Optimal Model Selection Using MP Criterion for Uncertain Multivariable 2×2 Systems Based on IMC

2008 ◽  
Author(s):  
Inbal Shani ◽  
Neima Brauner ◽  
Coleman B. Brosilow
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Controller Design ◽  
Optimal Model ◽  
Time Constants ◽  
The Real ◽  
Real Process ◽  
Decoupled Control ◽  
The Mathematical Model ◽  
Performance Variations

IMC controller design for a process is based on choosing a mathematical model that describes the real process. The mathematical model describing such process is often not unique because the real variables of the process can vary within an interval. In such cases the performance of the control system varies, possibly substantially, as process parameters change. To limit such performance variations, we have developed an algorithm for choosing the model gains and the filter time constants of the IMC controller, to minimize the amount of interaction between outputs due to set point changes and disturbances for multivariable decoupled control systems. Some examples illustrate the algorithm.

scholarly journals Simulation of the Distribution of Nanoplates in a Liquid

2021 ◽  
Vol 27 (4) ◽  
pp. 647-655
Author(s):  
A. M. R. Al-Mashhadani ◽  
V. F. Pershin
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Critical Concentration ◽  
Solid Particles ◽  
The Real ◽  
Model Based ◽  
Real Process ◽  
Layered Crystals ◽  
The Mathematical Model

The general regularities of exfoliation of layered crystals are considered. A physical model based on the analogy of the spatial packing of polydisperse spherical solid particles is proposed to simulate the distribution of nanoplates in a liquid. Mathematical dependences have been obtained for calculating the critical concentration of aggregation of nanoplates, using graphene as an example. The verification of the adequacy of the mathematical model to the real process was carried out.

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Distribution of Combat Capabilities on Objectives by Using a Transport Problem

2017 ◽  
Vol 23 (1) ◽  
pp. 15-20
Author(s):  
Alexandru Baboș ◽  
Alina-Mihaela Baboș
Keyword(s):  
Mathematical Model ◽  
Transportation Problem ◽  
Practical Problem ◽  
Transport Problem ◽  
Resources Allocation ◽  
Real Problem ◽  
Optimal Plan ◽  
Military Action ◽  
The Real ◽  
The Mathematical Model

Abstract The transport problem finds its application in situations where the upper echelons must draw up an optimal plan of resources allocation for combat capabilities on objectives. In order to achieve more reliable results for the real problem, the data needed to formulate the mathematical model are extracted from an order of operations. This paper presents the optimization of military action, showing how to solve a practical problem using the transportation problem.

scholarly journals Simulation of a Synchronous Planar Magnetically Levitated Motion System Based on a Real-Time Analytical Force Model

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6367
Author(s):  
Ruotong Peng ◽  
Tong Zheng ◽  
Xing Lu ◽  
Xianze Xu ◽  
Fengqiu Xu
Keyword(s):  
Mathematical Model ◽  
Simulation Method ◽  
Physical Object ◽  
Force Model ◽  
The Real ◽  
Motion System ◽  
Testing Data ◽  
Magnetically Levitated ◽  
Yaw Angle ◽  
The Mathematical Model

The existing simulation method for the control of linear or planar magnetically levitated actuators always ignores the characteristics of the real physical object, which deteriorates the accuracy of the simulation. In this work, the proposed emulator for the magnetically levitated actuator is developed to consider both the force characteristics and the control algorithm. To model the real controlled object, the mathematical model for 1D (one-dimensional) and 2D (two-dimensional) magnetic arrays is derived where the yaw angle is taken into consideration using the coordinate transformation. The solution of the mathematical model is compared with the commercial BEM (boundary element method) software and the measurements from a force and torque testing setup to highlight the accuracy of the proposed mathematical model. Compared with the traditional simulation method of the motion control systems founded on the simplified system transfer function, the proposed simulation method has higher consistency and is closer to reality. The accuracy and efficiency of the proposed magnetic force model are further verified by the emulator based on the numerical force model and the testing data of the real setup.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

scholarly journals Research on Mathematical Model for Non-Uniformly Qualitative Suspension Cable

