Abstract
It was found that thermoacoustic solar-power generators with resonant control are more powerful than passive ones. To continue the work, this paper focuses on the synthesis of robustly resonant controllers that guarantee single-mode resonance not only in steady states, but also in transient states when modelling uncertainties happen and working temperature temporally varies. Here the control synthesis is based on the loop shifting and the frequency-domain identification in advance thereof. Frequency-domain identification is performed to modify the mathematical modelling and to identify the most powerful mode, so that the DSP-based feedback controller can online pitch the engine to the most powerful resonant-frequency robustly and accurately. Moreover, this paper develops two control tools, the higher-order van-der-Pol oscillator and the principle of Dynamical Equilibrium, to assist in system identification and feedback synthesis, respectively.
Highlights
Thermoacoustic dynamics can be represented into a feedback-loop interconnected by the heat-transfer dynamics of heating source and the acoustic dynamics of working gas
The heat-flux fluctuation from the heating subsystem initiates acoustic velocity that excites the acoustic motions distributed in the chamber [1,2], and forms the feedback loop
Imposed on those mean-flow conditions which characterize large loop-gains, the thermoacoustic dynamics can become linearly unstable up to limit-cycling, or even up to mean-flow buckling. Such thermoacoustic instability can be utilized for fast-time propulsion in thermoacoustic engines [3,4,5,6], but should be suppressed in combustion chambers to avert a variety of combustion instabilities [7,8,9,10]
Summary
Thermoacoustic dynamics can be represented into a feedback-loop interconnected by the heat-transfer dynamics of heating source and the acoustic dynamics of working gas. The heat-flux fluctuation from the heating subsystem initiates acoustic velocity that excites the acoustic motions distributed in the chamber [1,2], and forms the feedback loop Imposed on those mean-flow conditions which characterize large loop-gains, the thermoacoustic dynamics can become linearly unstable up to limit-cycling (nonlinear vibration), or even up to mean-flow buckling (turbulence, streaming, vortex, etc.). Due to the mean-flow bucking, acoustic motions begin to disappear when the amplitude of acoustic vibration exceeds some level of the mean-flow pressure, and bulk motions of fluid are instead observed This compressible-flow nature limits the power-rating of an individual thermoacoustic engine. The feedback dynamics is to-be-synthesized based on the loop shifting to robustly keep sustained oscillation of thermoacoustic wave at the most powerful resonant-frequency. Therein the Euler discretization transforms the feedback dynamics into an iterated computation of addition and multiplication to utilize the DSP-engine fabricated for fast calculation of addition and multiplication of floating numbers in a dsPIC chip
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