Slope seeking and application to compressor instability control

This work introduces slope seeking, a new idea for non-model based adaptive control. It involves driving the output of a plant to a value corresponding to a commanded slope of its reference-to-output map. To achieve this objective, we introduce a slope reference input into a sinusoidal perturbation-based extremum seeking scheme; derive a stability test for single parameter slope seeking, and then develop a systematic design algorithm based on standard linear SISO control methods to satisfy the stability test. We then extend the results to the multi variable case of gradient seeking. Finally, we illustrate near-optimal compressor operation under slope seeking feedback through a simulation study upon the well-known Moore-Greitzer model of compressor instability.