Search results for: derivative
117 Coding Structures for Seated Row Simulation of an Active Controlled Vibration Isolation and Stabilization System for Astronaut’s Exercise Platform
Authors: Ziraguen O. Williams, Shield B. Lin, Fouad N. Matari, Leslie J. Quiocho
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Simulation for seated row exercise was a continued task to assist NASA in analyzing a one-dimensional vibration isolation and stabilization system for astronaut’s exercise platform. Feedback delay and signal noise were added to the simulation model. Simulation runs for this study were conducted in two software simulation tools, Trick and MBDyn, software simulation environments developed at the NASA Johnson Space Center. The exciter force in the simulation was calculated from motion capture of an exerciser during a seated aerobic row exercise. The simulation runs include passive control, active control using a Proportional, Integral, Derivative (PID) controller, and active control using a Piecewise Linear Integral Derivative (PWLID) controller. Output parameters include displacements of the exercise platform, the exerciser, and the counterweight; transmitted force to the wall of spacecraft; and actuator force to the platform. The simulation results showed excellent force reduction in the active controlled system compared to the passive controlled system, which showed less force reduction.
Keywords: Simulation, counterweight, exercise, vibration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 292116 Stability of Fractional Differential Equation
Authors: Rabha W. Ibrahim
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We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3700115 Probabilistic Wavelet Neural Network Based Vibration Analysis of Induction Motor Drive
Authors: K. Jayakumar, S. Thangavel
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In this paper proposed the effective fault detection of industrial drives by using Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate, and execution time.Keywords: Biorthogonal Wavelet Transform, Posterior Probabilistic Neural Network, Induction Motor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1014114 Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals
Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan
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The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.
Keywords: Fractional Derivatives and Integrals, Hypergeometric functions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1505113 Neural Network Supervisory Proportional-Integral-Derivative Control of the Pressurized Water Reactor Core Power Load Following Operation
Authors: Derjew Ayele Ejigu, Houde Song, Xiaojing Liu
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This work presents the particle swarm optimization trained neural network (PSO-NN) supervisory proportional integral derivative (PID) control method to monitor the pressurized water reactor (PWR) core power for safe operation. The proposed control approach is implemented on the transfer function of the PWR core, which is computed from the state-space model. The PWR core state-space model is designed from the neutronics, thermal-hydraulics, and reactivity models using perturbation around the equilibrium value. The proposed control approach computes the control rod speed to maneuver the core power to track the reference in a closed-loop scheme. The particle swarm optimization (PSO) algorithm is used to train the neural network (NN) and to tune the PID simultaneously. The controller performance is examined using integral absolute error, integral time absolute error, integral square error, and integral time square error functions, and the stability of the system is analyzed by using the Bode diagram. The simulation results indicated that the controller shows satisfactory performance to control and track the load power effectively and smoothly as compared to the PSO-PID control technique. This study will give benefit to design a supervisory controller for nuclear engineering research fields for control application.
Keywords: machine learning, neural network, pressurized water reactor, supervisory controller
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 491112 Backstepping Design and Fractional Derivative Equation of Chaotic System
Authors: Ayub Khan, Net Ram Garg, Geeta Jain
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In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Keywords: Backstepping method, Fractional order, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2131111 Neural Network Based Predictive DTC Algorithm for Induction Motors
Authors: N.Vahdatifar, Ss.Mortazavi, R.Kianinezhad
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In this paper, a Neural Network based predictive DTC algorithm is proposed .This approach is used as an alternative to classical approaches .An appropriate riate Feed - forward network is chosen and based on its value of derivative electromagnetic torque ; optimal stator voltage vector is determined to be applied to the induction motor (by inverter). Moreover, an appropriate torque and flux observer is proposed.Keywords: Neural Networks, Predictive DTC
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1375110 Some Remarks About Riemann-Liouville and Caputo Impulsive Fractional Calculus
Authors: M. De la Sen
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This paper establishes some closed formulas for Riemann- Liouville impulsive fractional integral calculus and also for Riemann- Liouville and Caputo impulsive fractional derivatives.Keywords: Rimann- Liouville fractional calculus, Caputofractional derivative, Dirac delta, Distributional derivatives, Highorderdistributional derivatives.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1416109 Analysis of a Hydroelectric Plant connected to Electrical Power System in the Physical Domain
Authors: Gilberto Gonzalez-A, Octavio Barriga
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A bond graph model of a hydroelectric plant is proposed. In order to analyze the system some structural properties of a bond graph are used. The structural controllability of the hydroelctric plant is described. Also, the steady state of the state variables applying the bond graph in a derivative causality assignment is obtained. Finally, simulation results of the system are shown.Keywords: Bond graph, hydraulic plant, steady state.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1957108 A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations
Authors: Sachin Bhalekar
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In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Keywords: Caputo derivative, delay, stability, chaos.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2657107 A New Quadrature Rule Derived from Spline Interpolation with Error Analysis
Authors: Hadi Taghvafard
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We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2210106 Globally Exponential Stability for Hopfield Neural Networks with Delays and Impulsive Perturbations
Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati
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In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.
