Feedback control of sector-bound nonlinear systems with applications to aeroengine control

This dissertation is divided into two parts. In the first part we consider the problem of feedback stabilization of nonlinear systems described by state-space models. This approach is inherited from the methodology of sector bounded or passive nonlinearities, and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. In close connection to gain scheduling and switching control, a path of equilibria is programmed based on the assumption of centered-epsilon-cover which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. In the second part we tackle the problem of control for fluid flows described by the incompressible Navier-Stokes equation. We are particularly interested in film cooling for gas turbine engines which we model with the jet in cross-flow problem setup. In order to obtain a model amenable to the controller design presented in the first part, the well-known Proper Orthogonal Decomposition (POD)/Galerkin projection is employed to obtain a nonlinear state-space system called the reduced order model (ROM). We are able to stabilize the ROM to an equilibrium point via our design method and we also present direct numerical simulation (DNS) results for the system under state feedback control

A generalized sector bound approach to feedback stabilization of nonlinear control systems

This paper proposes and develops a generalized sector bound approach to feedback stabilization of nonlinear control systems described by state-space models. This approach is inherited from the methodology of the sector bounded or passive nonlinearities, and influenced by the concept of absolute stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. Similar to gain scheduling control, a path of equilibria is programmed based on the assumption of centered - cover which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method. © 2012 AACC American Automatic Control Council)

A generalized sector-bound approach to feedback stabilization of nonlinear control systems

Summary This paper proposes and develops a generalized sector-bound approach to feedback stabilization of nonlinear control systems described by state-space models. This approach is inherited from the methodology of the sector-bounded or passive nonlinearities and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. More importantly, it has a close connection to gain scheduling and switching control. A path of equilibria is programmed on the basis of the assumption of centered- ε-cover, which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method. © 2012 John Wiley & Sons, Ltd