Modern Control Methods for First Order Hyperbolic Partial Differential Equations

• Author / Creator

  Alavi Shoushtari, Navid

• This work is focused on two control methods for first order hyperbolic partial differential equations (PDE). The first method investigated is output regulation by employing the internal model control (IMC) principle where the controller generates the internal dynamic of the exosystem in order to asymptotically track the trajectory and reject the disturbances. This method is implemented on both systems with in-domain and boundary actuation. The actuator is distributed throughout the system in the first approach, while it is limited at the boundary in the second one. The second method revolves around designing full state feedback controller using so-called backstepping method. Backstepping converts the unstable system to a stable target plant by an integral transformation. This method is assessed for a general first order hyperbolic PDE. Finally, the backstepping method is expanded to a special case in which the boundaries are coupled. This case represents tubular reactors with recycle and exhibits interesting response under controller implementation. Results show that both methods are able to successfully stabilize first order hyperbolic PDEs at the origin. Results are illustrated with simulations.

• Subjects / Keywords

  • Output Regulation
  • First Order Hyperbolic
  • Partial Differential Equation
  • Backstepping

• Graduation date

  Fall 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3J67925K

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.