2018 ◽  
Vol 175 ◽  
pp. 03039
Author(s):  
Hu Yong ◽  
Du Yuxin ◽  
Cao Yong ◽  
Wang MaoSen ◽  
Ma Yuchi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Radio Telescope ◽  
Theoretical Basis ◽  
Transcendental Function ◽  
Concentrated Loads ◽  
Real Situation ◽  
The Real ◽  
Suspension Cable ◽  
The Mathematical Model

Catenary theory is recognized as the most effective suspension theory which can reflect the real situation of suspension. Catenary equation belongs to transcendental function, so there are some difficulties in calculation and application. Parabola theory, suspension curve theory and perturbation method are gradually formed as the theoretical basis for the study of suspension cables. This paper takes the 500m spherical radio telescope project as the background. The modeling method of suspension cable under multiple concentrated loads is analyzed, and the mathematical model of supporting cable after load is derived. The research in this paper provides a reference for the establishment of mathematical model of suspension cable in practice.

MODELLING THE OZONE PENETRATION IN A GRAIN LAYER / OZONO SKVERBTIES GRŪDŲ SLUOKSNYJE MODELIAVIMAS

2012 ◽  
Vol 20 (4) ◽  
pp. 292-300 ◽  
Author(s):  
Aušra Steponavičienė ◽  
Dainius Steponavičius ◽  
Algirdas Raila ◽  
Aurelija Kemzūraitė
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Initial Concentration ◽  
Real Process ◽  
Grain Moisture ◽  
Grain Drying ◽  
Ozonation Time ◽  
Grain Surface ◽  
The Mathematical Model ◽  
Ozonation Process

Studies of grain drying with ozone-air mixture were carried out to detect the ozone penetration patterns through the grain mound of various moisture content (14.6 ≤ w 0 ≤ 23.0%) at different ozone concentrations (500 ≤ C 0 ≤ 1250 ppb) in the supplied air. The ozone penetration through the grain layer depends on the initial ozone concentration in the supplied air, ozonation time, velocity of the supplied air, height of the grain mound, initial grain moisture content and mycobiotic contamination of grain surface. It was determined that in a 60 cm height of the grain layer ozone is first recorded after 12 h, and at 105 cm – only after 34 h at w 0 = 19.0%, C 0 = 500 ppb. If the initial concentration of ozone is higher, it is first recorded sooner. Ozone penetration through the grain layer with higher moisture level is slower, and ozone reaction with grain surface and microflora present on it is longer. Hypothesis about the adequacy of the model (how it reflects the real process) has been verified by calculating reproduction and adequacy variance. The mathematical model could be applied for prediction of the course of grain ozonation process. Santrauka Grūdų džiovinimo ozono ir oro mišiniu tyrimai atlikti siekiant išaiškinti ozono skverbties per skirtingo drėgnio grūdų sampilą dėsningumus (14,6 ≤ w 0 ≤ 23,0%), esant skirtingoms ozono koncentracijoms (500 ≤ C 0 ≤ 1250 ppb) tiekiamame ore. Ozono skverbtis grūdų sluoksnyje priklauso nuo pradinės ozono koncentracijos tiekiamame ore, ozonavimo trukmės, tiekiamo oro greičio, grūdų sampilo aukščio, pradinio grūdų drėgnio ir jų paviršiaus mikobiotinio užterštumo. 60 cm grūdų sluoksnio aukštyje ozonas pradėtas fiksuoti po 12 h, o 105 cm – tik po 34 h, kai w 0 = 19,0%, C 0 = 500 ppb. Padidinus pradinę ozono koncentraciją, ozonas pradedamas fiksuoti greičiau. Ozonuojant drėgnesnius grūdus, ozonas per jų sluoksnį skverbiasi lėčiau, vyksta ilgesnė jo reakcija su grūdų paviršiumi ir ant jų esančia mikroflora. Hipotezė apie modelio adekvatumą (kaip jis atspindi realų procesą) buvo patikrinta apskaičiavus reprodukcijos ir adekvatumo dispersijas. Sudarytas matematinis modelis gali būti taikomas grūdų ozonavimo procesui prognozuoti.

