On stable right-inversion of non-minimum-phase systems

Elobaid, Mohamed; Mattioni, Mattia; Monaco, Salvatore; Normand‐Cyrot, D.

doi:10.1109/cdc42340.2020.9303851

Cited by 1 publication

(2 citation statements)

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“…Note that, these properties are not achievable if the underlying system is nonminimum phase. Furthermore, unlike minimum phase systems, for non-minimum phase systems there are many fundamental limitations associated with: 1) the achievable closed loop transfer matrix [7], 2) the achievable closed loop gain margin [8], 3) the achievable perfect tracking [9] 4) the LQG loop transfer recovery [10,11], 5) the sensitivity or complementary sensitivity minimization [12,13], 6) the model reference adaptive control [8], 7) the stable inverse [14], and so on. It should be mentioned that the aforementioned characteristics are not totally the same for all non-minimum phase systems; for example, some non-minimum phase systems behave "almost as good as" minimum phase ones, whereas some others which are indeed "almost impossible" to control.…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of unstable zeros and in the case of right invertiblity, perfect tracking of any reference signal becomes possible, i.e., the L 2 norm of the tracking error can be made arbitrarily small. However, in the presence of unstable zeros (non-minimum phase or open right half plane (RHP) zeros), the tracking error increases as the signal frequencies tend to those of the unstable zeros [22,27], see also [14]. For the problem of tracking any reference signal generated by a known exo-system, [28] proved that the smallest achievable L 2 norm of the tracking error equals the least amount of control energy needed to stabilize the zero dynamics of the error system [8,15].…”

Section: Introductionmentioning

confidence: 99%

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Minimum phase Properties Based on High-Gain Output Feedback Stability Analysis

Foghahaayee

Menhaj

2023

Preprint

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In this paper, a new definition of the minimum phase property based on high gain output feedback stability (HGS) is introduced. The minimum phase systems with respect to this definition have stable inverses leading to no performance limitations. In other words, the minimum norm of regulation or tracking error for these systems approaches zero. This set of minimum phase linear systems includes systems with stable zeros (i.e., the zeros with negative real parts and/or simple imaginary zeros); however, the usual definition of minimum phase systems considers only systems with zeros located in the open left half plane (LHP). The difficulty of minimum phase determination in nonlinear systems highlights better the main objective of the paper to look for a way to modify the minimum phase concept in some extent to obtain more feasible conditions, which can be applied to a larger class of systems. It should be noted that based on this new definition, the minimum phase determination can be easily checked out through stability analysis of the closed loop system. Furthermore, knowing the fact that both performance limitation and stable inverse criteria can be potentially extended to nonlinear systems, this paper employs these concepts to reflect better the strength of the proposed minimum phase property. Finally, we apply the proposed method to two nonlinear systems. The simulation results easily approve the effectiveness of the method developed fully in the paper.

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