Real-time feedback control of flow-induced cavity tones—Part 2: Adaptive control

An adaptive generalized predictive control (GPC) algorithm was formulated and applied to the cavity flow-tone problem. The algorithm employs gradient descent to update the GPC coefficients at each time step. Past input–output data and an estimate of the open-loop pulse response sequence are all that is needed to implement the algorithm for application at fixed Mach numbers. Transient measurements made during controller adaptation at fixed Mach number revealed that the controller coefficients converged to a steady state in the mean, and this implies that adaptation can be turned off at some point with no degradation in control performance. The control algorithm demonstrated multiple Rossiter mode suppression at fixed Mach numbers of 0.275, 0.32, and 0.38, provided the plant model was updated for each Mach number. However, as in the case of fixed-gain GPC, the adaptive GPC was limited by spillover in sidebands around the suppressed Rossiter modes. The algorithm was also able to maintain suppression of multiple cavity tones as the freestream Mach number was varied over a modest range (0.275–0.29). Beyond this range, stable operation of the control algorithm was not possible due to the fixed plant model in the algorithm.