Keywords: Hopfield Neural Networks, Exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2338105 Steady State of Passive and Active Suspensions in the Physical Domain
Authors: Gilberto Gonzalez-A, Jorge Madrigal
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The steady state response of bond graphs representing passive and active suspension is presented. A bond graph with preferred derivative causality assignment to get the steady state is proposed. A general junction structure of this bond graph is proposed. The proposed methodology to passive and active suspensions is applied.Keywords: Bond graph, steady state, active suspension.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1715104 Time-Derivative Estimation of Noisy Movie Data using Adaptive Control Theory
Authors: Soon-Hyun Park, Takami Matsuo
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This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1864103 Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method
Authors: Sachin Bhalekar, Varsha Daftardar-Gejji
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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2326102 An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations
Authors: Gholamreza Hojjati, Kourosh Parand
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In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.
Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3159101 A New Sufficient Conditions of Stability for Discrete Time Non-autonomous Delayed Hopfield Neural Networks
Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati
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In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1955100 A Genetic Algorithm for Optimum Design of PID Controller in Load Frequency Control
Authors: T. Hussein
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In this paper, determining the optimal proportionalintegral- derivative (PID) controller gains of an single-area load frequency control (LFC) system using genetic algorithm (GA) is presented. The LFC is notoriously difficult to control optimally using conventionally tuning a PID controller because the system parameters are constantly changing. It is for this reason the GA as tuning strategy was applied. The simulation has been conducted in MATLAB Simulink package for single area power system. the simulation results shows the effectiveness performance of under various disturbance.Keywords: Load Frequency Control (LFC), PID controller and Genetic Algorithm (GA).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 373299 Application of 0-1 Fuzzy Programming in Optimum Project Selection
Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari
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In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 171798 Modeling of Sensitivity for SPR Biosensors- New Aspects
Authors: Volodymyr Chegel
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The computer modeling is carried out for parameter of sensitivity of optoelectronic chemical and biosensors, using phenomena of surface plasmon resonance (SPR). The physical model of SPR-sensor-s is described with (or without) of modifications of sensitive gold film surface by a dielectric layer. The variants of increasing of sensitivity for SPR-biosensors, constructed on the principle gold – dielectric – biomolecular layer are considered. Two methods of mathematical treatment of SPR-curve are compared – traditional, with estimation of sensor-s response as shift of the SPRcurve minimum and proposed, for system with dielectric layer, using calculating of the derivative in the point of SPR-curve half-width.Keywords: Surface Plasmon Resonance, modeling, sensitivity, biosensor
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 205997 Fuzzy Logic PID Control of Automatic Voltage Regulator System
Authors: Aye Aye Mon
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The application of a simple microcontroller to deal with a three variable input and a single output fuzzy logic controller, with Proportional – Integral – Derivative (PID) response control built-in has been tested for an automatic voltage regulator. The fuzzifiers are based on fixed range of the variables of output voltage. The control output is used to control the wiper motor of the auto transformer to adjust the voltage, using fuzzy logic principles, so that the voltage is stabilized. In this report, the author will demonstrate how fuzzy logic might provide elegant and efficient solutions in the design of multivariable control based on experimental results rather than on mathematical models.Keywords: Fuzzy logic system, PID Controller, control systems, controlled A V R
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 387396 Model Predictive 2DOF PID Slip Suppression Control of Electric Vehicle under Braking
Authors: Tohru Kawabe
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In this paper, a 2DOF (two degrees of freedom) PID (Proportional-Integral-Derivative) controller based on MPC (Model predictive control) algorithm fo slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method aims to improve the safety and the stability of EVs under braking by controlling the wheel slip ration. There also include numerical simulation results to demonstrate the effectiveness of the method.
