scholarly journals The Analysis of Controllability and Stability of an Approximate Model of Heat Transfer in an Autoclave

2018 ◽  
Vol 28 (3) ◽  
pp. 416-428 ◽  
Author(s):  
Sergey A. Mokrushin ◽  
Valeri S. Khoroshavin ◽  
Sergey I. Ohapkin ◽  
Alexander V. Zotov ◽  
Victor S. Grudinin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Transfer Functions ◽  
Structural Transformations ◽  
Space Representation ◽  
Proportional Integral ◽  
State Space Representation ◽  
The Matrix ◽  
The Stability ◽  
The Time Domain

Introduction.Ensuring the safety of country food industry in terms of the duration of storage and the quality of products is impossible without sterilizing products in autoclaves. The effectiveness of the sterilization processes depends on the degree of their automation. In the last twenty years, the improvement of automatic and automated control systems was primarily based on the development of technical means for automation without theoretical justification of decision-making. The proposed work is aimed at identifying the links between the parameters and connections of the sterilization process and the choice of structural and parametric features of the control system. Materials and Methods. A qualitative analysis is carried out based on the modern theory of automatic control for an approximative model of the thermal process of steam heating in an autoclave, taking into account the laws of heat transfer and the sufficiency of using a twodimensional model depending upon the structural and functional features of the model, which have regard to the parameters and relationships of the process, namely, the Kalman’s controllability properties of the model in the time domain in the state-space representation (the transition from the transfer function with zeros in the numerator to the normal differential system differential equations is also described). There were also analized the stability properties of the model in the frequency domain by means of transfer functions and structural transformations and the relationship of parameters in the form of inequalities with the subsequent choice of proportional-integral-differential configuration components for a real autoclave using the matrix of expert estimates. Results. It is shown that to make a qualitatively study of the issues of controllability and stability of the approximative model of the thermal process of water heating by steam in an autoclave, depending on the process parameters, it is necessary to represent the model the time domain (in the state-space representation) and in the frequency domain (in the form of transfer functions). The analysis of the controllability of the process is based on three approaches: the first (formalized) approach is based on the representation of the model in the form of a normal system of ordinary differential equations in the Cauchy form with the development of a method of decreasing the order of the higher derivatives of coordinates and introducing additional control signals taking into account the control derivatives; the second (unformalized) is based on the exclusion of management derivatives through structural transformation; the third (direct) approach uses the first-order heat balance and heat conduction equations derived from physical considerations. Under the conditions of Kalman’s controllability, dependencies between the parameters of the process and the degree of its controllability have been obtained.The analysis of the stability of the process is based on studying the poles of the transfer functions in the frequency domain and the characteristic roots of the equations of state in the time domain. On the basis of structural transformations, a closed canister heating loop with water with inertia, depending on the autoclave charging parameters, is isolated. Transient processes in this circuit take an amplifying, aperiodic or integral character, which affects the nature of the transient processes of the control system as a whole. The formalized choice of the components of the proportional-integral-differential regulation law is carried out depending on the frequency of application of the degree of loading and the need for the components of the proportional-integral-differential regulator using the matrix of expert estimates. Conclusions. The results of the research will serve as the material for the development of a real model of the autoclaving process, taking into account the static and dynamic characteristics of measuring, conversion and actuating elements, investigating the influence and compensation of inertia and nonlinearities of real elements, followed by the development of an automated system for controlling the sterilization process in autoclaves. The results of the work can be used to study general and applied problems of optimal control in both food and other industries, for example, in the production of building materials and the production of rubber products.

scholarly journals Regular design equations for the discrete reduced-order Kalman filter

2012 ◽  
Vol 22 (2) ◽  
pp. 175-189
Author(s):  
Peter Hippe
Keyword(s):  
Kalman Filter ◽  
Frequency Domain ◽  
Time Domain ◽  
Filter Design ◽  
Minimum Variance ◽  
Reduced Order ◽  
Regular Design ◽  
The Stability ◽  
The Time Domain ◽  
Standard Software

Regular design equations for the discrete reduced-order Kalman filter In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.

Dynamics and Stability of Plunge Milling Operations

2006 ◽  
Vol 129 (1) ◽  
pp. 32-40 ◽  
Author(s):  
Jeong Hoon Ko ◽  
Yusuf Altintas
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Cutting Forces ◽  
Milling Process ◽  
Body Motion ◽  
Plunge Milling ◽  
Milling Operations ◽  
Tool Setting ◽  
The Stability ◽  
The Time Domain

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of the spindle axis which has the highest structural rigidity. This paper presents a comprehensive model of plunge milling process by considering rigid body motion of the cutter, and three translational and torsional vibrations of the structure. The time domain simulation model allows prediction of cutting forces, torque, and vibrations while considering tool setting errors and time varying process parameters. The stability law is formulated as a four-dimensional eigenvalue problem, and the stability lobes are predicted directly with analytical solution in frequency domain. Time domain prediction of cutting forces and vibrations, as well as the frequency domain and chatter stability solution are verified with a series of plunge milling experiments.

scholarly journals Pipeline Leak Detection by Transient-Based Method Using MATLAB® Functions

2017 ◽  
Author(s):  
Albert Carbó-Bech ◽  
Salvador A. De Las Heras ◽  
Alfredo Guardo
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Transfer Functions ◽  
Leak Detection ◽  
Pipeline System ◽  
Model Transfer ◽  
Time Domain Response ◽  
Frequency Domain Response ◽  
The Time Domain ◽  
Dissipative Model

This paper shows a method for pipeline leak detection using a transient-based method with MATLAB® functions. The simulation of a pipeline systems in the time domain are very complex. In the case of the dissipative model, transfer functions are hyperbolic Bessel functions. Simulating a pipeline system in the frequency domain using a dissipative model we could find an approximate transfer function with equal frequency domain response to in order get the pipeline system's time domain response. The method described in this paper can be used to detect, by comparison, to detect a leak in a pipeline system model.

