A Reduced-Order Model for Dynamic Vacuum Arc Remelting Pool Depth Estimation and Control

2011 ◽  
Author(s):  
Luis Felipe Lopez ◽  
Joseph J. Beaman ◽  
Rodney L. Williamson
Keyword(s):  
Depth Estimation ◽  
Liquid Pool ◽  
Reduced Order Model ◽  
Vacuum Arc ◽  
State Variables ◽  
Order Model ◽  
Operating Condition ◽  
Reduced Order ◽  
Vacuum Arc Remelting ◽  
Pool Depth

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. A reduced-order model of the growing and solidifying ingot was developed specifically for dynamic control and estimation of the depth of molten liquid pool atop the ingot in a VAR process. This model accounts only for the thermal aspects of the system ignoring high-fidelity physics such as fluid flow and electromagnetic effects. Spectral methods were used to obtain a set of nonlinear dynamic equations which capture the transient characteristics of liquid pool shape variations around a quasi-steady operating condition. These nonlinear equations are then linearized about this operating condition and further simplified by suppressing fast modes. The resulting system can be described by only six state variables. The reduced order model compares favorably to pool depth changes predicted by an accurate finite-volume model. A first approach to use this model in the design of a dynamic VAR pool depth estimator and controller is also proposed.

A Nonlinear Reduced Order Model for Estimation and Control of Vacuum Arc Remelting of Metal Alloys

2005 ◽  
Author(s):  
Joseph J. Beaman ◽  
Rodney L. Williamson ◽  
David K. Melgaard ◽  
Jon Hamel
Keyword(s):  
Moving Boundary ◽  
Reduced Order Model ◽  
Vacuum Arc ◽  
State Variables ◽  
Order Model ◽  
Electrode Gap ◽  
Reduced Order ◽  
Vacuum Arc Remelting ◽  
Integral Methods ◽  
Estimation And Control

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The VAR process is carried out in a vacuum with the aim of melting a large consumable electrode (.4 m in diameter and 3000 kg in mass and larger) in such a way that that the resulting ingot has improved homogeneity. The VAR control problem consists of adjusting arc current to control electrode melt rate, which also depends on the electrode temperature distribution and adjusting electrode ram speed to control the arc gap between the electrode and the ingot. The process is governed by a 1 dimensional heat conduction partial differential equation with a moving boundary, which leads to an infinite dimensional, nonlinear system. In addition to the process nonlinearity, the inputs and all of the available measurements are corrupted with noise. In order to design a controller and a Kalman based estimator for this process, integral methods are used to derive a set of two coupled nonlinear ordinary differential equations in time, which capture the steady state and transient characteristics of melting in a VAR furnace. The model with the experimentally measured noise is then used to construct an estimator and a controller. The system can be described by two state variables that change in time: thermal boundary layer and melted length or alternatively electrode gap. The reduced order model compares favorably to an accurate finite difference model as well as melting data acquired for Ti-6Al-4V. It will be shown how this model can be used to obtain dynamic closed loop melt rate control while simultaneously controlling electrode gap. This controller and estimator were tested on a laboratory furnace at Timet.

scholarly journals Reduced-Order DC Terminal Dynamic Model for Multi-Port AC-DC Power Electronic Transformer

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2130 ◽  
Author(s):  
Zhe Wang ◽  
Yaohua Li ◽  
Zixin Li ◽  
Cong Zhao ◽  
Fanqiang Gao ◽  
...  
Keyword(s):  
Dominant Mode ◽  
The State ◽  
Reduced Order Model ◽  
Power Electronic ◽  
State Variables ◽  
Order Model ◽  
Energy Storage Devices ◽  
Reduced Order ◽  
Electronic Transformer ◽  
Power Electronic Transformer

As new electric power conversion equipment, a multi-port power electronic transformer (MP-PET), including a power electronic converter, high-frequency transformer, and multiple ac or dc interconnection interfaces, has a broad application in the hybrid distribution network. However, high integration and a large number of energy storage devices has led to very a high-order model of the system. To address this issue, a reduced-order small signal model of MP-PET is established in this paper. By taking the participation factors of the system mode to the state variables, the reduced-order model is derived based on the state variables, which are highly correlated with the dc voltage dominant mode. Compared with the full-order model, the proposed reduced-order model is accurate enough and simplified, and the validity of the simplified model is verified against simulations on a 10 kV/3 MVA MP-PET. The simulation results indicate that the proposed reduced-order model coincides well with the dynamic performance of the MP-PET.

scholarly journals Modeling and Control Design of the Symmetrical Interleaved Coupled-Inductor-Based Boost DC-DC Converter with Clamp Circuits

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3432 ◽  
Author(s):  
Márcio Rodrigo Santos de Carvalho ◽  
Fabrício Bradaschia ◽  
Leonardo Rodrigues Limongi ◽  
Gustavo Medeiros de Souza Azevedo
Keyword(s):  
Mathematical Model ◽  
High Gain ◽  
Reduced Order Model ◽  
State Variables ◽  
Order Model ◽  
Eighth Order ◽  
Loop Control ◽  
Modeling And Control ◽  
Reduced Order ◽  
Point Tracking

The symmetrical input-interleaved high-gain DC-DC converters are suitable candidates to be used as the first stage in PV microinverters and as parallel-connected power optimizers. In both applications, they are responsible for boosting the PV module DC voltage to a higher value and executing the maximum power point tracking control. However, such converters have many state variables, some of them discontinuous, and many operation stages, which make the development of the small-signal model a challenging task. Therefore, the aim of this paper is to propose a reduced-order improved average method (ROIAM) to model the family member of converters that present characteristics such as symmetry, interleaved operation, and discontinuous state-space variables. ROIAM is applied to model for the first time in the literature the symmetrically-interleaved coupled inductor-based boost (SICIBB), leading to a fourth-order mathematical model (reduced-order model). The complete eighth-order mathematical model is developed as well to prove that the reduced-order model represents correctly the dynamic behavior of the SICIBB converter by employing only four state variables, reducing considerably the effort of the modeling. Based on the reduced-order proposed model, a closed-loop control is designed and tested in a 300-W prototype of the SICIBB converter.

scholarly journals Flutter Analysis for Turbomachinery Using Volterra Series

2014 ◽  
Author(s):  
Meng-Sing Liou ◽  
Weigang Yao
Keyword(s):  
Volterra Series ◽  
Aerodynamic Force ◽  
Reduced Order Model ◽  
Structural Deformation ◽  
Mode Shapes ◽  
Order Model ◽  
Steady State Condition ◽  
Operating Condition ◽  
Reduced Order ◽  
Flutter Boundary

The objective of this paper is to describe an accurate and efficient reduced order modeling method for aeroelastic (AE) analysis and for determining the flutter boundary. Without losing accuracy, we develop a reduced order model based on the Volterra series to achieve significant savings in computational cost. The aerodynamic force is provided by a high-fidelity solution from the Reynolds-averaged Navier-Stokes (RANS) equations; the structural mode shapes are determined from the finite element analysis. The fluid-structure coupling is then modeled by the state-space formulation with the structural displacement as input and the aerodynamic force as output, which in turn acts as an external force to the aeroelastic displacement equation for providing the structural deformation. NASA’s rotor 67 blade is used to study its aeroelastic characteristics under the designated operating condition. First, the CFD results are validated against measured data available for the steady state condition. Then, the accuracy of the developed reduced order model is compared with the full-order solutions. Finally the aeroelastic solutions of the blade are computed and a flutter boundary is identified, suggesting that the rotor, with the material property chosen for the study, is structurally stable at the operating condition, free of encountering flutter.

Sign in / Sign up

Export Citation Format

Share Document