M-MRAC for nonlinear systems with bounded disturbances

Abstract

Abstract-This paper presents design and performance analysis of a modified reference model MRAC (M-MRAC) architecture for a class of multi-input multi-output uncertain nonlinear systems in the presence of bounded disturbances. M-MRAC incorporates an error feedback in the reference model definition, which allows for fast adaptation without generating high frequency oscillations in the control signal, which closely follows the certainty equivalent control signal. The benefits of the method are demonstrated via a simulation example of an aircraft's wing rock motion.

Certainty equivalence M-MRAC for systems with unmatched uncertainties

“…Then, it can be concluded from equation (16) that c determines the damping and γ determines the frequency of the signalη i (t). It follows from the results of [5], that choosing c ≥ 2 √ δ 1 γ damps the oscillations inη(t) and guarantees the bound…”

“…Lemma 3.4: Let the estimatesx(t) andη(t) be generated by the identification model (4) and (5). In addition, let x(t) and u(t) be bounded.…”

“…The approach is based on the identification scheme, which is completely separated from the control design. To enable a fast adaptation without generating high frequency oscillations in the adaptive signals, it employs an error feedback term, like in the modified reference model MRAC (M-MRAC) architecture introduced in [5]. It is shown that the state prediction error converges to zero independent of the control design.…”

Indirect M-MRAC for systems with time varying parameters and bounded disturbances

“…Since E(t) L∞ = a 0 − λ 0 , we obtain 1 − γ ψ 2 (t) L1 E(t) L∞ = 2λ 0 a −1 0 . Then, according to [8], it follows from the expression (24) that…”

“…An alternative method, which guarantees desired transient behavior of the closed-loop system, has been proposed in [8]. It is based on the modification of the reference model by the tracking error feedback, and is called modified reference model MRAC (M-MRAC).…”