Derived Nodes Approach for Improving Accuracy of Machining Stability Prediction

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Le Cao ◽  
Xiao-Ming Zhang ◽  
Tao Huang ◽  
Han Ding
Keyword(s):  
State Space ◽  
Polynomial Interpolation ◽  
Recursive Estimation ◽  
Machining Process ◽  
Stability Prediction ◽  
State Variables ◽  
Piecewise Polynomials ◽  
Discrete Equations ◽  
Runge Phenomenon ◽  
The Stability

Machining process dynamics can be described by state-space delayed differential equations (DDEs). To numerically predict the process stability, diverse piecewise polynomial interpolation is often utilized to discretize the continuous DDEs into a set of linear discrete equations. The accuracy of discrete approximation of the DDEs generally depends on how to deal with the piecewise polynomials. However, the improvement of the stability prediction accuracy cannot be always guaranteed by higher-order polynomials due to the Runge phenomenon. In this study, the piecewise polynomials with derivative-continuous at joint nodes are taken into consideration. We develop a recursive estimation of derived nodes for interpolation approximation of the state variables, so as to improve the discretization accuracy of the DDEs. Two different temporal discretization methods, i.e., second-order full-discretization and state-space temporal finite methods, are taken as demonstrations to illustrate the effectiveness of applying the proposed approach for accuracy improvement. Numerical simulations prove that the proposed approach brings a great improvement on the accuracy of the stability lobes, as well as the rate of convergence, compared to the previous recorded ones with the same order of interpolation polynomials.

scholarly journals State-Space Model of Quasi-Z-Source Inverter-PV Systems for Transient Dynamics Studies and Network Stability Assessment

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4150
Author(s):  
Lluís Monjo ◽  
Luis Sainz ◽  
Juan José Mesas ◽  
Joaquín Pedra
Keyword(s):  
Power Systems ◽  
State Space ◽  
State Space Model ◽  
Pv System ◽  
Pv Systems ◽  
Renewable Power ◽  
Ac Networks ◽  
Transient Interactions ◽  
The Stability ◽  
Averaged Model

Photovoltaic (PV) power systems are increasingly being used as renewable power generation sources. Quasi-Z-source inverters (qZSI) are a recent, high-potential technology that can be used to integrate PV power systems into AC networks. Simultaneously, concerns regarding the stability of PV power systems are increasing. Converters reduce the damping of grid-connected converter systems, leading to instability. Several studies have analyzed the stability and dynamics of qZSI, although the characterization of qZSI-PV system dynamics in order to study transient interactions and stability has not yet been properly completed. This paper contributes a small-signal, state-space-averaged model of qZSI-PV systems in order to study these issues. The model is also applied to investigate the stability of PV power systems by analyzing the influence of system parameters. Moreover, solutions to mitigate the instabilities are proposed and the stability is verified using PSCAD time domain simulations.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

Robust active disturbance attenuation control of an uncertain quadrotor

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nigar Ahmed ◽  
Ajeet kumar Bhatia ◽  
Syed Awais Ali Shah
Keyword(s):  
Control Algorithm ◽  
Sliding Mode ◽  
The State ◽  
Disturbance Attenuation ◽  
State Variables ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Content Type ◽  
Highly Nonlinear ◽  
The Stability

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

scholarly journals Neural networks and dynamical system techniques for volcanic tremor analysis

1996 ◽  
Vol 39 (2) ◽  
Author(s):  
R. Carniel
Keyword(s):  
Dynamical System ◽  
State Space ◽  
Structural Changes ◽  
Volcanic Tremor ◽  
Lag Time ◽  
State Variables ◽  
Stromboli Volcano ◽  
Structural Configuration ◽  
Experimental Time Series ◽  
Tremor Analysis

A volcano can be seen as a dynamical system, the number of state variables being its dimension N. The state is usually confined on a manifold with a lower dimension f, manifold which is characteristic of a persistent «structural configuration». A change in this manifold may be a hint that something is happening to the dynamics of the volcano, possibly leading to a paroxysmal phase. In this work the original state space of the volcano dynamical system is substituted by a pseudo state space reconstructed by the method of time-delayed coordinates, with suitably chosen lag time and embedding dimension, from experimental time series of seismic activity, i.e. volcanic tremor recorded at Stromboli volcano. The monitoring is done by a neural network which first learns the dynamics of the persistent tremor and then tries to detect structural changes in its behaviour.

Analytical and experimental stability analysis of AU4G1 thin-walled tubular workpieces in turning process

2020 ◽  
Vol 234 (6-7) ◽  
pp. 1007-1018 ◽  
Author(s):  
Zied Sahraoui ◽  
Kamel Mehdi ◽  
Moez Ben-Jaber
Keyword(s):  
Stability Analysis ◽  
Feed Rate ◽  
Experimental Studies ◽  
Rake Angle ◽  
Machining Process ◽  
Structural Damping ◽  
Turning Process ◽  
Process Stability ◽  
Thin Walled ◽  
The Stability

The development of the manufacturing-based industries is principally due to the improvement of various machining operations. Experimental studies are important in researches, and their results are also considered useful by the manufacturing industries with their aim to increase quality and productivity. Turning is one of the principal machining processes, and it has been studied since the 20th century in order to prevent machining problems. Chatter or self-excited vibrations represent an important problem and generate the most negative effects on the machined workpiece. To study this cutting process problem, various models were developed to predict stable and unstable cutting conditions. Stability analysis using lobes diagrams became useful to classify stable and unstable conditions. The purpose of this study is to analyze a turning process stability using an analytical model, with three degrees of freedoms, supported and validated with experimental tests results during roughing operations conducted on AU4G1 thin-walled tubular workpieces. The effects of the tubular workpiece thickness, the feed rate and the tool rake angle on the machining process stability will be presented. In addition, the effect of an additional structural damping, mounted inside the tubular workpiece, on the machining process stability will be also studied. It is found that the machining stability process is affected by the tubular workpiece thickness, the feed rate and the tool rake angle. The additional structural damping increases the stability of the machining process and reduces considerably the workpiece vibrations amplitudes. The experimental results highlight that the dynamic behavior of turning process is governed by large radial deformations of the thin-walled workpieces. The influence of this behavior on the stability of the machining process is assumed to be preponderant.

Stability analysis in machining process by using adaptive closed-loop feedback control system in turning process

2020 ◽  
pp. 107754632095261
Author(s):  
Kashfull Orra ◽  
Sounak K Choudhury
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Closed Loop ◽  
Machining Process ◽  
Feedback Control System ◽  
Turning Process ◽  
Tool Vibration ◽  
Loop Feedback ◽  
Closed Loop Feedback ◽  
The Stability

The study presents model-based mechanism of nonlinear cutting tool vibration in turning process and the strategy of improving cutting process stability by suppressing machine tool vibration. The approach used is based on the closed-loop feedback control system with the help of electro–magneto–rheological damper. A machine tool vibration signal generated by an accelerometer is fed back to the coil of a damper after suitable amplification. The damper, attached under the tool holder, generates counter forces to suppress the vibration after being excited by the signal in terms of current. The study also discusses the use of transfer function approach for the development of a mathematical model and adaptively controlling the process dynamics of the turning process. The purpose of developing such mechanism is to stabilize the machining process with respect to the dynamic uncut chip thickness responsible for the type-II regenerative effect. The state-space model used in this study successfully checked the adequacy of the model through controllability and observability matrices. The eigenvalue and eigenvector have confirmed the stability of the system more accurately. The characteristic of the stability lobe chart is discussed for the present model-based mechanism.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

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