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

{{HTDB paper
| authors = Yong Wang
| title = Effects of Actuator Limits in Bifurcation Control with Applications to Active Control of Fluid Instabilities in Turbomachinery
| source = PhD Dissertation, California Institute of Technology, June 2000
| year = 
| type = PhD Dissertation
| funding = AFOSR
| url = http://www.cds.caltech.edu/~murray/preprints/yw00-phd.pdf
| abstract = 
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.
<p>
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.
<p>

| flags = 
| tag = yw00-phd
| id = 2000
}}