A new approach for nonlinear process identification using orthonormal bases and ordinal splines

Macarthur, J. W.

doi:10.1016/j.jprocont.2011.12.011

Cited by 20 publications

(8 citation statements)

References 30 publications

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“…By considering the constraints mentioned in (19) and (20), Equation (23a) should be solved as a constrained quadratic problem. Considering 𝜗 T 𝜗 as the goal function in the minimisation problem, in many practical cases, the elements of vector 𝜗 become less than the constraints mentioned in (21).…”

Section: Lemma 1 Consider the Vectors 𝛼 =mentioning

confidence: 99%

“…] ineq f and 𝛽 [. ] ineqg in constraints (19) and (20) do not depend on f ′ and g ′ . Moreover, the acceptable range of set of parameters in f ′ and g ′ should satisfy the above linear inequalities.…”

Section: Pre-known Information About Non-linear Functionsmentioning

confidence: 99%

“…Applying this theorem on the system of linear equations given in Theorem 1 and Theorem 2 (or Proposition 1 and Proposition 2 for MIMO systems) and also the constraints in (19) and (20) will result the identified H-W model. In the following section, the proposed algorithm for identification of H-W model is applied on a PCV as a case study.…”

Section: Theorem 3 Consider the Vectors 𝛼 =mentioning

confidence: 99%

“…For example in [17,18], non-linear functions are approximated by cubic splines and also the least-squares-based iterative technique for special case with two-segment polynomial input block and backlash output block characteristics. Furthermore, there are frequency based methods which consider a combination of sinusoids with a random phase as the system input [19], while some methods use pseudorandom binary sequence (PRBS) signals [20]. Apart from these methods, the identification problem is also solved by using refined instrumental variable method [21], particle swarm optimisation [22], the data filtering-based recursive generalised extended least squares algorithm [23] and maximum likelihood method [24].…”

Section: Introductionmentioning

confidence: 99%

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Hammerstein–Wiener identification of industrial plants: A pressure control valve case study

Esmaeilani

Ghaisari

Bagherzadeh

2020

IET Control Theory & Appl

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Hammerstein-Wiener (H-W) identification problem is investigated under practical considerations for industrial plants. The main consideration in these cases is inability to apply arbitrary input signals. An algorithm is proposed to identify H-W model for industrial systems, in the presence of noise and disturbance. The identification problem is changed into a constrained optimisation problem and is solved by minimising the non-linear functions modelling error. To improve the efficiency of the proposed method, the known information about non-linear functions are used. To make the proposed method applicable for general systems with hard non-linearities, non-linear functions are described by some ordered pairs. A pressure control valve that is used for anti-surge protection of an air compressor in the second refinery of South Pars Gas Complex is considered as the case study to demonstrate the effectiveness of the proposed algorithm. Seventy-five percent of the gathered data during the time is used for identification and the remaining 25% is used for verification of the resulted model. Verification of the obtained H-W model showed that accuracy of the identified model is more than 95%.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Lemma 1 Consider the Vectors 𝛼 =mentioning

confidence: 99%

Section: Pre-known Information About Non-linear Functionsmentioning

confidence: 99%

Section: Theorem 3 Consider the Vectors 𝛼 =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hammerstein–Wiener identification of industrial plants: A pressure control valve case study

Esmaeilani

Ghaisari

Bagherzadeh

2020

IET Control Theory & Appl

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“…), can be applied to different system classes, such as single-input single-output (SISO) systems (Valencia-Palomo and Rossiter, 2012; Wang, 2001, 2004), nonlinear systems (Saghatoleslami and Toroghi, 2011) and multi-input multi-output (MIMO) systems (Efe, 2003; Rossiter and Wang, 2008; Wang et al, 2013). Other researchers have adopted the use of other orthogonal bases in the case of linear time-invariant (LTI) and stable systems (Badwe et al, 2011; Douik et al, 2007; Malti et al, 1998) or in the case of nonlinear systems (Tufa et al, 2011; Ward MacArthur, 2012). For a MIMO system, the developed approach consists in decomposing the MIMO transfer matrix on the generalized orthogonal bases (GOB) (Douik et al, 2007; Ninness et al, 1995).…”

Section: Introductionmentioning

confidence: 99%

Laguerre-based modelling and predictive control of multi-input multi-output systems applied to a communicating two-tank system (CTTS)

Mbarek

Bouzrara

Garna

et al. 2015

Transactions of the Institute of Measurement and Control

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In this paper, a novel method is constructed for model predictive control (MPC) of multi-input multi-output (MIMO) systems. The latter are represented by a discrete-time MIMO ARX model expansion on Laguerre orthonormal bases. The resulting model, entitled the MIMO ARX-Laguerre model, provides a recursive representation with parameter number reduction. This reduction is strongly linked to the choice of Laguerre poles, and therefore we propose a new algorithm to optimize the Laguerre poles of the resulting model. The recursive formulation of the MIMO ARX-Laguerre model is used to obtain the MPC strategy. An ℓ 2 -norm finite moving horizon cost function is used to obtain a control law which is implemented as a quadratic programming (QP) problem. The effectiveness of the proposed controller that takes into account physical constraints is illustrated by a numerical simulation example and by a practical validation on an experimental communicating two-tank system (CTTS).

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Parameters estimation for the Hammerstein‐Wiener models with colored noise based on hybrid signals

Li,

Han

2023

Adaptive Control & Signal

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SummaryA three‐stage estimation approach of the Hammerstein‐Wiener model with colored noise using hybrid signals is considered in this article. The Hammerstein‐Wiener model where a linear dynamic block is embedded between two static nonlinear elements, in which two nonlinear elements represented by two independent neural fuzzy models and a linear element represented by autoregressive exogenous model. The designed hybrid signals that consist of separable signals and random signals are devoted to estimating independently. First, the characteristics of separable signals in the action of the static nonlinear element are analyzed, then the output nonlinear element parameters are estimated utilizing two groups of separable signals with a multiple. Moreover, least squares based on correlation analysis method is applied to estimate linear element using one set of separable signals, which handles the interference of colored process noise. Finally, the recursive extended least squares algorithm is derived to estimate the input nonlinear element and the autoregressive moving average noise model, which improves parameters estimation accuracy owing to estimating colored noise model parameters in recursive estimate process. The feasibility of the presented estimation technique is demonstrated by an illustrative simulation example and a practical nonlinear process.

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A new approach for nonlinear process identification using orthonormal bases and ordinal splines

Cited by 20 publications

References 30 publications

Hammerstein–Wiener identification of industrial plants: A pressure control valve case study

Hammerstein–Wiener identification of industrial plants: A pressure control valve case study

Laguerre-based modelling and predictive control of multi-input multi-output systems applied to a communicating two-tank system (CTTS)

Parameters estimation for the Hammerstein‐Wiener models with colored noise based on hybrid signals

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