Unit Step Load Research Articles

Implementation of PWM AC chopper controller for capacitor run induction motor drive via bacterial foraging optimization algorithm

<p>This paper focuses on design of closed-loop control for pulse width modulated AC chopper controlled capacitor run induction motor drive engaging enriched optimization algorithm based on foraging of bacteria. Capacitor run induction motor is a non-linear device and its parameter varies under different functional point of the system. A linearized increment model for PWM AC chopper is illustrated for a particular functional point of the drive. The conventional method does not provide acceptable performance under different load conditions. Bacteria foraging optimization technique categorizes accurate control parameters for the superlative dynamic response under unit step load variations. Field Programmable Gate Array is implemented practically for a particular functional point of the drive to exhibit accurate performance. Experimental and simulated results are obtained to authenticate the effectiveness of the optimized controller.</p><p> </p>

Design of Rowen's Model for Heavy Duty Gas Turbine (HDGT)

In this paper, the parameters of Rowen’s model for heavy duty gas turbines in dynamic studies are estimated by use of available operational and performance data. The transfer function model of heavy duty gas turbine is required for the analysis and development of optimal controllers. The speedtronic controller derived from Rowen’s model has three controller namely, speed, acceleration and temperature. The model with all these controllers is developed with MATLAB/Simulink to study their response and arrive at the simplified model. The speed controller may have isochronous or drooping governor characteristics. The choice of governor characteristics for the simplified model is made from the response of the system simulated for an unit step load disturbance. The equations are to be validated with the response of the system simulated using MATLAB/Simulink.

Uncertain dynamic responses of imprecisely defined arbitrary order fractionally damped beam subject to various loads

PurposeRecently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.Design/methodology/approachHere, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.FindingsVIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.Originality/valueUncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

Simultaneous design of proportional–integral–derivative controller and measurement filter by optimisation

A method for optimization of PID controller parameters and measurement filter time constant is presented. The method differs from the traditional approach in that the controller and filter parameters are simultaneously optimized, as opposed to standard, sequential, design. Control performance is maximized through minimization of the integrated absolute error (IAE) caused by a unit step load disturbance. Robustness is achieved through Hinf constraints on sensitivity and complementary sensitivity. At the same time, noise attenuation is enforced by limiting either the H2 or Hinf norm of the transfer function from measurement noise to control signal. The use of exact gradients makes the synthesis method faster and more numerically robust than previously proposed alternatives. (Less)

A viscoelastic Timoshenko shaft finite element for dynamic analysis of rotors

A new shaft element is proposed for viscoelastic rotors in a spinning frame considering the shear deformation in addition to bending deformation. The Maxwell–Wiechert model is considered here to replicate linear viscoelastic behavior. This model considers additional internal damping displacement variables between elastic and viscous elements and the stress depends not only on the elastic strain and elastic strain rate, but also on additional strains and their rates corresponding to the damping variables. The present work assumes that these additional strains can be derived from continuous fictitious displacement variables, which in turn are interpolated from their nodal values using the Timoshenko beam shape functions. Therefore, in addition to the standard degrees of freedom for a three-dimensional shaft, extra degrees of freedom are defined at the nodes. The finite element matrices are assembled in state space. The time domain equations are then used for stability analysis and computation of response to a unit step load and an unbalance.

Uncertain Dynamic Responses of Fuzzy Arbitrary-Order Damped Beam

Uncertain dynamic responses of fuzzy fractionally damped beams have been studied using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads. Uncertainties are assumed to be present in the initial conditions, and these are modeled through triangular convex normalized fuzzy sets. Using the alpha-cut form, the corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying a double-parametric form of fuzzy numbers. Finally, homotopy perturbation method (HPM) has been used to solve the same for obtaining the general fuzzy responses. Various numerical examples are taken into consideration. The results are plotted.

