Phase Compensation Strategies for Modulated-Demodulated Control With Application to Pulsed Jet Injection

Abstract

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.

Transverse jet mixing characteristics

“…After exiting the seeder, the gas mixture was exhausted into a Plexiglas pipe below the test section using four symmetrically oriented inlet fittings. Below this pipe was a Plexiglas plenum, housing either a loudspeaker or a piston-based actuator, used in separate studies to apply controlled longitudinal acoustic excitation (M'Closkey et al 2002;Davitian et al 2010b;Hendrickson & M'Closkey 2012). Above this Plexiglas plenum was a PVC pipe of sufficient length for full development of laminar pipe flow, alleviating any asymmetries associated with the inlet fittings (Gevorkyan 2015).…”

Realization of a class of compensators by modulated-demodulated structures with application in tracking of biased sinusoids

“…Writing the above expressions in Laplace domain, the fol-lowing relationships are readily obtained: e 2jγ y − − = y cγ + jy sγ ; e −2jγ y + + = y cγ − jy sγ (14) e 2jβ y − − = y cβ + jy sβ ; e −2jβ y + + = y cβ − jy sβ (15) We also introduce the following transfer functions, in terms of transfer function A(s) and phase angle γ:…”

“…Such systems have been used in applications such as, radio frequency transmitters [8], micro-gyroscopes [11], [20], [21], rotating gravity gradiometers [1], [7], [14], and pulsed jet injection [15].…”

“…In [17], [18], for a single-channel modulated-demodulated structure, some performance limitations were investigated using an approximate method. Tracking of sinusoidal references with zero bias was recently investigated in a modulated-demodulated control system [15].…”

“…The proposed realization method is used to design modulated-demodulated tracking control systems for a marginally stable non-minimum-phase plant. Compared to the tracking method in [15] that cannot handle biased references, we suggest two different methods for injecting biased sinusoidal references into modulated-demodulated control systems. Efficacy of the proposed methods are also investigated by simulations performed in presence of biased sinusoidal disturbances.…”