Detecting oscillation with Unfalsified Adaptive Control and its application in managed pressure drilling for oil

This paper investigates how to stabilize a SISO and time-invariant unmodeled plant with Unfalsified Adaptive Control when the reference signal is known a prior. A new cost function is constructed with filtered data, while the filter is stable and has the zeros exactly same with the unstable poles of the reference signal. The new cost function has the property called cost-detectability. When used in Unfalsified Adaptive Control for a LTI plant, it guarantees that UAC not only stabilizes the plant, but also detects and prevents bounded oscillations that otherwise would not be detected by the existing standard ℒ₂ gain-related cost function. That is, a controller critically stabilizing the plant will be definitely falsified. This approach is useful in managed pressure drilling for oil and gas to detect and prevent oscillation in response to step commands. Simulations shows it works, even when the plant is nonlinear.