Dynamic phase compensation in Modulated-Demodulated Control for Pulsed jet injection

Abstract

This paper proposes the addition of dynamic phase compensation to modulated-demodulated controllers used for disturbance rejection/reference tracking and demonstrates a novel application of repetitive control for pulsed jet injection. In cases where a plant has rapidly varying phase near the frequency or frequencies to be controlled, conventional static phase compensation may be inadequate due to the propensity to create peaking in the sensitivity function. Dynamic phase compensation improves the disturbance rejection characteristics of modulated-demodulated controllers by inverting the plant phase over some frequency band in the "baseband" coordinates. Both static and dynamic phase compensation controllers are compared on an experimental apparatus that is used to study pulsed jet injection. The controllers are used to track a square wave in the temporal velocity profile of a pulsed jet of air using active forcing. In this application pulsing the jet improves the mixing and spread of the jet which are useful for energy generation and aerospace applications.

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

“…An industrial blower driven by an adjustable-speed electric motor introduces the crossflow, and several screens and a honeycomb flow-straightener section condition the crossflow before entering the test section, which is 12 × 12 cm in cross section and 30 cm in length. This apparatus has been employed in a wide range of unforced [20,21] and forced experimental studies [6][7][8]18,22], in which the jet-to-crossflow velocity ratio varies between 1.15 and 10, and the jet-to-crossflow density ratio varies between 0.14 (pure helium) and 1.00 (pure air). In the present study, the control technique is demonstrated without a crossflow.…”

“…Linear models of the pulsed jet can be developed from data generated with low-amplitude test inputs. Controllers developed using the models are then adequate for low-amplitude reference tracking [18,22]. At forcing amplitudes exceeding 0.5 ms −1 rms though, the nonlinear response of the velocity measurement (the regulated variable) can destabilize the closed-loop system.…”

“…Poles at jkω 0 provide asymptotic tracking of a periodic signal at kω 0 . An additional analysis of the dynamics of the inner loop from both the measurement and baseband perspectives is given in [18,22]. Measurement of the inner-loop complementary sensitivity function ( Fig.…”