Suppressing breathing oscillations in Hall thrusters by superimposing a compensation voltage on the anode power-supply circuit generally requires discharge-current response data corresponding to the applied voltage. However, such response data are costly to obtain, and a limited number of experimental current waveforms are insufficient for direct controller training and validation. To enable controller training and offline evaluation under limited response data, this paper develops a breathing-oscillation suppression method that combines an experimentally constrained two-zone zero-dimensional (0D) model with fast-slow hierarchical active control.
The two-zone 0D model is used to describe the dominant coupling among neutral replenishment, ionization, electron transport, wall-related losses, and discharge-current formation. Its parameters are constrained by experimental current features, including the dominant frequency, mean current, AC root-mean-square value, band energy, and cycle-shape characteristics associated with the rise and recovery stages. The experimental dataset contains 17 discharge-current waveforms covering nine power conditions. After parameter identification and waveform screening, 13 representative experimental parameter anchors are retained. Constrained domain randomization around these anchors generates 795 training samples while maintaining the experimental feature constraints. A local secondary-path model consisting of an equivalent gain, a first-order response, and a pure delay is further introduced to describe the discharge-current increment induced by the compensation voltage and to construct training samples containing control responses.
The controller adopts a fast-slow hierarchical structure. The fast loop employs an in-phase/quadrature filtered-x least-mean-square (I/Q-FXLMS) scheme to generate zero-mean AC compensation while accounting for the secondary-path dynamics. The slow loop uses an echo state network (ESN) to extract the oscillation state from recent discharge-current measurements and a soft actor-critic (SAC) policy to adjust the starting phase, duration, and strength of the compensation. This structure separates high-frequency compensation generation from the slower adjustment of the compensation window and intensity.
Final offline evaluation directly uses experimentally measured uncontrolled discharge-current waveforms as baseline signals. For the representative 3.5 kW condition, the controlled-to-uncontrolled ratios of the peak-to-peak current, AC root-mean-square current, and band energy are 0.580, 0.546, and 0.295, respectively. For the 13.5 kW condition, the corresponding ratios are 0.616, 0.557, and 0.307. In both cases, the spectral peaks near the dominant breathing-oscillation frequency are reduced, and the average operating point remains nearly unchanged. To further evaluate the influence of secondary-path mismatch, 323 representative response tests and 1275 full-factor tests are performed. With fixed nominal parameters, the joint pass rate in the 323 representative tests is 57.28%; after gain-and-delay correction and synchronous updating of the three secondary-path parameters, it increases to 99.07% and 99.69%, respectively, and reaches 100% when the predefined backup parameter set is enabled. In the 1275 full-factor tests, the joint pass rate is 99.76%. Only three cases fail to meet the prescribed 0.8 threshold at the combined boundary where the equivalent gain reaches 1.20 times its nominal value and the response time constant decreases to 0.70 times its nominal value.
These results show that the experimentally constrained 0D model and constrained parameter generalization can provide physically bounded samples for controller training, while the hierarchical control structure can suppress breathing-related current fluctuations under multiple operating conditions. The offline evaluation also demonstrates the sensitivity of the control performance to local voltage-current response mismatch and identifies its finite applicability boundary, thereby providing a methodological basis for subsequent closed-loop Hall-thruster experiments.