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

Abstract

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.

A High-Precision Continuous Scan and Step Scan System for Compact Spectrometer Applications

“…Closed-loop stability is achieved by appropriate selection of {a, b, K} and the process is thoroughly described in [35], however, briefly, if H denotes the closed-loop frequency response e 2 /d 2 in Fig. 8, then {a, b} are selected so that ∠(ja + b) + ∠H(ω 0 ) = −90 • while constraining a 2 + b 2 = 1 (the phase of the complex number c is denoted ∠c).…”

“…The walking stage has a stroke of 5.2 cm and is capable of achieving nanometer-level positioning accuracy in pointto-point tasks, however, periodic contact of the piezoelectric elements that push the stage on the linear guide produce jitter while moving. The short-stroke stage is designed so that its shuttle is passively isolated from walking stage disturbances between 35 Hz and 2 kHz. A 300 Hz bandwidth feedback loop further regulates the shuttle position using a voice coil and extends the rejection of walking stage disturbances to DC.…”