scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

scholarly journals Mathematical model of the road vibrating roller

2020 ◽  
Vol 1 (1) ◽  
pp. 133-139
Author(s):  
Pavel Aleksandrovich KORCHAGIN ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Road Construction ◽  
Well Being ◽  
Point Of View ◽  
Engineering Industry ◽  
Supporting Surface ◽  
The Road ◽  
Vibration Protection ◽  
The Mathematical Model

Introduction. The process of compaction of the soil foundation by a road vibrating roller is considered as the object of the study. The main purpose of vibrating rollers used in road construction is to reduce the energy consumption of the compaction process and increase the productivity of the operations performed Since the 80s of the last century, the engineering industry has noted a tendency to abstention the production of static rollers. By reducing the amplitude of oscillations or completely disconnecting the vibrator, you can get the same static modes, and accordingly the results of rolling. In addition, the reduction of dynamic impacts positively affects the physical condition of an operator of the road-building machine, stabilizes the well-being and increases productivity. Materials and methods. The mathematical model of the dynamic system “Supporting surface–roller–operator” is presented. The main components of the dynamic system are described in the form of ordered and interacting subsystems. The forces acting on the dynamic system are determined; they are sources of dynamic effects. The calculation schemes of the subsystems “Operator” and “Roller”, which are of the greatest interest from the point of view of vibration protection, are reflected. Results. The result of the work can be considered the compilation of generalized scheme of the dynamic system; calculation scheme of the dynamic system; mathematical model “Supporting surface–operator–roller”; implementation of the mathematical model in MathLab, its additional Simulink extension package. Discussion and conclusion. The presented mathematical model allows carrying out research of the processes occurring in the dynamic system “Supporting surface–roller–operator”. The most rational mathematical model can be used in the development of methods and tools aimed at improving the vibration protection system for operators of road rollers. The mathematical model of a road roller is planned to be used as a basis for creating a robotic complex with an automated control system designed to perform operations to compact coatings and foundations in road construction.

scholarly journals Mathematical model parameter estimation of a generating unit operating in the Polish National Power System

2016 ◽  
Vol 64 (2) ◽  
pp. 409-416
Author(s):  
Ł. Majka ◽  
S. Paszek
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Power System ◽  
Objective Function ◽  
Model Parameters ◽  
Gradient Algorithms ◽  
Hybrid Optimization Algorithm ◽  
National Power ◽  
The Mathematical Model ◽  
Paper Method

Abstract In the paper, a method and results of parameter estimation of the mathematical model of a generating unit operating in the Polish National Power System are presented. Computations of the parameters were carried out based on measurement and simulation of dynamic waveforms of selected quantities of the generating unit. The problem of parameter identification was brought to minimization of the objective function determined by the vector of deviations between the approximated and approximating waveforms computed on the basis of the models expressed by the searched parameters. A hybrid optimization algorithm, being a serial combination of genetic and gradient algorithms, was used for minimization of the objective function. A methodology for filtering the recorded measurement signals is proposed in the paper. Method and results calculation of the sensitivity to changes of the model parameters of selected dynamic waveforms are also presented.

Theoretical and Experimental Researches Regarding the Influence of the Suspension Car Stiffness on the Dynamic Behavior of Vehicles

2016 ◽  
Vol 822 ◽  
pp. 36-43
Author(s):  
Dumitru Neagoe ◽  
Dumitru Bolcu ◽  
Loreta Simniceanu ◽  
Mario Trotea
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Dynamic Behavior ◽  
Experimental Research ◽  
Experimental Results ◽  
Negative Effects ◽  
Experimental Researches ◽  
The Mathematical Model ◽  
Theoretical Results

In this paper the authors present the results of theoretical and experimental research in order to optimize suspension rigidity in case of Daewoo Nubira vehicle. The paper presents the mathematical model obtained by assimilating car with a dynamic system with 5 rigid solids with elastic and viscous linking between them. Theoretical results obtained based on this model and the experimental results are presented, and it is presented a solution to optimize suspension in order to remove the negative effects observed driving on gravel runways or damaged runaways. Theoretical results, compared with the experimental ones, allow us to say that it is possible to optimize suspension by analyzing specific parameters equivalent mathematical model.

