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Effects of Actuator Limits in Bifurcation Control with Applications to Active Control of Fluid Instabilities in Turbomachinery

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Yong Wang

PhD Dissertation, California Institute of Technology, June 2000

Bifurcations are ubiquitous in engineering applications.
Subcritical bifurcations are typically associated with hysteresis
and catastrophic instability inception, while supercritical
bifurcations are usually associated with gradual and more benign
instability inception. With the assumption that the bifurcating
modes are linearly unstabilizable, we give a constructive procedure
of designing feedback laws to change the criticality of bifurcations
from subcritical to supercritical. Algebraic necessary and
sufficient conditions are obtained under which the criticality of a
simple steady-state or Hopf bifurcation can be changed to
supercritical by a smooth feedback. The effects of magnitude
saturation, bandwidth, and rate limits are important issues in
control engineering. We give qualitative estimates of the region of
attraction to the stabilized bifurcating equilibrium/periodic orbits
under these constraints.

We apply the above theoretical results to the Moore-Greitzer model
in active control of rotating stall and surge in gas turbine
engines. Though linear stabilizability can be achieved using
distributed actuation, it limits the practical usefulness due to
considerations of affordability and reliability. On the other hand,
simple but practically promising actuation schemes such as outlet
bleed valves, a couple of air injectors, and magnetic bearings will
make the system loss of linear stabilizability, thus the control
design becomes a challenging task. The above mentioned theory in
bifurcation stabilization can be applied to these cases. We analyze
the effects of magnitude and rate saturations in active control of
rotating stall using bleed valves. Analytic formulas are obtained
for the operability enhancement as a function of system parameters,
noise level, and actuator magnitude and rate limits. The formulas
give good qualitative predictions when compared with experiments.
Our conclusion is that actuator magnitude and rate limits are
serious limiting factors in stall control and must be addressed in
practical implementation to the aircraft engines.

PhD Dissertation
(PDF, 3725K, 255 pages)

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