Convergence of the identification algorithm applied to the mutual inductance of the induction motor

2012 ◽  
Vol 61 (3) ◽  
pp. 337-345
Author(s):  
Andrzej Jąderko ◽  
Jędrzej Pietryka
Keyword(s):  
Differential Equations ◽  
Induction Motor ◽  
Mutual Inductance ◽  
The State ◽  
Position Vector ◽  
Identification Algorithm ◽  
State Variables ◽  
Vector Length ◽  
Parameter Versus ◽  
Observer System

Convergence of the identification algorithm applied to the mutual inductance of the induction motor A new observer of induction motor state variables is proposed in the paper. A nonlinearity of the main magnetic path is expressed as a function of a properly chosen parameter versus the position vector length. The value of the mutual inductance received in the identification algorithm is calculated exploiting the estimated values of the state variables. The coefficients appearing in the differential equations of the observer system are modified in each step of the algorithm on the basis of the calculated mutual inductance. The analysis of convergence of the identification algorithm is shown in this paper.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

scholarly journals Specific Mathematical Aspects of Dynamics Generated by Coherence Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma
Keyword(s):  
Differential Equations ◽  
Complex Systems ◽  
Integral Equations ◽  
Quantum Physics ◽  
Initial Conditions ◽  
Coherence Function ◽  
Multiple Integral ◽  
The State ◽  
Integrodifferential Equations ◽  
State Variables

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of annth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed whennequals 4, 5, or 6.

scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

scholarly journals SYNTHESIS OF AN ADAPTIVE AUTOMATIC SYSTEM OF AIRCRAFT CONTROLS WITH MULTIDIMENSIONAL PI-REGULATOR

2019 ◽  
Vol 27 (4) ◽  
pp. 79-85
Author(s):  
Aramis Viktorovich Tishchenko ◽  
Anatoly Mikhailovich Kulabukhov ◽  
Victor Alexandrovich Masalskiy
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Minimum Mean Square Error ◽  
Center Of Mass ◽  
Control Object ◽  
The State ◽  
Quadratic Functional ◽  
State Variables ◽  
Control Actions ◽  
Conditional Minimization

The article presents the synthesis of a functional diagram of an adaptive automatic control system (ACS) for controlling an aircraft with an automatically reconfigurable multidimensional PI controller, which provides the minimum static and minimum mean square error of control with minimal energy consumption for the formation of the control exposure. The synthesis of ACS algorithms is performed as a result of solving the problem of conditionally minimizing the quadratic functional of the generalized work (taking into account restrictions on state variables and control actions given by differential equations of the control object (CO) and inequalities). The mathematical description of the multidimensional CO is carried out using the CO model in the state space, which automatically takes into account the mutual influence of individual control loops on each other. As the state variables of the aircraft, linear displacements, speeds and accelerations of the center of mass of the aircraft, and angular displacements, speeds and accelerations of the rotational movement of the aircraft relative to the center of mass are used. The matrix equation of dynamics of the aircraft is formed by a system of nonlinear differential equations of the first order of forces and moments of forces acting on the aircraft. To ensure the minimum static control error, integrators are included in the ACS (for each control action). The algorithm for the formation of control actions of the extended CO, providing the declared properties of the ACS, is obtained as a result of solving the problem of conditional minimization of the generalized work functional. The task of conditional minimization of a functional with constraints is performed by the maximum principle. The resulting two-point boundary value problem is transformed by the invariant immersion method into a Cauchy problem for optimal values of state variables. The evaluation of the characteristics of a specific adaptive ACS for the spacecraft is expected to be obtained as a result of further research by mathematical modeling.

Nonlinear dynamic system identification using neuro-fractional-order Hammerstein model

2017 ◽  
Vol 40 (13) ◽  
pp. 3872-3883 ◽  
Author(s):  
Mohammad-Reza Rahmani ◽  
Mohammad Farrokhi
Keyword(s):  
Fractional Order ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic System ◽  
Lyapunov Stability Theory ◽  
The State ◽  
Order System ◽  
Hammerstein Model ◽  
Identification Algorithm ◽  
State Variables ◽  
State Matrix

This paper presents a neuro-fractional-order Hammerstein model with a systematic identification algorithm for identifying unknown nonlinear dynamic systems. The proposed model consists of a Radial Basis Function Neural Network (RBF NN) followed by a Fractional-Order System (FOS). The proposed identification scheme is performed in two stages. First, the fractional-order and the number of state variables (or degree) of the state-space realization of the FOS are estimated in the frequency domain. Then, the parameters of the RBF NN (the weights, centers and widths of the Gaussian functions) and the state matrix of the FOS are determined using the time domain data via the Lyapunov stability theory. Simulating as well as experimental examples are provided to verify the effectiveness of the proposed method. The identification results show that the proposed neuro-fractional-order Hammerstein modeling is superior as compared with the existing Hammerstein modeling in literature.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

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