Model and Parameters Identification of Non-Linear Joint by Force-State Mapping in Frequency Domain

2007 ◽  
Vol 23 (4) ◽  
pp. 367-380 ◽  
Author(s):  
J.-H. Wang ◽  
H.-Y. Huang
Keyword(s):  
Mathematical Model ◽  
Frequency Domain ◽  
Measurement Data ◽  
Optimal Model ◽  
Identification Procedure ◽  
Non Linear ◽  
Allowable Range ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Nonlinear Joints

AbstractGenerally, the Force-State Mapping (FSM) is an effective method to identify the parameters of nonlinear joints provided that the joint model is exactly known in advance. However, the variation of the non-linear joints is so large that the mathematical models of non-linear joints generally are not known in advance. Therefore, the model and the parameters of a non-linear joint should be identified simultaneously in practice. In this work, a new identification procedure which was based on the FSM method in frequency domain was proposed to identify the mathematical model and parameters of a non-linear joint simultaneously. Generally, there are many feasible combinations of models and parameters which can satisfy the measurement data within an allowable range of error. In this work, an iteration procedure was used to update the feasible models to result in an optimal model with its parameters. The simulation results show that a proper mathematical model and accurate parameters can be identified simultaneously by the new procedure even that the measurement data are contaminated by noise.

scholarly journals PARAMETER IDENTIFICATION IN ESTUARINE MODELING

1980 ◽  
Vol 1 (17) ◽  
pp. 143
Author(s):  
Wen-Sen Chu ◽  
William W-G. Yeh
Keyword(s):  
Mathematical Model ◽  
Parameter Identification ◽  
Transport Equation ◽  
Hydraulic Model ◽  
Physical Point ◽  
The Real ◽  
The Past ◽  
Estuarine Modeling ◽  
The Mathematical Model ◽  
Hydrodynamics Equations

Parameter Identification (PI) algorithm is an optimization procedure that systematically searches the parameters embedded in a mathematical model. These parameters are not measurable from a physical point of view. The optimization is based on the minimization of a selected norm of the differences between the solution of the mathematical model and scattered observations collected from the system. Parameter identification (or inverse problem) has been studied in groundwater systems extensively for the past decade (15), and it has also drawn many researchers in the fields of open-channel flow and estuarine modeling since 1972 (1,2,9,17). All the past estuarine PI works in the literature are confined to the one-dimensional case, and hydrodynamics and transport equations are treated separately. This study deals with PI in a two-dimensional vertically-averaged estuarine salinity model. The salinity transport equation is coupled with the hydrodynamics equations. The coupled relationship introduces extra density terms in the hydrodynamics equations, which must be solved simultaneously with the transport equation. One of the most difficult problems in PI is the collection of needed observations from the system which is being modeled. With limited exception, the currently available data from the prototype estuaries are not adequate for the purposes of developing a PI algorithm. This is usually critical in quantity (the number of stations and/or the period of time) and in quality (noise of data). However, if an operational hydraulic model is available, the data could then be obtained economically and accurately under an ideally controlled environment. The large amount of data that can be collected from a hydraulic model of an estuary will provide a sufficient number of observations and the required initial and boundary conditions for the development of a PI algorithm. The use of the estuary hydraulic model could provide a better source of prototype data than would be available from the real estuary. It will be much easier to distinguish between the inadequacy of the mathematics and the inadequacy of our understanding of the prototype. Thus, it will give us an idea of how well we could expect to mathematically model the real estuary if we had an unlimited amount of prototype data. Additionally, when these types of data are used in PI, parameters can be optimally identified and the mathematical model can then be used conjunctively with the hydraulic model for prototype applications, provided that the mathematical model is consistently formulated. How well a hydraulic model simulates the prototype estuary is not considered in this study.

scholarly journals Pemecahan Problem Efisiensi Faktor Produksi dengan Metode Linear Programming

2018 ◽  
Vol 20 (1) ◽  
pp. 20
Author(s):  
Surahman Surahman
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Problem Solving ◽  
Decision Maker ◽  
Real Condition ◽  
The Real ◽  
The Mathematical Model

<p>The problem solving of the production element efficiency by using linear programming can be done by formulating the mathematical model. The principles that have to be kept first are:</p><ol><li>The whole set of the problems can be divided into activity parts.</li><li>Each of the activities must have been determined precisely (about the quantity)</li><li>The quantity must have devided precisely</li><li>The limit of the capacity should be determined</li><li>Making the model</li></ol><p>After that, the next step is finding the solution. However, one thing to remember is that the problem solving using linear programming is only a medium. About the application depends on the decision maker or the user that will not be out from the real condition.</p>

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