# Bifurcation Control of Rotating Stall with Actuator Magnitude and Rate Limits

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### Yong Wang, Simon Yeung, Richard Murray

*Automatica* 38(4):597-610 and 611-625

Nonlinear qualitative analysis is performed on the Moore-Greitzer

model to evaluate the tradeoff of fluid noise, actuator magnitude saturation, bandwidth, rate limits, and the shape of compressor characteristics in active control of rotating stall in axial compressors with bleed valve actuators. Model order reduction is achieved by approximating the dynamics on the invariant manifold that captures the bifurcations and instabilities. Bifurcations and qualitative dynamics are obtained by analyzing the reduced system. The operability enhancement is defined as the extension of operating range for which fully developed rotating stall is avoided. Analytic formulas are derived for the operability enhancement as a function of noise level, actuator saturation limits, and the shape of the compressor characteristic, which is the major nonlinearity in the model. The shape of the compressor characteristic, especially the unstable part, is critical to the rate required for robust operability near the peak for the closed loop system. Experiments are carried out on a single-stage low-speed axial compressor using different level of steady air injections to generate different compressor characteristics. The theoretical formulas give good qualitative estimates to experimental data and simulations using a high fidelity model (37 states).

- Preprint (parts I & II): http://www.cds.caltech.edu/~murray/preprints/wym99-automatica.pdf
- Project(s): Template:HTDB funding::AFOSR