LS-optimal fuzzy modelling and its application to pneumatic drives

IEEE Trans. Fuzzy Syst.

Bernd²,

Trott

2000

The performance of model-based controller design relies heavily on the quality and suitability of the utilized process model. This contribution proposes a fuzzy network based nonlinear controller design methodology. Fuzzy networks are a model approach combining high approximation quality with high interpretability. The input/output (I/O) models commonly used for identification are transformed to fuzzy state-space models. Transferring and adjusting methods from linear state-space theory a control concept consisting of a fuzzy state controller and an adaptive set-point filter for nonlinear dynamic processes is deduced. The capability of the method is demonstrated for a hydraulic drive.

Section: B Identificationmentioning

confidence: 99%

“…The identification algorithm is only sketched as it has been described in detail elsewhere (e.g., [17], [20]). …”

Section: Dynamical Fuzzy I/o Modelsmentioning

confidence: 99%

Fuzzy network model-based fuzzy state controller design

IEEE Trans. Fuzzy Syst.

Bernd²,

Trott

2000

“…This holds even if the parameters of linear conclusion functions are nonlinear in the model's output. By adding this third stage, which optimises all parameters simultaneously via a nonlinear optimisation method, the error can be decreased substantially [11].…”

Section: Parameter Identificationmentioning

confidence: 99%

“…The results presented in Section 4 are obtained by optimising the fuzzy models via Marquardt's method [7], and in some cases, via a hybrid method which combines Marquardt's and the LMS method [11]. The optimisation requires first derivatives which are calculated analytically.…”

Section: Parameter Identificationmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Black Box Modelling – Fuzzy Networks versus Neural Networks

Bernd

Kleutges

Neural Computing & Applications

1999

Fuzzy networks and neural networks offer two different approaches of nonlinear black box modelling. Efficient identification methods have been developed to calculate the parameters for a given structure and have been applied successfully in many examples. But the applications proposed in the literature usually miss the comparison of the alternative method, so that the selection of the more suitable approach for a given task is difficult. This paper aims to ease the decision for one of the two methodologies by considering one well-known high quality approximator of each network type, and presenting a fair comparison. For this purpose, two mathematical and three complex technical examples of nonlinear systems are considered. Generally, fuzzy networks and neural networks face the problem of overtraining causing poor validation/generalisation results. A modification of the established identification methods is proposed as a significant improvement for both approaches.

Zur approximativen Maximum-Likelihood-Schätzung dynamischer Multi-Modelle vom Typ Takagi-Sugeno: Methodik und Anwendung auf einen Servo-Pneumatikantrieb

At - Automatisierungstechnik

Fischer

2021

Zusammenfassung Dieser Beitrag adressiert die Identifikation von Takagi-Sugeno-Modellen für nichtlineare stochastische dynamische Systeme. Ist Wissen über die stochastischen Eigenschaften eines dynamischen Prozesses (bspw. bzgl. Verteilungsfunktion, Korreliertheit) verfügbar, so kann dies zur Verbesserung der Modellparameterschätzung genutzt werden. Dabei trifft die oft gemachte Annahme unabhängig und identisch normalverteilter Zufallsgrößen bei technischen Systemen häufig nicht zu. Dies ist bspw. bei mechatronischen Antrieben in Folge von Reibung oft der Fall. Im Beitrag werden deshalb die Dichtefunktionen der Zufallsgrößen als Gaußsche Mischmodelle mittels eines Multistart-Expectation-Maximization-Algorithmus geschätzt. Da die Residualdichtefunktionen zu Beginn der Identifikation nicht verfügbar sind, werden diese aus der Streuung von Wiederholexperimenten approximativ ermittelt und zur approximativen Maximum-Likelihood-Schätzung von Takagi-Sugeno-Modellen genutzt. Wegen der ausgeprägten Multimodalität der resultierenden Likelihood-Funktion wird dazu Partikelschwarm-Optimierung eingesetzt. Die Vorgehensweise wird an einem industriellen servo-pneumatischen Linearantrieb mit reibungsbedingten Unsicherheiten demonstriert. Dabei lässt sich der mittlere Validierungsfehler um 9 % gegenüber einer Least-Squares-Schätzung reduzieren.