Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Anbumani, K.; Patnaik, L. M.; Sarma, I. G.

doi:10.1109/tac.1981.1102751

Cited by 64 publications

(12 citation statements)

References 2 publications

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“…Consider the system described by (1). The following stacked vector of the unknown input, v k , is introduced [11]:…”

Section: Parity Equationsmentioning

confidence: 99%

“…Block oriented models have been used for modelling such phenomena as for instance: infant EEG seizures [4], a radio frequency amplifier [5], a glucose-insulin process in diabetes type I patient [3], ionospheric dynamics [12] or human operator dynamics [19]. Furthermore, such models are also used for control purposes [1,6,7] and fault detection [9,10]. This paper deals with the problem of unknown/unmeasur-able input reconstruction for Hammerstein-Wiener systems, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive unknown input reconstruction scheme for Hammerstein-Wiener systems

Sumisławska

Burnham

2014

2014 UKACC International Conference on Control (CONTROL)

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In this paper an adaptive time-varying filter for unknown/unmeasurable input reconstruction is proposed. The algorithm is based on parityequations and is applicable to Hammerstein-Wiener systems, i.e. systems composed of a linear dynamic part followed and preceded by a memoryless nonlinearity. An error-in-variables case is considered, i.e. known input and output signals are both subjected to measurement uncertainties. The scheme forms an extension to a filter previously proposed by the authors. As the input reconstruction involves transformation of noisy signals through memoryless static functions, measurement noise is either amplified or reduced, depending on the gradient of the nonlinear function. Thus, in the proposed scheme the bandwidth of the filter is adjusted depending on the operating point allowing for a trade-off between noise attenuation and a phase lag.

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“…Consider the system described by (1). The following stacked vector of the unknown input, v k , is introduced [11]:…”

Section: Parity Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive unknown input reconstruction scheme for Hammerstein-Wiener systems

Sumisławska

Burnham

2014

2014 UKACC International Conference on Control (CONTROL)

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“…Model based control for the Hammerstein system has been well studied (Anbumani, Patnaik, and Sarma 1981;Bloemen, van den Boom, and Verbruggen 2000;Bloemen et al 2001). A popular treatment of handling the Hammerstein model is to remove the nonlinearity via an inversion (Fruzzetti, Palazoglu, and Mcdonald 1997;Patwardhan, Lakshminarayanan, and Shah 1998;Bloemen et al 2000).…”

Section: Introductionmentioning

confidence: 99%

“…Different nonlinear model representations result in variations in controller design algorithms. For example, in Anbumani et al (1981) and Zhu, Warwick, and Douce (1991) the nonlinear static function is based on an explicit polynomial function of the input. The optimal control law satisfies a polynomial equation of the input, which is then found via root solving.…”

Section: Introductionmentioning

confidence: 99%

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

Hong

Mitchell

Chen

2012

International Journal of Systems Science

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In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach. . For example, it is a suitable model for signal processing applications involving any nonlinear distortion followed by a linear filter, the modelling of the human heart in order to regulate the heart rate during treadmill exercises (Su 2007), and the modelling of hydraulic actuator friction dynamics (Kwak, Yagle, and Levitt 1998). The Hammerstein model has been widely researched (Billings and Fakhouri 1979;Stoica and So¨derstro¨m 1982;Greblicki and Pawlak 1986;Greblicki 1989Greblicki , 2002Verhaegen and Westwick 1996;Lang 1997;Bai and Fu 2002;Chen 2004;Chaoui, Giri, Rochdi, Haloua, and Naitali 2005). The model characterisation/representation of the unknown nonlinear static function is fundamental to the identification of Hammerstein model. Various approaches have been developed in order to capture the a priori unknown nonlinearity by use of both parametric (Verhaegen and

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“…Model based control for the Hammerstein system has been well studied [1,3,4]. The implementation of model based control for an a priori unknown Hammerstein model requires system identification including modelling and identification of the nonlinear static function.…”

Section: Introductionmentioning

confidence: 99%

B-Spline Neural Networks Based PID Controller for Hammerstein Systems

Hong

İplikçi

Chen

et al. 2012

Communications in Computer and Information Science

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Abstract. A new PID tuning and controller approach is introduced forHammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches.

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Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Cited by 64 publications

References 2 publications

Adaptive unknown input reconstruction scheme for Hammerstein-Wiener systems

Adaptive unknown input reconstruction scheme for Hammerstein-Wiener systems

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

B-Spline Neural Networks Based PID Controller for Hammerstein Systems

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