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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, 2002

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).

Note: this paper appeared in two parts in *Automatica*:

- Part I (Wang, Murray): Model reduction and qualitative dynamics
(pp. 597-610)
- Part II (Wang, Yeung, Murray): control synthesis and comparison with experiments
(pp. 611-625)

Preprint (parts I & II) (PDF, 1.6M, 42 pages)

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Richard Murray
(murray@cds. caltech.edu)