Backstepping Observer and Controller Design for Parabolic PDE with Time-Varying Domain

In this work a PDE backstepping based observer and control law for one-dimensional unstable heat equatio with time-varying spatial domain are developed. The underlying parabolic partial differential equation (PDE) with time-varying domain is the model emerging from process control applications such as crystal growth. In backstepping observer and control law synthesis [1], a characteristic feature is that the PDE describing the transformation kernel of the associated Volterra integral is time-dependent. In this work, the kernel PDE is solved numerically and both observer and state-feedback controller are simulated for the application of temperature regulation in the Czochralski crystal growth process.

[1] M. Krstic and A. Smyshlyaev, Boundary control of PDEs: A course on backstepping designs. Philadelphia: SIAM, 2008.