Keywords: Model predictive control, PID controller, Two degrees of freedom, Electric Vehicle, Slip suppression.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 183595 Robust Cerebellar Model Articulation Controller Design for Flight Control Systems
Authors: Y. J. Huang, T. C. Kuo, B. W. Hong, B. C. Wu
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This paper presents a robust proportionalderivative (PD) based cerebellar model articulation controller (CMAC) for vertical take-off and landing flight control systems. Successful on-line training and recalling process of CMAC accompanying the PD controller is developed. The advantage of the proposed method is mainly the robust tracking performance against aerodynamic parametric variation and external wind gust. The effectiveness of the proposed algorithm is validated through the application of a vertical takeoff and landing aircraft control system.Keywords: vertical takeoff and landing, cerebellar modelarticulation controller, proportional-derivative control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 162094 A Quadcopter Stability Analysis: A Case Study Using Simulation
Authors: C. S. Bianca Sabrina, N. Egidio Raimundo, L. Alexandre Baratella, C. H. João Paulo
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This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.
Keywords: Controllers, drones, quadcopter, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 104493 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method
Authors: Changqing Yang, Jianhua Hou, Beibo Qin
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A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 257492 Stabilization of a New Configurable Two- Wheeled Machine Using a PD-PID and a Hybrid FL Control Strategies: A Comparative Study
Authors: M. Almeshal, M. O. Tokhi, K. M. Goher
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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.
Keywords: double inverted pendulum, modelling, robust control, simulation,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 152791 Multivariable Predictive PID Control for Quadruple Tank
Authors: Qamar Saeed, Vali Uddin, Reza Katebi
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In this paper multivariable predictive PID controller has been implemented on a multi-inputs multi-outputs control problem i.e., quadruple tank system, in comparison with a simple multiloop PI controller. One of the salient feature of this system is an adjustable transmission zero which can be adjust to operate in both minimum and non-minimum phase configuration, through the flow distribution to upper and lower tanks in quadruple tank system. Stability and performance analysis has also been carried out for this highly interactive two input two output system, both in minimum and non-minimum phases. Simulations of control system revealed that better performance are obtained in predictive PID design.Keywords: Proportional-integral-derivative Control, GeneralizedPredictive Control, Predictive PID Control, Multivariable Systems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 325790 The Exploitation of Balancing an Inverted Pendulum System Using Sliding Mode Control
Authors: Sheren H. Salah, Ahmed Y. Ben Sasi
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The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.Keywords: Inverted pendulum (IP) proportional-integralderivative (PID), sliding mode control (SMC).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 204689 Experimental Studies of Position Control of Linkage based Robotic Finger
Authors: N. Z. Azlan, H. Yamaura
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The experimental study of position control of a light weight and small size robotic finger during non-contact motion is presented in this paper. The finger possesses fingertip pinching and self adaptive grasping capabilities, and is made of a seven bar linkage mechanism with a slider in the middle phalanx. The control system is tested under the Proportional Integral Derivative (PID) control algorithm and Recursive Least Square (RLS) based Feedback Error Learning (FEL) control scheme to overcome the uncertainties present in the plant. The experiments conducted in Matlab Simulink and xPC Target environments show that the overall control strategy is efficient in controlling the finger movement.Keywords: Anthropomorphic finger, position control, feedback error learning, experimental study
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 156788 New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components
Authors: Xingyuan Qu, Shouming Zhong
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In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Keywords: Delay-dependent stability, time-varying delays, Lyapunov functional, linear matrix inequality (LMI).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1603