Identification and control of nonlinear harmonic coupling for pulsed jet injection

This paper describes an approach to periodic reference tracking in a fundamental pulsed jet injection experimental study. The objective is to match the jet´s temporal velocity profile to a periodic reference for purposes of studying the mixing dynamics between the jet and surrounding fluid. 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. We approach the problem by demodulating the jet velocity measurement at harmonic frequencies represented in the desired waveform into baseband components. In a neighborhood of a desired operating point, an empirical relationship is developed by perturbing the baseband components and measuring their effect on neighboring harmonics. We demonstrate that this relationship can be reasonably modeled as a linear MIMO gain for nearby operating points. This knowledge is exploited to create a stabilizing feedback control that asymptotically drives the jet velocity to its reference.