Boundary control of transient temperature in internal pipe flow heat transfer by POD-galerkin ROM

The aim of this thesis is to investigate the model reduction and modern control methods used in study of fluid stability and control. Some of the modern methods of reduced order modeling and control are applied to a simplified problem of transient heat transfer of an internal pipe flow forced convection, which will constitute a novel enviroment for the application of these methods. The reduced order modeling is done by Proper Orthogonal Decomposition(POD)-Galerkin method that is applicable to a more general case of nonlinear partial differential equations(PDEs) and it is applied to this particular problem to obtain a state space model under fluctuating disturbances, that represents the dynamics optimally based on average fluctuating energy captured. This is followed by design of optimal controllers by linear matrix inequality(LMI) formulation. The obtained state space realization is used for controller synthesis and compared with open loop system and the controller from the hinfsyn.m function in MATLAB. The considered control problems were disturbance attenuation and reference tracking. These cases were simulated using a numerical solver on the full order model and the methods were shown to be successful.