Model Based Temperature Control in RTP Yielding ±0.1 °C accuracy on A 1000 °C, 2 second, 100 °C/s Spike Anneal

1998 ◽  
Vol 525 ◽  
Author(s):  
Peter Vandenabeele ◽  
Wayne Renken
Keyword(s):  
Differential Equations ◽  
Temperature Control ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
System Response ◽  
Model Based Control ◽  
First Order ◽  
Model Based ◽  
Measured System ◽  
Spike Anneal

ABSTRACTA Model Based Control method is presented for accurate control of RTP systems. The model uses 4 states: lamp filament temperature, wafer temperature, quartz temperature and TC temperature. A set of 4 first order, nonlinear differential equations describes the model. Feedback is achieved by updating the model, based on a comparison between actual (measured) system response and modeled system response.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Elena Adomaitienė ◽  
Skaidra Bumelienė ◽  
Gytis Mykolaitis ◽  
Arūnas Tamaševičius
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
Mean Field ◽  
Electrical Circuit ◽  
Voltage Source ◽  
Dc Voltage

A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed.

scholarly journals Integrability via Functional Expansion for the KMN Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1819
Author(s):  
Radu Constantinescu ◽  
Aurelia Florian
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
First Order ◽  
Second Order Differential Equations ◽  
Functional Expansion ◽  
Wave Solutions ◽  
First Time

This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.

Dynamic Response of Spinning Blades Subjected to Gyroscopic Motion

1994 ◽  
Vol 116 (1) ◽  
pp. 6-15 ◽  
Author(s):  
T. H. Young ◽  
G. T. Liou
Keyword(s):  
Differential Equations ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Parametric Instability ◽  
Spin Axis ◽  
System Response ◽  
First Order ◽  
System Equations ◽  
Element Technique ◽  
Gyroscopic Motion

This paper presents an investigation into the vibration and stability of a blade spinning with respect to a nonfixed axis. Due to the motion of the spin axis, parametric instability of the blade may occur in certain situations. In this work, the discretized equations of motion are first formulated by the finite element technique. Then the system equations are transformed, by a special modal analysis procedure, into independent sets of first-order simultaneous differential equations. Each set of differential equations is solved analytically by the method of multiple scales if the precessional speed of the spin axis is assumed to be small compared to the spin rate of the blade, yielding the system response and the expressions for the boundaries of the unstable regions. Finally, the effects of system parameters on the changes in these boundaries are studied numerically.

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