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In a recent paper (Megerianet al.,J. Fluid Mech., vol. 593, 2007, pp. 93–129), experimental exploration of the behaviour of transverse-jet near-field shear-layer instabilities suggests a significant change in the character of the instability as jet-to-crossflow velocity ratiosRare reduced below a critical range. The present study provides a detailed exploration of and additional insights into this transition, with quantification of the growth of disturbances at various locations along and about the jet shear layer, frequency tracking and response of the transverse jet to very strong single-mode forcing, creating a ‘lock-in’ response in the shear layer. In all instances, there is clear evidence that the flush transverse jet's near-field shear layer becomes globally unstable whenRlies at or below a critical range near 3. These findings have important implications for and provide the underlying strategy by which active control of the transverse jet may be developed.

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Modulated-demodulated control is an effective method for asymptotic disturbance rejection and reference tracking of periodic signals, however, conventional static phase compensation often limits the loop gain in order to avoid sensitivity function peaking in a neighborhood of the frequencies targeted for rejection or tracking. This paper introduces dynamic phase compensation for modulated-demodulated control which improves disturbance rejection characteristics by inverting the plant phase in a neighborhood of the control frequency. Dynamic phase compensation is implemented at baseband which enables the use of low-bandwidth compensators to invert high frequency dynamics. Both static and dynamic phase compensation methods are used to demonstrate a novel application of repetitive control for pulsed jet injection. In this application pulsing an injectant has been shown to produce advantageous effects such as increased mixing in many energy generation and aerospace systems. The sharpness of the pulse can have a large impact on the effectiveness of control. Modulated-demodulated control is used to maximize the sharpness of a pulsed jet of air using active forcing by tracking a square wave in the jet’s temporal velocity profile.

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.