Skip to main content
Feedback Control of a Thermal Fluid Based on a Reduced Order Observer
  • Weiwei Hu
  • John R. Singler, Missouri University of Science and Technology
  • Yangwen Zhang
We discuss the problem of designing a feedback control law based on a reduced order observer, which locally stabilizes a two dimensional thermal fluid modeled by the Boussinesq approximation. We consider mixed boundary control for the Boussinesq equations in an open bounded and connected domain. In particular, the controllers are finite dimensional and act on a portion of the boundary through Neumann/Robin boundary conditions. A linear Luenberger observer is constructed based on point observations of the linearized Boussinesq equations. The current setting of the system leads to a problem with unbounded control inputs and outputs. Linear Quadratic Gaussian (LQG) balanced truncation is employed to obtain the reduced order model for the linearized system. The feedback law can be obtained by solving an extended Kalman filter problem. The numerical results show that the nonlinear system coupled with the reduced order observer through the feedback law is locally exponentially stable.
Meeting Name
10th IFAC Symposium on Nonlinear Control Systems (2016: Aug. 23-25, Monterey, CA)
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
  • Control Theory,
  • Feedback Control,
  • Fluid Dynamics,
  • Linearization,
  • Boussinesq Approximations,
  • Exponentially Stable,
  • Feedback Control Law,
  • Linear Quadratic Gaussian,
  • Linearized Boussinesq Equations,
  • Luenberger Observers,
  • Reduced Order Models,
  • Reduced Order Observers,
  • Feedback
Document Type
Article - Conference proceedings
Document Version
File Type
© 2016 Elsevier B.V., All rights reserved.
Publication Date
Citation Information
Weiwei Hu, John R. Singler and Yangwen Zhang. "Feedback Control of a Thermal Fluid Based on a Reduced Order Observer" IFAC-PapersOnLine Vol. 49 Iss. 18 (2016) p. 116 - 121 ISSN: 24058963
Available at: