@MASTERSTHESIS\{IMM2017-06965,
    author       = "K. K. Nielsen",
    title        = "Modelling and Control of Float Zone Silicon crystal growth",
    year         = "2017",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "Supervisors: Niels Kj{\o}lstad Poulsen, nkpo@dtu.dk, {DTU} Compute, John Bagterp J{\o}rgensen, jbjo@dtu.dk, {DTU} Compute, Nico Werner, Project Manager at Topsil GlobalWafers A/{S,} Nicolai Hanssing, M.Sc. Control Engineering \& Automation at Topsil GlobalWafers A/S",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/6965-full.html",
    abstract     = "This thesis deals with the application of offset free control, using a model predictive controller, on the process of producing silicon wafers operating in a stable state subject to unknown disturbances. Because of the disturbances the process would experience offset errors in the outputs.
A linear model was derived from a non-linear model developed through the work of Nico Werner in his PhD thesis. The model was then analysed to verify that it could be used as a basis for the model predictive control. A simple disturbance model used in the estimation of the unknown disturbances and used in the control to achieve offset free control.
The control solution was implemented and simulated in {MATLAB,} excited by different disturbances and evaluated, with respect to the controllers ability to keep the controlled outputs at their steady states.
The results showed that the controller was able to control and track reference changes to the system. They also showed that it could remove offset errors in the crystal diameter, with a small offset in the the lower zone height. This is due to the uncontrollable marginally stable poles in the system."
}