On the problem of simulation of influence flooded compartment on the dynamics of the ship's navigation.

2021 ◽  
pp. 67-72
Author(s):  
В.В. Макарова ◽  
В.М. Набока ◽  
Ю.П. Потехин
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Inverse Fourier Transform ◽  
Simulation Models ◽  
Hydrodynamic Problem ◽  
The Stability ◽  
The Time Domain ◽  
Stability Of The Solution

В статье рассматривается возможность применения имеющихся в настоящее время решений задачи о влиянии динамического переливания жидкости в аварийных отсеках 2-й категории или успокоительных цистернах на качку судна в системах имитационного моделирования динамики плавания аварийных судов. Существующие решения получены в интересах исследования качки в частотной области и формально могут быть перенесены во временну́ю область, отвечающую существованию имитационных моделей, посредством обратного преобразования Фурье, что связано с определенными затруднениями. В работе показано, что при определенной формулировке гидродинамической задачи о колебаниях жидкости в отсеке или цистерне во временно́й области могут быть использованы непосредственно исходные уравнения. Выполнены расчеты, подтверждающие корректность такого подхода с позиций обеспечения устойчивости решения задачи и физической адекватности результатов реально наблюдаемым процессам. The article discusses the possibility of using the currently available solutions to the problem of the effect of dynamic fluid overflow in emergency compartments of the 2nd category or damping tanks on the pitching of a ship in systems for simulation of the dynamics of navigation of damaged ships. The existing solutions were obtained in the interests of studying the pitching in the frequency domain and can formally be transferred to the time domain corresponding to the existence of simulation models by means of the inverse Fourier transform, which is associated with certain difficulties. It is shown in the work that with a certain formulation of the hydrodynamic problem of fluid oscillations in a compartment or tank in the time domain, the original equations can be used directly. Calculations have been performed that confirm the correctness of this approach from the standpoint of ensuring the stability of the solution to the problem and the physical adequacy of the results to the actually observed processes.

Practical Implementation of the Polynomial Representation of Potential Damping in Time Domain Simulations

2005 ◽  
Author(s):  
Hermione J. van Zutphen ◽  
Joost den Haan
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Least Square ◽  
Space Representation ◽  
Practical Implementation ◽  
Damping Force ◽  
State Space Representation ◽  
Limit Value ◽  
The Time Domain

Time domain simulations are required when analyzing nonlinear vessel behaviour. The usual approach conducting time domain simulations is to transform a complex valued function of frequency dependent damping and added mass to a convolution integral in the time domain. Evaluating the integrals during time domain simulations is computational expensive and the accuracy of the calculation of the limit value of added mass in diffraction calculations is dependent on the panel size of the model. In this paper, an alternative approach based on a polynomial model for damping proposed by K.E. Kaasen et al is extended from a single degree of freedom to a 6 degrees of freedom model of a heavy lift barge. Polynomials for contributions of velocity to the damping force are constructed generically using a least square curve fitting method. The polynomials then are transformed to the time domain counterpart using a state space representation. The quality of the fits of the damping function has a large influence on the resulting damping force in time domain. Furthermore, the higher the order of the differential equation, the larger the number of variables to integrate during a time domain simulation. Consequently, the presented method is not necessarily more efficient in simulations than the traditional retardation functions.

Application of Optimal Input Synthesis to Aircraft Parameter Identification

1976 ◽  
Vol 98 (2) ◽  
pp. 139-145 ◽  
Author(s):  
N. K. Gupta ◽  
R. K. Mehra ◽  
W. E. Hall
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Time Domain ◽  
Stability And Control ◽  
Input Design ◽  
Short Period ◽  
Control Derivatives ◽  
The Stability ◽  
The Time Domain ◽  
And Control

This paper considers an application of the Frequency Domain Input Synthesis procedure reference [12] for identifying the stability and control derivatives of an aircraft. In previous studies, the input design has mostly been carried out in the time-domain. However, by using a frequency-domain approach, one can handle criteria that are not easily handled by the time-domain approaches. Numerical results are presented for optimal elevator deflections to estimate the longitudinal stability and control derivatives subject to root-mean square constraints on the input. The applicability of the steady state optimal inputs to finite duration flight testing is investigated. It is shown that the steady state approximation of frequency-domain synthesis is good for data lengths greater than two time cycles for the short period mode of the aircraft longitudinal motions. For data lengths shorter than this, the phase relationships between different frequency components becomes important. The frequency domain inputs are shown to be much better than the conventional doublet inputs.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

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