State Equations

2004 ◽  
pp. 119-127
Author(s):  
Andrzej Służalec
Keyword(s):  
State Equations

scholarly journals An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

2016 ◽  
Vol 26 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Andreas Rauh ◽  
Luise Senkel ◽  
Harald Aschemann ◽  
Vasily V. Saurin ◽  
Georgy V. Kostin
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Control Strategies ◽  
Open Loop ◽  
Distributed Parameter ◽  
Dimensional System ◽  
State Equations ◽  
Large Space ◽  
Finite Dimensional ◽  
Spatially Distributed

Abstract In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

On krylov matrices and controllability of n-dimensional linear time-invariant state equations

1996 ◽  
Vol 3 (1-2) ◽  
pp. 99-109
Author(s):  
Andrzej Maćkiewicz ◽  
Francisco López Almansa ◽  
José A. Inaudi
Keyword(s):  
Linear Time ◽  
Invariant State ◽  
State Equations ◽  
Linear Time Invariant ◽  
Time Invariant

Modeling and simulation of saturated double rotor induction machine

2018 ◽  
Vol 37 (3) ◽  
pp. 1139-1165
Author(s):  
Koosha Choobdari Omran ◽  
Ali Mosallanejad
Keyword(s):  
Temperature Effects ◽  
Power Efficiency ◽  
Reactive Power ◽  
Induction Machine ◽  
Transient Behavior ◽  
State Equations ◽  
Content Type ◽  
Proposed Model ◽  
The Difference ◽  
Park Transformation

Purpose Double rotor induction machine (DRIM) is a particular type of induction machine (IM) that has been introduced to improve the parameters of the conventional IM. The purpose of this study is to propose a dynamic model of the DRIM under saturated and unsaturated conditions by using the equations obtained in this paper. Also, skin and temperature effects are considered in this model. Design/methodology/approach First, the DRIM structure and its performance will be briefly reviewed. Then, to realize the DRIM model, the mathematical equations of the electrical and mechanical part of the DRIM will be presented by state equations in the q-d axis by using the Park transformation. In this paper, the magnetizing fluxes saturation is included in the DRIM model by considering the difference between the amplitudes of the unsaturated and saturated magnetizing fluxes. The skin and temperature effects are also considered in this model by correcting the rotor and stator resistances values during operation. Findings To evaluate the effects of the saturation and skin effects on DRIM performance and validate the model, the machine is simulated with/without consideration of saturation and skin effects by the proposed model. Then, the results, including torque, speed, stator and rotor currents, active and reactive power, efficiency, power factor and torque-speed characteristic, are compared. In addition, the performance of the DRIM has been investigated at different speed conditions and load variations. The proposed model is developed in Matlab/Simulink for the sake of validation. Originality/value This paper presents an understandable model of DRIM with and without saturation, which can be used to analyze the steady-state and transient behavior of the motor in different situations.

An Adaptive State Filtering Algorithm for Systems With Partially Known Dynamics

2002 ◽  
Vol 124 (3) ◽  
pp. 364-374 ◽  
Author(s):  
Alexander G. Parlos ◽  
Sunil K. Menon ◽  
Amir F. Atiya
Keyword(s):  
Neural Networks ◽  
Case Studies ◽  
Feedforward Neural Networks ◽  
Complex Case ◽  
State Equations ◽  
Estimation Errors ◽  
Filter Performance ◽  
On Line ◽  
Noise Statistics ◽  
On Line Learning

On-line filtering of stochastic variables that are difficult or expensive to directly measure has been widely studied. In this paper a practical algorithm is presented for adaptive state filtering when the underlying nonlinear state equations are partially known. The unknown dynamics are constructively approximated using neural networks. The proposed algorithm is based on the two-step prediction-update approach of the Kalman Filter. The algorithm accounts for the unmodeled nonlinear dynamics and makes no assumptions regarding the system noise statistics. The proposed filter is implemented using static and dynamic feedforward neural networks. Both off-line and on-line learning algorithms are presented for training the filter networks. Two case studies are considered and comparisons with Extended Kalman Filters (EKFs) performed. For one of the case studies, the EKF converges but it results in higher state estimation errors than the equivalent neural filter with on-line learning. For another, more complex case study, the developed EKF does not converge. For both case studies, the off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. On-line training further enhances filter performance, decoupling the eventual filter accuracy from the accuracy of the assumed system model.

Technique and results of experimental determination of the compressibility factor of the natural gas

2021 ◽  
pp. 35-40
Author(s):  
Denis Y. Kutovoy ◽  
Igor A. Yatsenko ◽  
Vladimir B. Yavkin ◽  
Aydar N. Mukhametov ◽  
Petr V. Lovtsov ◽  
...  
Keyword(s):  
Natural Gas ◽  
Equations Of State ◽  
Compressibility Factor ◽  
High Accuracy ◽  
State Equations ◽  
Actual Problem ◽  
Temperature Range ◽  
Relative Value ◽  
Compressibility Coefficient

The actual problem of the possibility of using the equations of state for the gas phase of natural gas at temperatures below 250 K is considered. To solve it, the compressibility coefficients of natural gas obtained experimentally with high accuracy are required. The technique was developed and experimental study was carried out of compressibility factor aiming expanding temperature range of the state equations GERG-2004 and AGA8-DC92. The proposed technique is based on the fact that to assess the applicability of the equation of state, it is sufficient to obtain the relative value of the compressibility coefficient and not to determine its absolute value. The technique does not require complex equipment and provides high accuracy. The technique was tested on nitrogen, argon, air and methane. Uncertainty of determination of the compressibility factor is not greater than 0.1 %. For two different compositions of natural gas, obtained experimental data were demonstrated that the equations of state GERG-2004 and AGA8-92DC provide uncertainty of the calculation of the compressibility coefficient within 0.1 % in the temperature range from 220 K to 250 K and pressure below 5 MPa.

Validation of a new method for determination of free fatty acid turnover

1987 ◽  
Vol 252 (3) ◽  
pp. E431-E438 ◽  
Author(s):  
J. M. Miles ◽  
M. G. Ellman ◽  
K. L. McClean ◽  
M. D. Jensen
Keyword(s):  
Steady State ◽  
Fatty Acid ◽  
Free Fatty Acid ◽  
Clearance Rate ◽  
Experimental Period ◽  
Metabolic Clearance ◽  
Metabolic Clearance Rate ◽  
State Equations ◽  
Tracer Methods

The accuracy of tracer methods for estimating free fatty acid (FFA) rate of appearance (Ra), either under steady-state conditions or under non-steady-state conditions, has not been previously investigated. In the present study, endogenous lipolysis (traced with 14C palmitate) was suppressed in six mongrel dogs with a high-carbohydrate meal 10 h before the experiment, together with infusions of glucose, propranolol, and nicotinic acid during the experimental period. Both steady-state and non-steady-state equations were used to determine oleate Ra ([3H]oleate) before, during, and after a stepwise infusion of an oleic acid emulsion. Palmitate Ra did not change during the experiment. Steady-state equations gave the best estimates of oleate inflow approximately 93% of the known oleate infusion rate overall, while errors in tracer estimates of inflow were obtained when non-steady-state equations were used. The metabolic clearance rate of oleate was inversely related to plasma concentration (P less than 0.01). In conclusion, accurate estimates of FFA inflow were obtained when steady-state equations were used, even under conditions of abrupt and recent changes in Ra. Non-steady-state equations, in contrast, may provide erroneous estimates of inflow. The decrease in metabolic clearance rate during exogenous infusion of oleate suggests that FFA transport may follow second-order kinetics.

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