Distributed parameter control of heat diffusion with solidification

Petrus, Bryan

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https://hdl.handle.net/2142/50691 Copy

Description

Title

Distributed parameter control of heat diffusion with solidification

Author(s)

Petrus, Bryan

Issue Date

2014-09-16

Director of Research (if dissertation) or Advisor (if thesis)

• Bentsman, Joseph
• Thomas, Brian G.

Doctoral Committee Chair(s)

• Bentsman, Joseph
• Thomas, Brian G.

Committee Member(s)

• Hovakimyan, Naira
• Basar, Tamer

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Control systems
• Distributed parameter control
• Solidification
• Modeling

Abstract

Continuous casting is an important engineering process which produces nearly all steel currently used worldwide. Regulation of the temperature of the steel during casting with water sprays is known to be important to final product quality and safely operating the caster. Yet most current control methods are effectively open-loop, due to the complicated nature of the process. Measurements of the steel temperature cannot be made reliably due to the high temperatures and constant water spray in the caster. Even if feedback could be obtained, the temperature of the steel is governed by a nonlinear partial differential equation (PDE), which presents a challenge for existing control techniques. In the first part of this dissertation, the state-of-the art in industrial control systems for this process is described. The primary difficulty this system deals with is the sensing problem. Instead of physical sensors, a real-time computational model of the caster is used as a ``software sensor.'' Using the model for feedback, a simple proportional integral (PI) controller bank is able to adequately regulate the surface temperature. Using multiple independent 1-D models interpolated to provide a 2-D prediction of the steel temperature, the model is able to run in real-time even at the high casting speeds of a thin-slab steel caster. The model is calibrated through steady state measurements of the thin-slab caster from reliable pyrometer measurements outside the spray zone and metallurgical length detection trials. The use of independent 1-D models is verified by comparing model predictions with transient measurements of roll forces in another caster. The model is further used to perform a computational study of the temperature and shell thickness in a caster during sudden speed changes. In the second part, the control problem is studied for a simpler, but still fundamentally nonlinear PDE model of the caster. Using Lyapunov stability theory for infinite-dimensional systems, a control law is designed that matches the entire distributed temperature of a 1-D slice through control of the heat flux at the steel surface. In the first version, the control law is based on only examining the temperature error, and produces a control law with sharply varying and unbounded heat flux. In the second version, a control law that performs much better is found by considering the error in enthalpy for feedback. The second control design is also proven to work for models better approximating the real system, in particular limits on the heat flux due to the spray water piping system design. In the final part, the control law designed in the second part is simulated on a model including some of the most important difficulties of the real system, namely non-symmetric boundary conditions and actuator saturation, and performs admirably. The controller still uses a software sensor, as in the first part, so the uncertainty of the model is quantitatively examined. Finally, some additional unproven conjectures are offered that are based on simulation evidence. In particular, a boundary sensing solution is proposed that is not yet proved, but works well in simulation.

Graduation Semester

2014-08

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http://hdl.handle.net/2142/50691

Copyright and License Information

Copyright 2014 Bryan Petrus

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