Dynamic response of imprecisely defined beam subject to various loads using Adomian decomposition method

Present paper proposes a new technique based on double parametric form of fuzzy numbers to solve an uncertain beam equation using Adomian decomposition method subject to unit step and impulse loads. Uncertainties appear in the initial conditions are considered in terms of triangular convex normalized fuzzy sets. Using the single parametric form viz. α-cut form of fuzzy numbers, the fuzzy beam equation is converted first to an interval based fuzzy differential equation. Next this differential equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same is solved by Adomian decomposition method symbolically to obtain the uncertain bounds of the dynamic response. Obtained results are depicted in term of plots to show the efficiency and powerfulness of the present analysis.

Dynamic responses of fractionally damped mechanical system using homotopy perturbation method

This paper investigates the numerical solution of a fractionally damped dynamic system. A single degree of freedom spring-mass mechanical system with fractional damping of order 1/2 is considered for the analysis. Homotopy perturbation method (HPM) is used to compute the dynamic responses of the system subjected to unit step and unit impulse loads. Obtained results are depicted in terms of plots. Comparisons are made with the analytic solutions obtained by using fractional green function of Podlubny (1999) [5] and numerical solution of [20,25] in the special cases, to show the effectiveness and validation of the present analysis.

Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers

Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM) to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.

Two Fracture Dynamics Problems of Fiber Reinforced Ceramics

After fiber reinforced ceramics occur a crack, its bridging fibers must engender, moreover the crack usually runs in the format of similarity. In order to analyze easily dynamic problems of fiber reinforced ceramics, bridging fiber segment is substituted for loads. When a crack moves at high speed, its fibers will break continuously. By application of the built dynamic model and the ways of self-similar functions, analytical solutions of the displacements, stresses and dynamic stress intensity factors under the action of a running increasing force Px2/t2 and a motive unit step load, respectively, can be gained, and it is also used to attain the concrete solution by means of superposition theorem.

Dislocation Distribution Function of the Mode III Dynamic Crack Subjected to Moving Unit Step Load from a Point

Dislocation distribution functions of the edges of mode III propagation crack subjected to Moving unit step load from a point was studied by the methods of the theory of complex variable functions.By the methods, the problems researched can be facilely transformed into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements, dynamic stress intensity factor and dislocation distribution function were obtained by the methods of the theory of self-similar functions.In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were attained.

General Viscoelastic Solutions for Multilayered Systems Subjected to Static and Moving Loads

Since the linear elastic layer solution for the layered systems was developed in the 1940s, the linear elastic layer analysis has been systemized and widely used for the designs of roadway pavements as a tool for evaluating the structural soundness of pavements. The primary assumption made in the analysis is that the layered system consisting of materials that are linear elastic; and hence, an application of the elastic layer analysis to asphalt mixtures, which is a well-known viscoelastic material, has been limited. Therefore, the intention of the study was to derive a viscoelastic solution able to take into account the time- and rate-dependent nature of the viscoelastic materials in the multilayered system. In this paper, a linear viscoelastic solution for the multilayered system subjected to a cylindrical unit step (static) load was derived from the elastic solution by using the principle of elastic-viscoelastic correspondence and the numerical inversion of Laplace transforms. The solution was then extended to simulating pavement responses subjected to a moving load by employing the Boltzmann’s superposition principle. The soundness of output from the viscoelastic solution was confirmed by comparing them to those of the finite-element analysis (FEA). Compared to the time and effort required in FEA, the analysis based on the viscoelastic solution was much faster. Therefore, it is expected that the viscoelastic solutions derived in this study will be an effective tool for the design of flexible pavements.

Dislocation Distribution Function of Two Fracture Dynamics Problems Concerning Aluminum Alloys

By the approaches of the theory of complex functions, dynamic propagation problems on the surfaces of mode I crack subjected to unit-step loads and instantaneous impulse loads located at the origin of the coordinates were studied for Aluminum alloys, respectively. Analytical solutions to stresses, displacements, dynamic stress intensity factors and dislocation distribution functions are gained by the methods of self-similar functions. The problems considered can be very facilely transformed into Riemann-Hilbert problem and their closed solutions are obtained rather straightforward by Muskhelishvili’s measure.

