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

Abstract

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.

Switching-based Adaptive Output Regulation for Uncertain Systems Affected by a Periodic Disturbance

“…It is worth noting that the main difference between ( 19) and ( 26) lies in the coefficient of ξ 1 2 , where θσ is replaced with θη . Consequently, negattive semi-definiteness of Vβ can be ensured by the condition (24) and suitable selections of α, ε and μ of the form ε ∈ (0, ε * ), α ∈ (0, α ε), μ ∈ (0, µ ε) with ε * is given by (20) and…”

“…However, issues related to asymptotic stability and the problem of non-singularity of the control law were not fully addressed. An alternative approach known as Adaptive Harmonic Steady-state Control (AHSC) was developed in [18], [20], which assume that the plant model is in steady-state and neglect the dynamic interaction between the plant dynamics and the particular AFC algorithm employed. Under the assumption that frequency of disturbance is known, recent works [12] [21] have proposed a multiple-model adaptive control scheme and a state-normestimator-based switching strategy, respectively, that indeed remove the necessity of SPR-like conditions.…”

Removing SPR-Like Conditions in Adaptive Feedforward Control of Uncertain Systems

“…Therein, the analysis assumed that the plant model is in steady-state, hence the dynamic interaction between the AFC algorithm and the plant dynamics was neglected. The same type of assumption was made for the adaptive solution proposed in [16]. Robustness with respect to unstructured dynamic uncertainty acting on a known nominal plant model was considered in [17], [18].…”