ℒ/sub 1/ controller design for a high-order 5-pool irrigation canal system

Malaterre, Pierre‐Olivier; Khammash, Mustafa

doi:10.1109/cdc.2000.912189

Cited by 6 publications

(3 citation statements)

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“…Such a way, the magnitude of measured output signal is minimized with respect to bounded, yet persistent input disturbances. l 1 optimal controllers have already found an application in some irrigation channel regulation problem, see [24] for instance.…”

Section: Proofmentioning

confidence: 99%

Numerical algorithms for polynomial plus/minus factorization

Hromčík

Šebek

2006

Intl J Robust & Nonlinear

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Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete-time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H 2optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by-product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l 1 optimal controller design example.where p þ ðzÞ has all roots inside and p À ðzÞ outside the unit disc. Clearly, the scalar plus/minus factorization is unique up to a scaling factor.Polynomial plus/minus factorization has many applications in control and signal processing problems. For instance, efficient algebraic design methods for time-optimal controllers [1], quadratically optimal filters for mobile phones [2,3], and l 1 optimal regulators [4], to name just a few, all recall the þ=À factorization as a crucial computational step. EXISTING METHODSIn any case, the plus/minus factors for n55 cannot be achieved by a finite number of algebraic operations. This conclusion is due to the Galois's theorem stating that the roots of a polynomial of degree greater or equal to five cannot be expressed in a closed form. Therefore, all numerical algorithms for plus/minus factorization are iterative in nature and give just an approximation to the genuine factors. Some existing approaches to this problem are mentioned in this section.The most natural way is based on the computation of polynomial roots. Having determined the roots r 1 ; r 2 ; . . . ; r n of pðzÞ via any standard procedure for polynomial roots [5] and considering that pðzÞ=0 for all jzj ¼ 1 by assumption, one can divide the roots into two groups R þ ¼ fr i : m $ ðr i Þ ¼ 0; jr i j51g; R À ¼ fr i : m $ ðr i Þ ¼ 0; jr i j > 1g: Clearly, R þ and R À are the sets of roots of p þ ðzÞ and p À ðzÞ; respectively.Performance of this procedure heavily hinges on the accuracy of the computed polynomial roots. If these roots are distinct and separated enough, standard numerical routines [5] can determine them with good precision. However, it is well known that the relative accuracy of a computed root decreases as its multiplicity grows [5], and so does the accuracy of the spectral factor thus obtained.In addition, if the degree of the involved polynomial is high, say over 50, the very computation of the spectral factor coefficients is problematic due to rounding errors. It means that even if the desired roots of the spectral factor are evaluated with good accuracy, its particular coefficients, which are typically required in applications, are not accurate...

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Section: Proofmentioning

confidence: 99%

Numerical algorithms for polynomial plus/minus factorization

Hromčík

Šebek

2006

Intl J Robust & Nonlinear

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“…Despite of its simple implementation, it does not however take into account the time delay explicitly, and including a Smith predictor makes the control sensitive to modeling errors. In order to better take into account perturbations and modeling errors, robust approaches have been developed ( Malaterre et al [2000], Litrico et al [2006]). A predictive approach has also been investigated in Rodellar et al [1989] or in Bogovich et al [2007].…”

Section: Introductionmentioning

confidence: 99%

A New Nonlinear Control Methodology for Irrigation Canals Based on a Delayed Input Model

Benayache¹,

Besançon²,

Duby

2008

IFAC Proceedings Volumes

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“…From the available approaches, we select the 1 norm optimization concept (Dahleh and Diaz-Bobillo [3]), because the synthesis problem is solved using linear programming, and applications to real process have already been published (Malaterre and Kammash [8]; Tadeo and Grimble [14]; Tadeo et al [16]), albeit for the symmetric case. In Vidyasagar [17] this problem was first formulated.…”

Section: Introductionmentioning

confidence: 99%

Control of systems with asymmetric bounds using linear programming: Application to a hydrogen reformer

Naib

Tadeo

Benzaouia

2006

Mathematical Problems in Engineering

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This paper studies controller design for feedback systems in the presence of asymmetrically bounded signals, using a case study. An asymmetric objective functional is used to consider the asymmetrically bounded signals, which makes possible to derive a linear programming problem. Solving this LP makes possible to design controllers that minimize certain outputs, fulfilling at the same time hard constraints on certain signals. The method is presented by application to a hydrogen reformer, a system in petrochemical plants that produces hydrogen from hydrocarbons: a mixed sensitivity problem is stated and solved, with an additional constraint given by the asymmetric limitations on the magnitude and rate of the control signal, and the asymmetricity in the disturbances.

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ℒ/sub 1/ controller design for a high-order 5-pool irrigation canal system

Cited by 6 publications

References 10 publications

Numerical algorithms for polynomial plus/minus factorization

Numerical algorithms for polynomial plus/minus factorization

A New Nonlinear Control Methodology for Irrigation Canals Based on a Delayed Input Model

Control of systems with asymmetric bounds using linear programming: Application to a hydrogen reformer

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