Adaptive backstepping nonlinear controller design for shock position control of supersonic engine

A Shock position control law of a ramjet engine with variable nozzle throat is proposed. To address the nonlinearity of engine internal nature, an engine model structure which defines sequentially propagated internal flows from inlet to nozzle throat is used such that the effectiveness of nozzle throat variance to intake shock position is mechanized. The specified engine model with equilibrium manifold and shock motion assumed 1^st order dynamics is employed to design the control logic. The steady state shock position is approximately expressed as a function of nozzle throat area, and, using its explicit relation, an adaptive backstepping controller design procedure is accomplished. Unknown parameters which represent the model uncertainties or errors are compensated by the adaptive law and it is expected to give stable control architecture for the shock motion under the changes of internal combustion and flight condition. Some numerical simulations are accomplished to verify the performance of the controller which shows the stable tracking of shock position command.