Stall events in axial compressor systems have been a limiting factor for efficiency of such systems and a source of safety concerns. The detection of the onset of stall, and in many cases the precursor of the onset of stall, have been of interest in the axial compressor community for many decades. As such, development of algorithms along with active control could lower cost, reduce emissions, improve safety, and increase market competitiveness. To gain an understanding of these stall phenomena, past and current research has focused on modeling axial compressors as dynamic systems, with a focus on obtaining descriptive formulations of the physical aspects of stall. Some of these approaches allow for active control measures that extend the stall margin of the compressor system to increase safety and efficacy. This paper reviews the major contributions in these listed pursuits and presents the latest methods and algorithms for stall precursor detection in low-speed axial compressors. In particular, a review is presented in the types and characteristics of stalls, the major mathematical models used to describe these systems, influences of physical attributes such as tip clearance, guide vanes, and groove casing—operating as passive control elements—but also active control utilities such as air injection are discussed along with a detailed review of existing stall precursor detection algorithms. In addition, a forward-looking projection is presented that includes the use of machine learning algorithms to further the understanding and the capability of stall precursor detection.

An approach for model-based reinforcement learning (MBRL) gets presented utilizing system identification and fuzzy reward formulation. Minimum order estimation gets applied first to determine the system order. This aids transfer function approximation of the linear time-invariant system. A Mamdani fuzzy inference mechanism defines the reward signal. The model obtained integrates into the Q-learning process to simulate experiences bypassing the environment. The proposed framework showcases sample-efficient learning without interacting with the true system. The applicability currently limits to linear systems. Extending the techniques to nonlinear, time-varying dynamics could increase applicability to real-world systems. This paper contributes an initial demonstration of MBRL using simple dynamics approximation and fuzzy rewards. Performance analysis provides evidence of learning improvement without explicitly communicating with the actual plant. A reduction in steady state error and settling time gets achieved.

Safe and sample-conscious controller synthesis for nonlinear dynamics benefits from reinforcement learning that exploits an explicit plant model. A nonlinear mass–spring–damper with hardening effects and hard stops is studied, and off-plant Q-learning is enabled using two data-driven surrogates: (i) a piecewise linear model assembled from operating region transfer function estimates and blended by triangular memberships and (ii) a global nonlinear autoregressive model with exogenous input constructed from past inputs and outputs. In unit step reference tracking on the true plant, the piecewise linear route yields lower error and reduced steady-state bias (MAE = $0.03$; SSE = $3\%$) compared with the NLARX route (MAE = $0.31$; SSE = $30\%$) in the reported configuration. The improved regulation is obtained at a higher identification cost (60,000 samples versus 12,000 samples), reflecting a fidelity–knowledge–data trade-off between localized linearization and global nonlinear regression. All reported performance metrics correspond to deterministic validation runs using fixed surrogate models and trained policies and are intended to support methodological comparison rather than statistical performance characterization. These results indicate that model-based Q-learning with identified surrogates enables off-plant policy training while containing experimental risk and that performance depends on modeling choices, state discretization, and reward shaping.

Safe and sample-conscious controller synthesis for nonlinear dynamics benefits from reinforcement learning that exploits a model of the plant. A nonlinear mass–spring–damper with hardening effects and hard stops is considered. Two data-driven models are employed to enable off-plant training: a piecewise linear model assembled from operating-region linear descriptions and blended by triangular memberships, and a global nonlinear autoregressive model with exogenous input constructed from past inputs and outputs. Q-learning is performed with the model in the loop using an error-indexed discrete state space, a finite force alphabet, and a reward that balances absolute tracking error with its short-horizon decrease. When the trained agents are deployed on the true plant for reference tracking, the piecewise linear model tends to yield tighter regulation near the setpoint and reduced steady-state bias, while the nonlinear autoregressive route requires less prior structural knowledge and a simpler data-collection campaign, at the cost of larger residual error in the tested scenario. These findings indicate that model-based Q-learning with data-driven models enables off-plant policy learning while containing experimental risk. Observed performance reflects a trade-off between fidelity obtained from localized linearization and generality afforded by global nonlinear regression, as well as design choices in state discretization and reward shaping. Prospective improvements include adaptive membership shaping, richer regressors, and limited on-plant refinement to reduce model–plant mismatch.