# A Design Study for Thermal Control of a CVD Reactor for YBCO

### Martha Gallivan, David Goodwin, and Richard M. Murray

1998 Conference on Control Applications

A reactor for the deposition of superconducting \ybcolong\;thin films is modeled and studied from a control perspective to determine the heat transfer dynamics of the reactor under active thermal control. A nonlinear wavelength-dependent heat transfer model is developed to predict reactor heat transfer throughout the film growth process, and preliminary component testing is conducted to validate the model. The model is linearized about a typical operating point and analyzed with linear feedback control methods to determine the performance of the reactor under observer-based feedback control with film growth disturbances. The controller and observer are selected through linear quadratic regulator and linear quadratic estimator methods. Rates of convergence of the controller and observer are determined through examination of the eigenvalues of the linearized system, and disturbance rejection is assessed with ${\mathcal H}_2$ and ${\mathcal H}_\infty$ norms. The eigenvalue and norm analysis is applied to varying reactor design parameters to quantify performance tradeoffs. The maximum errors associated with control and with estimation of a nominal design case are both 21 K, and the longest time scales are 45 seconds and 10 seconds for the controller and observer, respectively.

- Conference paper: http://www.cds.caltech.edu/~murray/preprints/ggm98-cca.pdf
- Project(s): Template:HTDB funding::NSF, Template:HTDB funding::AFOSR, Template:HTDB funding::DARPA