Adaptive harmonic steady-state control for rejection of sinusoidal disturbances acting on a completely unknown system

This paper presents an adaptive harmonic steady-state (AHSS) controller that addresses the problem of rejecting sinusoids with known frequencies that act on a completely unknown asymptotically stable linear time-invariant system. We analyze the stability and closed-loop performance of AHSS for multi-input multi-output systems that are square (ie, the number of controls equals the number of performance measurements). In this case, we show that AHSS asymptotically rejects disturbances, that is, the performance measurement tends to 0. We also present a numerical study of the steady-state and transient performance of AHSS for square and nonsquare systems.