Identification of the Mathematical Model of Failure Frequency of Overhead Lines of Power System Main Grid

2020 ◽  
pp. 100-111
Author(s):  
N.E. Zubov ◽  
I.M. Galiaskarov ◽  
V.N. Ryabchenko
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
A Priori ◽  
Original Method ◽  
Linear Matrix ◽  
Time Interval ◽  
Identification Algorithm ◽  
Electrical Grid ◽  
Failure Frequency ◽  
The Mathematical Model

Based on the analysis of accidents of 500 kV over-head lines of the main electric electrical grid of a wide region over a long-time-interval, the failure frequency (failure flux parameter) was determined under the influence of natural and socio-economic factors. It is proposed to consider the indicated failure rate as the output signal of a discrete positive dynamic system with many difficult formalizable inputs. To identify the mathematical model of a dynamic system, it is proposed to use the original method, the identifiability criterion of which is based on the compatibility condition of the linear matrix equation, and the numerical identification algorithm is based on the solution formula using zero-divisors and generalized inverse matrices. The method does not require a priori information about the parameters of the mathematical model of the electric electrical grid, does not involve solving the forecasting problem, and does not apply statistical calculations

Modeling of an Electrostatic Micromotor Based on a Levitated Rotor

2007 ◽  
Author(s):  
Xi Chen ◽  
Fengtian Han ◽  
Yunfeng Liu
Keyword(s):  
Mathematical Model ◽  
Rotational Speed ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Electrostatic Force ◽  
Element Model ◽  
Micro Electro Mechanical Systems ◽  
Position Sensing ◽  
And Control ◽  
The Mathematical Model

This paper presents a mathematical model developed for an electrostatically levitated micromotor in which the ring-shaped rotor is levitated by electrostatic force in five degrees of freedom (DOFs). A glass/silicon/glass sandwich structure is utilized in this electrostatic micromotor, which is based on the technology of micro-electro-mechanical systems (MEMS). In the center of ring-shaped cavity formed by ICP between the top and bottom glass plates, the rotor is levitated by the five DOFs position servo system and driven by speed control system. In this paper, the mathematical model for the motion control of the rotor in five DOFs is developed. This model describes the capacitances and electrostatic forces between the rotor and associated electrodes, and moments of two rotations about the x, y-axis. The rotational torque model governing the rotor’s rotational speed is also described. In order to obtain the analytical nonlinear models for error analysis, these integral equations are expanded using the Taylor’s series. Moreover the finite element model and its simulation results are obtained by using ANSYS. In terms of comparison between the simulated results and the nonlinear models, the modeling accuracy of the micromotor can be evaluated. Furthermore, the error characteristics of the linearized models via rotor displacement are analyzed. Thus, position sensing and control of both the rotor’s motion, and the rotational speed, can be achieved based on these linearized models of electrostatically levitated micromotors.

scholarly journals Small-size inertia sensor

2018 ◽  
pp. 82-86
Author(s):  
V. N. Kitaev ◽  
R. L. Afanas’Ev ◽  
M. V. Petrov ◽  
V. V. Pol
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Permanent Magnet ◽  
Magnetic System ◽  
Fine Tuning ◽  
Sensor Parameter ◽  
The Mathematical Model ◽  
Inertia Sensor

The study introduces the design and principle of operation of the inertia sensor IV29 with a permanent magnet. According to the mathematical model developed, we consider the results of the sensor parameter estimation, and propose the options for a possible optimization of the magnetic system of the sensor for a better fine-tuning of its actuation data

Simulation of the Dynamic Behaviors of the C Axis Drive by the Turning Center

2009 ◽  
Vol 147-149 ◽  
pp. 356-361
Author(s):  
J. Křepela ◽  
Vladislav Singule
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
3D Model ◽  
Worm Gear ◽  
Turning Center ◽  
The Difference ◽  
Axis Drive ◽  
Torsion Stiffness ◽  
Multi Body ◽  
The Mathematical Model

The paper describes the mathematical model for C axis of the multifunction turning center with worm gear. Talks about the mathematical model with multi-body mass dynamic system. The drive works in the positional feedback and his mathematical model is specified for detection of the dynamical behaviors of the C axis. The turning center is designed for a heavy roughing forged piece from high carbon steels by the power of main motor 71kW. The C axis must be designed as accurate angle position axis and with big dynamic stability of regulation by step or pulse loading. The C axis drive is constructed with help of a hydraulic connected up the worm gearing on a spindle. The driven side of the worm gear is created two dual worms with own servomotors. Worm wheel is solved as one part with two gears. Servomotors are controlled with the mode speed/torque coupling (MASTER-SLAVE), which guarantees the constant torque prestressing between the servomotors. The difference of a torques guarantees leaning of both worm teeth on opposite tooth faces of both gears of the worm wheel. In the dynamic model are involved the friction on the worm gears, torsion stiffness located with help of the FEM and moment of inertia for all parts. 3D models of the C axis is designed in the program ProEngineer. From complete 3D model of the C axis are transfered individual parts to the FEM in surroundings Ansys as volume parts. In this paper is main output influence of the diference between the 3D and 2D for calculation of the stiffness in the contact of the worm gear on the whole dynamic system of the C axis. The value of the torsion stiffness by more situation of the load on the worm gear is used subsequently to the multi-body mass system of the C axis drive and to the eigen frequencies analyses. Results of this paper will be sensitivity check of the changing torsion stiffness on the worm gear by the loading changing on the resulted position accuracy on the C axis. Next review is, if the control modul MASTER-SLAVE is partially this problem of the difference between values of stiffness from 2D or 3D model or also stiffness non-linearity eliminated.

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