Geometric approach to analysis and synthesis of system zeros Part 1. Square systems

Kouvaritakis,; Macfarlane,

doi:10.1080/00207177608922149

Cited by 153 publications

(25 citation statements)

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“…The transmission zeros and zero directions can be obtained from one of the above eigenvalue problems. The results show a certain analogy to those obtained by Kouvaritakis and MacFarlane (1976) …”

Section: Remarks On Theoremsupporting

confidence: 86%

On transmission zeros and zero directions of multivariable time-invariant linear systems with input-derivative control

Al-Nasr

Lovass‐Nagy

Powers

1981

International Journal of Control

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Section: Remarks On Theoremsupporting

confidence: 86%

On transmission zeros and zero directions of multivariable time-invariant linear systems with input-derivative control

Al-Nasr

Lovass‐Nagy

Powers

1981

International Journal of Control

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“…Reference [20] gave the inequality (23) for a square system, suggesting that X be obtained by solving this LMI numerically. However, it was shown in Reference [23] that for a square system, the eigenvalues of N AM are the transmission zeros of the system and the annihilators N and M can be always be selected such that NM = I. Given a square system with only stable transmission zeros, this selection reduces (23) to a Lyapunov equation where the matrix N AM is stable, and the existence of X > 0 satisfying this inequality is guaranteed.…”

Section: Finding Lmentioning

confidence: 99%

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Wiese¹,

Annaswamy²,

Muse³

et al. 2015

Journal of Guidance, Control, and Dynamics

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This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated.The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the KalmanYakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller.A numerical example based on a 6 degree-of-freedom nonlinear, scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The adaptive output feedback controller is applied to result in stable tracking of uncertainties that destabilize the baseline linear output feedback controller.

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“…Since the plant (2.1) is controllable and observable, p(s) corresponds to the pole polynomial of the plant (Kouvaritakis andKarcanias 1976). Further, we introduce a parallel feedforward compensator matrix F(s) as shown in Fig.…”

Section: Xm(t)t Um(t)t]t K(t) = [Kc(t) Kat) Ku(t)]mentioning

confidence: 99%

Realization of simple adaptive control by using parallel feedforward compensator

Iwai

Mizumoto

1994

International Journal of Control

130

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A problem is dealt with concerning a practical design scheme for a multi-input! multi-output simple adaptive control (SAC) system. The SAC method which was first derived as a sort of the direct model following adaptive control based on the command generator tracker (CGT) technique was fundamentally applicable to plants satisfying the so-called almost strictly positive real (ASPR) condition. However, the method can be applied to non-ASPR plants by using a parallel feedforward compensator (PFC), which makes the augmented plant including PFC be ASPR. Such a technique was proposed by Bar-Kana for plants satisfying the output feedback stabilizable condition. As an extension, the authors have proposed a simple and concrete PFC design procedure for SISO non-ASPR plants. The special feature of this proposal is that the method can be applicable to non-ASPR plants as the minimum phase system. The main aim of the paper is to give a practical design procedure of PFC for MIMO plants as a natural extension of the SISO case, so that an actual realization of MIMO SAC can be attained for a broad class of MIMO plants. The effectiveness of the proposed method is also confirmed through numerical simulations.

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Geometric approach to analysis and synthesis of system zeros Part 1. Square systems

Cited by 153 publications

References 0 publications

On transmission zeros and zero directions of multivariable time-invariant linear systems with input-derivative control

On transmission zeros and zero directions of multivariable time-invariant linear systems with input-derivative control

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Realization of simple adaptive control by using parallel feedforward compensator

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