An overview of fuzzy modeling for control

Babuška, Robert; Verbruggen, H.B.

doi:10.1016/0967-0661(96)00175-x

Cited by 253 publications

(103 citation statements)

References 29 publications

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“…These simulations could be improved. Babuska and Verbruggen (1996;Chandramohan and Kamalakkannan, 2014;Hussein and Nordin, 2014;Kareem, et al, 2014;Kahtan et al, 2014;Sridharan and Chitra, 2014) mentioned that modeling of complex systems will always remain an interactive approach. Thus, future study could consider the usage of other software packages or programming languages and incorporate graphic interface.…”

Section: Resultsmentioning

confidence: 99%

Estimated and Analysis of the Relationship Between the Endogenous and Exogenous Variables Using Fuzzy Semi-Parametric Sample Selection Model

MuhamadSafiih¹,

Kamil²,

Osman³

2014

American Journal of Applied Sciences

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An important progress within the last decade in the development of the selectivity model approach to overcome the inconsistent results if the distributional assumptions of the errors terms are made this problem is through the use of semi-parametric method. However, the uncertainties and ambiguities exist in the models, particularly the relationship between the endogenous and exogenous variables. A new framework of the relationship between the endogenous and exogenous variables of semi-parametric sample selection model using the concept of fuzzy modelling is introduced. Through this approach, a flexible fuzzy concept hybrid with the semi-parametric sample selection models known as Fuzzy Semi-Parametric Sample Selection Model (FSPSSM). The elements of vagueness and uncertainty in the models are represented in the model construction, as a way of increasing the available information to produce a more accurate model. This led to the development of the convergence theorem presented in the form of triangular fuzzy numbers to be used in the model. Besides that, proofs of the theorems are presented. An algorithm using the concept of fuzzy modelling is developed. The effectiveness of the estimators for this model is investigated. Monte Carlo simulation revealed that consistency depends on bandwidth parameter. When bandwidth parameters, c are increased from 0.1, 0.5, 0.75 and 1 as the numbers of N increased (from 100 to 200 and increased to 500), the values of mean approaches (closed to) the real parameter. Through the bandwidth parameter also reveals that the estimated parameter is efficient, i.e., the S.D, MSE and RMSE values become smaller as N increased. In particular, the estimated parameter becomes consistent and efficient as the bandwidth parameters approaches to infinity, c→∞ as the number of observations, n tend to infinity, n→∞.

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Section: Resultsmentioning

confidence: 99%

Estimated and Analysis of the Relationship Between the Endogenous and Exogenous Variables Using Fuzzy Semi-Parametric Sample Selection Model

MuhamadSafiih¹,

Kamil²,

Osman³

2014

American Journal of Applied Sciences

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“…In general however, the inversion of nonlinear models is more involved and analytical solutions may not exist such that solutions have to be found numerically. In the case of local linear networks, the linearity can be exploited directly and an analytical solution can be obtained (Babuška and Verbruggen, 1996;Sousa et al, 1997;Xie and Rad, 2000). Following the local model approach, a separate inversion of each local linear model is performed.…”

Section: Internal Model Control Designmentioning

confidence: 99%

“…For that matter, various approaches have been proposed (Babuška and Verbruggen, 1996) which compute nonlinear dynamic models from inputoutput measurement data, e.g., fuzzy clustering, tree construction algorithms, or neuro-fuzzy approaches. In this paper, the LOLIMOT (local linear model tree) algorithm (Nelles, 2000) is applied for nonlinear model identification.…”

Section: Local Linear Neuro-fuzzy Modelsmentioning

confidence: 99%

“…On the one hand, their transparent architecture allows the combination of prior knowledge about the process with measured identification data. On the other hand, classical linear control design methods can be utilized for nonlinear controller design (Babuška and Verbruggen, 1996;Hunt and Johansen, 1997). For the IMC approach, this local linearity can be exploited directly and a nonlinear gain-scheduled controller can be obtained.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Internal Model Control for Miso Systems Based on Local Linear Neuro-Fuzzy Models

Fink

Nelles

Isermann

2002

IFAC Proceedings Volumes

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The internal model control (IMC) scheme has been widely applied in the field of process control. So far, IMC has been mainly applied to linear processes. This paper discusses the extension of the IMC scheme to nonlinear processes based on local linear models where the properties of linear design procedures can be exploited. The IMC scheme results in controllers that are comparable to gain-scheduled PI or PID controllers which are the standard controllers in process industry. In practice, the tuning of conventional PI or PID controllers can be very time-consuming whereas the IMC design procedure is very simple and reliable. In this paper, the design effort of the IMC and conventional controller design methods will be discussed and control results will be compared by application to nonlinear control of an industrial-scale heat exchanger.

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“…3. Other m.f.s distributions can modify in a desired way the B-FC nonlinearities (Babuška and Verbruggen, 1996). The inference engine in B-FC employs Mamdani's MAX-MIN compositional rule of inference assisted by the rule base in Table 1, and the centre of gravity method for singletons is used for defuzzification.…”

Section: A Class Of Mamdani Fuzzy Controllers With Dynamicsmentioning

confidence: 99%

Stability Analysis of Fuzzy Control Systems. Multivariable Point of View

Precup

Preitl

2005

IFAC Proceedings Volumes

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The paper proposes a new global stability analysis method dedicated to fuzzy control systems containing Mamdani fuzzy controllers with dynamics to control SISO linear / linearized plants. The method is expressed in terms of relatively simple steps based on the generalization of the describing function method to the MIMO case and on the application of the least squares method to approximate the describing functions. The method is applied to the stability analysis of a class of PI-fuzzy controlled servo systems and validated by a case study.

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An overview of fuzzy modeling for control

Cited by 253 publications

References 29 publications

Estimated and Analysis of the Relationship Between the Endogenous and Exogenous Variables Using Fuzzy Semi-Parametric Sample Selection Model

Estimated and Analysis of the Relationship Between the Endogenous and Exogenous Variables Using Fuzzy Semi-Parametric Sample Selection Model

Nonlinear Internal Model Control for Miso Systems Based on Local Linear Neuro-Fuzzy Models

Stability Analysis of Fuzzy Control Systems. Multivariable Point of View

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