The Best Achievable<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>ℋ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>Tracking Performances for SIMO Feedback Control Systems

Hara, Shinji; Bakhtiar, Toni; Kanno, Masaaki

doi:10.1155/2007/93904

Cited by 15 publications

(8 citation statements)

References 15 publications

(24 reference statements)

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“…The results in [5] show that not only non-minimum phase zeros and unstable poles affect the optimal performance, but also the total variation of the plant direction with frequency. Similar results are presented in [6], where closed form expressions are derived for discrete time SIMO systems, and an unify view of both continuous and discrete-time results is discussed. The results in [5], [6] assume that the reference vector lies in the subspace spanned This work was supported by grants Anillo ACT53, FONDECYT 1100692, and CONICYT through the Advanced Human Capital Program.…”

Section: Introductionsupporting

confidence: 59%

“…Performance bounds in control systems have been the subject of much interest in the literature, and significant results have been obtained (see, e.g, [1], [2], [3], [4], [5], [6], and the references therein). The main contribution of these works is the development of closed form expressions for the best achievable performance, when a feedback control system is considered.…”

Section: Introductionmentioning

confidence: 99%

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Optimal tracking performance for unstable tall plant models

Valenzuela

Salgado

Silva

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

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This article focuses on the best achievable tracking performance of unstable tall plant models. The work is presented for discrete time, LTI systems, when an exponentially decaying signal is considered as reference. Closed form expressions for the best tracking performance for one and two degree of freedom control architectures are presented. As an application of those results, they are used in an example to compute the performance gains in the control of originally tall systems which have been squared-up by adding control input channels.Index Terms-Performance bounds, two degree of freedom control, augmented systems, optimal control, multivariable control.

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Section: Introductionsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Optimal tracking performance for unstable tall plant models

Valenzuela

Salgado

Silva

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

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“…Note that

f (1) = \frac{{(1 - p)}^{2}}{ε}

. In addition, one calculates

\begin{matrix} \inf_{Q \in {scriptR scriptℋ}_{\infty}} {(∥∥, \frac{W_{1}}{z - 1})}_{2}^{2} + {(∥∥, \frac{W_{2}}{z - 1})}_{2}^{2} \\ = \frac{- ε}{2 π} \int_{- π}^{+ π} \frac{\frac{ε}{{(1 - p)}^{2}} Re {f} - 1}{1 - \cos ω} normald ω . \end{matrix}

Applying the lemma 1 from yields that

\frac{1}{2 π} \int_{- π}^{+ π} \frac{\frac{ε}{{(1 - p)}^{2}} Re {f} - 1}{1 - \cos ω} d ω = \frac{ε}{{(1 - p)}^{2}} f^{'} (1) .

Hence, by invoking lemma 2 in , one has

\begin{matrix} \frac{ε}{{(1 - p)}^{2}} f^{'} (1) & = \frac{1}{2 π} \int_{- π}^{+ π} \log |\frac{ε}{{(1 - p)}^{2}} f (e^{jω})| \\ \times \frac{d ω}{1 - \cos ω} . \end{matrix}

…”

Section: Lower Bound Of Tracking Performancementioning

confidence: 95%

Tracking Performance Bound with Finite Control Energy and Erasure Channel Energy Constraint

Wang¹,

Zhang²,

Guan³

et al. 2015

Asian Journal of Control

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This paper studies the tracking performance of the single-input single-output (SISO), finite dimensional, linear and time-invariant (LTI) system under the channel input energy constraint over the Erasure channel. A new performance index is proposed which is minimized over all two-degree-of-freedom stabilizing controllers. The explicit expressions of the lower bound of the performance index and the minimum of the signal-to-noise ratio are obtained. The results show that the performance bound is correlated to unstable poles, non-minimum phase zeros and the packet loss probability.Finally, examples are given to validate the conclusions derived.

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“…This is because the underlying continuous domain descriptions cannot be obtained by setting sampling period to zero in the discrete domain approximations. In optimal tracking error control problem, for instance, contribution of nonminimum phase zeros for continuous and discrete-time systems are provided in completely different ways, see [3,7]. The delta operator has often been proven entailing many advantages in connecting discrete-time and continuoustime systems, such as control synthesis [4], control design [5], estimation [9] and filtering [11].…”

Section: Introductionmentioning

confidence: 99%

Mobius and Delta Transforms in the Unification of Continuous-Discrete Spaces

Bakhtiar

Samsurizal

Nuralaitiningtyas

2013

JMA

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It is well-known that in control theory the stability region of continuous- time system is laid in the left half plane of complex space, while that of discrete-time system is dwelled inside a unit circle. The former fact might be shown by exploiting the Laplace transform and the later by utilizing the corresponding zeta transform. In this paper we revealed the connectivity of both regions by employing M¨obius transform. We also used the same transform to derive continuous/discrete-time counterpart of several existing results, including Bode integral and Poisson-Jensen formula. We then demonstrated their uniﬁcation property by using delta transform. Some numerical examples were provided to verify our results.

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The Best Achievableℋ2Tracking Performances for SIMO Feedback Control Systems

Cited by 15 publications

References 15 publications

Optimal tracking performance for unstable tall plant models

Optimal tracking performance for unstable tall plant models

Tracking Performance Bound with Finite Control Energy and Erasure Channel Energy Constraint

Mobius and Delta Transforms in the Unification of Continuous-Discrete Spaces

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