Asymmetrical dynamic propagation problems on mode III interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode III interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.

Dislocation Distribution Function of the Surfaces of Mode III Dynamic Crack Subjected to Unit-Step Loads and Moving Increasing Loads

By the theory of complex functions, dislocation distribution function concerning mode dynamic crack propagation problem under the conditions of unit-step loads and moving increasing loads was studied respectively. Analytical solution representations are attained by the methods of self-similar functions. The problems investigated can be transformed into Riemann-Hilbert problems and their closed solutions are obtained rather simple by this approach.

Evaluation of various schemes for quasi-static boundary element analysis of polymers

The behaviour of polymers under quasi-static load is analysed by various boundary element schemes. Linear viscoelasticity, for which the correspondence principle applies, is assumed. The problem is first solved in the Laplace transform domain with the time-dependent response determined by numerical inversion. A solution is also obtained directly in the time domain using fundamental solutions for unit step load excitation. Two alternative time-domain schemes, applied until recently only to dynamic problems, are adapted to quasi-static conditions. Both are based on a reciprocity relation involving Riemann convolutions and use fundamental solutions for a Dirac impulse excitation. The second of those schemes, however, uses only the Laplace transforms of these fundamental solutions, which are directly formed from the corresponding elasticity solutions and thus not specific to the viscoelastic model used. Rapid derivation of time-dependent fundamental solutions for general standard linear solids enhances the applicability of time domain methods. Computer codes based on the different algorithms are developed and applied to benchmark problems in order to assess their relative accuracy, versatility and efficiency. The various BEM predictions are generally consistent and reliable. The numerical instability of the last, so called, mixed method is minimised through appropriate choice of modelling parameters.

An Evolutionary Approach for Speed Controller Design of A.C. Voltage Controller Fed-Induction Motor Drive

An induction motor is a non-linear device and its parameters vary with operating point. This article explains the application of the Genetic Algorithm (GA) to the design of an optimum controller structure for speed control of an a.c. voltage controller fed-induction motor drive application. An incremental model of an a.c. voltage controller fed-induction motor drive is derived and is used for simulation study. The GA is used to derive optimal values of the controller parameters so that the best dynamic response is obtained for unit step load disturbance, irrespective of motor operating point. High gain control theory is also used to derive the controller, and it is found that the two controller structures resemble each other.

Electron-beam heating control in thermodesorption spectroscopy investigations

An electron-beam high-power heating source for temperature controlled outgassing investigations of divertor tiles from the high temperature plasma installations type Tokamak is developed. A linear mathematical model for transforming the anode heating power into sample temperature is created. An electron-beam heating system as a controlled device is described. An efficient temperature control in LABVIEW environment is synthesized. Offset characteristics and transient responses of the samples heating process are experimentally obtained. Closed loop systems responses for unit step load disturbance and unit step reference input are presented.

Temperature controlled outgassing of graphite samples for thermodesorption spectroscopy investigations

In this paper, we describe a temperature controlled outgassing measurement in the case of electron-beam heating of graphite samples used in divertors of Tokamak-type installations. On the basis of a discrete-time process model in the state space, we developed finite-time settling control of the sample's temperature. We further present the response of closed-loop systems to a unit-step load disturbance and a unit-step reference input.

Analysis of Layered Viscoelastic System with Transient Temperatures

A method for quasi-static analysis of a layered viscoelastic system with transient temperatures is presented. First, the response, displacements and stresses of the system to the unit step load with a constant temperature is obtained from the corresponding elastic solution. The response to a transient load is then obtained through a linear superposition integral using the unit response as the kernel function. The effects of spatially homogeneous, transient temperature on the mechanical response of the system are taken into account through the time-temperature superposition principle. The method is not based on the Laplace transform-based correspondence principle and no transform-inversion process is required. An illustration of the method is presented through an analysis of the stresses and the displacements in a three-layer, elastic-viscoelastic composite half-space subjected to a distributed surface load under different temperature conditions.