Stabilization of a solid propellant rocket instability

A globally stabilizing feedback boundary control law for an arbitrarily fine discretization of a one-dimensional nonlinear PDE model of unstable burning in solid propellant rockets is presented. The PDE has a destabilizing boundary condition imposed on one part of the boundary. We discretize the original nonlinear PDE model in space using finite difference approximation and get a high order system of coupled nonlinear ODEs. Then, using backstepping design for parabolic PDEs, properly modified to accommodate the imposed destabilizing nonlinear boundary condition at the burning end, we transform the original system into a target system that is asymptotically stable in l/sup 2/-norm with the same type of boundary condition at the burning end, and homogeneous Dirichlet boundary condition at the control end. The control design is accompanied by a simulation study that shows that the feedback control law designed using only one step of backstepping (using just two temperature measurements) can successfully stabilize the actual system for a variety of different simulation settings.