Compensation of Nonlinear Harmonic Coupling for Pulsed-Jet-Velocity Shaping

This paper describes an approach to periodic reference tracking in a pulsed-jet-injection experimental study. The objective was to match the jet’s temporal velocity profile to a periodic reference. The challenge lies in controlling the highly nonlinear and poorly understood dynamics associated with the jet velocity. Although the actuator maintains good authority over the jet velocity, the nonlinear jet dynamics creates a high degree of coupling among neighboring harmonics that depends on the forcing level and the desired waveform. The coupling is quantified by demodulating the jet-velocity measurement into baseband components centered at the harmonic frequencies represented in the desired waveform. An empirical input–output relationship is developed by perturbing the baseband components and measuring their effect on neighboring harmonics, and it is shown that this relationship can be modeled as a linear multi-input/multi-output system. This knowledge is exploited to create stabilizing feedback controls that asymptotically drive the jet velocity to the desired waveforms over a wide range of forcing conditions.