  
J. Yuan ◽  
B. Shi ◽  
Yan Wang
Keyword(s):  
Stability Analysis ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
Fractional Integrator ◽  
Fractional Differential ◽  
Continuous Frequency ◽  
The Stability ◽  
Sliding Mode Dynamics

This paper revisits the stability analysis of sliding mode dynamics in suppression of a classof fractional chaotic systems by a different approach. Firstly, we convert fractional differential equationsinto infinite dimensional ordinary differential equations based on the continuous frequency distributedmodel of the fractional integrator. Then we choose a Lyapunov function candidate to proposethe stability analysis. The result applies to both the commensurate fractional systems and the incommensurateones.

scholarly journals Computation of time-delay for Delayed Network Controlled Temperature Control System

2021 ◽  
Vol 2070 (1) ◽  
pp. 012102
Author(s):  
V Venkatachalam ◽  
M Ramasubramanian ◽  
M Thirumarimurugan ◽  
D Prabhakaran
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Temperature Control ◽  
Closed Loop ◽  
Simulation Software ◽  
Loop System ◽  
Temperature Control System ◽  
Closed Loop System ◽  
The Stability ◽  
Time Invariant

Abstract This paper presents an Investigation on the stability of network controlled temperature control system having Time-Invariant feedback delays, by utilizing a direct method for TDS stability analysis. A PI controller based stability analysis for temperature control system with Time invariant feedback loop delay has been constructed in this paper. The stability problem has been formulated based on the transfer function model of the closed loop system with various time delays. For different subsets of the controller parameters, based on the stability criterion’s maximal permissible bound of the network link delay that the closed loop system can accommodate without losing the stability has been computed. The effectiveness of the obtained result was validated on a benchmark temperature control system using MATLAB simulation software.

Thermoacoustic Stability Analysis of a Kerosene-Fueled Lean Direct Injection Combustor Employing Acoustically and Optically Measured Transfer Matrices

2012 ◽  
Author(s):  
Bernhard C. Bobusch ◽  
Jonas P. Moeck ◽  
Christian Oliver Paschereit ◽  
Sermed Sadig
Keyword(s):  
Stability Analysis ◽  
Transfer Functions ◽  
Direct Injection ◽  
Network Models ◽  
Operating Conditions ◽  
Transfer Matrices ◽  
Test Rig ◽  
Lean Direct Injection ◽  
Calibration Measurement ◽  
The Stability

The assessment of the stability characteristics of kerosene-fueled, lean direct injection flames is an important issue for the design of low-emission aircraft engine combustion systems. To achieve this task, acoustic network models are widely used. In the present work, this technique is applied to determine the stability behavior of a liquid-fueled, lean direct injection combustor. The required transfer matrices have been measured in an atmospheric combustion test rig. The burner transfer matrix as well as the upstream and downstream reflection coefficients are obtained by using the multi-microphone method. Since the measurement of flame transfer functions for liquid-fueled flames is a complex task, two techniques are applied and compared. First, the flame response to loudspeaker forcing is measured with the multi-microphone technique. Second, a technique based on the simultaneous acquisition of different chemiluminescence signals is applied. The chemiluminescence response at four different wavelengths (310 nm, 407 nm, 431 nm, and 515 nm), corresponding to the species OH*, CH*, CO2* and C2*, respectively, are measured using photomultiplier tubes. With a calibration measurement at different operating conditions, it is possible to calculate the instantaneous heat release rate. Flame transfer functions and matrices are measured in the test rig with the two techniques. Additionally, all acoustically measured transfer matrices and optically measured transfer functions are used to predict possible unstable modes in the test rig. The experimental results and the stability analysis employing the measured flame transfer functions are in good agreement and demonstrate validity of the method.

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.

A Unified Transfer Function (UTF) Approach for the Modeling and Stability Analysis of Long Slender Bars in 3-D Turning Operations

1993 ◽  
Vol 115 (2) ◽  
pp. 193-204 ◽  
Author(s):  
I. N. Tansel
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Transfer Functions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Tool Geometry ◽  
Turning Operations ◽  
Chip Area ◽  
The Stability ◽  
Unique Relationship

A new approach is introduced to model 3-D turning operations that are used for the stability analysis of long slender bars. This approach utilizes the unique relationship between externally created feed direction tool displacements (input) and the resultant thrust direction workpiece vibrations (output) to estimate stability limits in three-dimensional turning operations from the data of a single dynamic cutting test. In this paper, this unique relationship is referred to as the “Unified Transfer Function ” (UTF) and its expressions are derived from conventional cutting and structural dynamics transfer functions. For the stability analysis, the uncut chip area variations of oblique cutting are represented by a linear model having different coefficients at different depths of cuts. These coefficients are found by using a tool geometry simulation program. An iterative procedure is developed for the stability analysis. The proposed approach considers in-process structural and cutting dynamics and can be automatically implemented without any input from the operator for the traverse turning of a long slender bar. Experimental studies have validated the proposed modeling and stability analysis techniques. The UTFs can also be used to monitor machine tool structure, tool wear, and the machinability of the material.

scholarly journals The Interaction Stability Analysis of a Multi-Inverter System Containing Different Types of Inverters

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2244 ◽  
Author(s):  
Chen Zheng ◽  
Qionglin Li ◽  
Lin Zhou ◽  
Bin Li ◽  
Mingxuan Mao
Keyword(s):  
Stability Analysis ◽  
Power Grid ◽  
Root Locus ◽  
Criterion A ◽  
Locus Method ◽  
Different Types ◽  
Simulation And Experiment ◽  
The Stability ◽  
Harmonic Resonance ◽  
Universal Interaction

The existing stability investigations of the system containing different types of inverters are insufficient. The paper aims to reveal the more universal interaction stability mechanism of the system containing different types of inverters. Firstly, the multi-inverter system is decomposed into an admittance network (AN) and excitation sources. Then, the interaction between two different inverters, as well as the interaction between the inverter and the power grid, are analyzed by the root locus method. This reveals that the stability of the interaction between the inverter and the power grid is exclusively determined by AN. However, the stability of the interaction between different inverters not only depends on AN but also relies on whether the two inverters have common right-half plane (RHP) poles. To make the multi-inverter system stable, the following two criteria must be satisfied: (a) AN is stable and (b) any two different inverters do not have the same RHP poles. If criterion (a) is not satisfied, the harmonic resonance will arise in all currents. Resonant harmonics will only circulate among partial inverters and will not inject into the power grid if criterion (a) is satisfied but criterion (b) is not satisfied. Theoretical analysis is validated by simulation and experiment results.

scholarly journals Stability Analysis of Distributed Order Fractional Chen System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Aminikhah ◽  
A. Refahi Sheikhani ◽  
H. Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Necessary Conditions ◽  
Chen System ◽  
Fractional Systems ◽  
Sufficient And Necessary Conditions ◽  
Fractional System ◽  
The Stability ◽  
Conditions Of Stability ◽  
Distributed Order

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

Root-locus approach to the stability analysis of interval matrices

1987 ◽  
Vol 46 (3) ◽  
pp. 817-822 ◽  
Author(s):  
YAU-TARNG JUANG ◽  
TE-SON KUO ◽  
CHEN-FA HSU ◽  
SHENG-DE WANG
Keyword(s):  
Stability Analysis ◽  
Root Locus ◽  
Interval Matrices ◽  
The Stability
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