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doi: 10.1177/0142331208090627pmid: N/A
Fuzzy system modelling (FSM) is one of the most prominent tools that can be used to identify the behaviour of highly non-linear systems with uncertainty. In the past, FSM techniques utilized Type 1 fuzzy sets in order to capture the uncertainty in the system. However, since Type 1 fuzzy sets express the belongingness of a crisp value x' of an input variable x in a fuzzy set A by a crisp membership value μA(x'), they cannot fully capture the uncertainties associated with higher-order imprecisions in identifying membership functions. In the future, we are likely to observe higher types of fuzzy sets, such as Type 2 fuzzy sets. The use of Type 2 fuzzy sets and linguistic logical connectives has drawn a considerable amount of attention in the realm of FSM in the last two decades. In this paper, we first review Type 1 fuzzy system models known as Zadeh, Takagi— Sugeno and Turkşen models; then we review potentially future realizations of Type 2 fuzzy systems again under the headings of Zadeh, Takagi—Sugeno and Turkşen fuzzy system models, in contrast to Type 1 fuzzy system models. Zadeh's and Takagi—Sugeno's models are essentially fuzzy rule base (FRB) models, whereas Turkşen's models are essentially fuzzy function (FF) models. Type 2 fuzzy system models have a higher predictive power. One of the essential problems of Type 2 fuzzy system models is computational complexity. In data-driven FSM methods discussed here, a fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure, ie, either the number of fuzzy rules or alternately the number of FFs.
doi: 10.1177/0142331208090629pmid: N/A
Product-sum-type fuzzy controllers are known to have similar characteristics to PD-type controllers. In the case of type-0 control systems, PID-type fuzzy controllers have been proposed in the literature in order to eliminate the steady-state error. However, these control methods, essentially based on conventional PID theory, have no predictive capabilities. The concept of grey system theory, which has a certain prediction capability, offers an alternative approach for various kinds of conventional control methods, such as PID control and fuzzy control. This paper proposes a grey prediction-based fuzzy PID controller that can overcome the stated shortcomings. In order to obtain a better controller performance, another fuzzy controller is designed to change the step size of the grey predictor. A non-linear liquid level system is taken as a test bed. The grey model developed is examined under several different conditions and it is shown that the proposed grey fuzzy PID controller can predict the future output value of the system. It is clear that the proposed adaptive PID-type fuzzy controller is effective in controlling such a non-linear system accurately by changing the step size adaptively for real-time working.
Tokat, S.; Eksin, I.; Guzelkaya, M.
doi: 10.1177/0142331208090672pmid: N/A
In this study, a sliding mode controller with a linear time-varying sliding surface is proposed for high-order systems by generalizing the co-ordinate transformed sliding surface design algorithm devised by the authors for second-order systems. The sliding mode control law is formulated for the sliding surface that has been defined by using a time-varying function. The equivalent control term of the proposed controller is expressed as a sum of the equivalent control term of the conventional sliding mode controller and an additive signal, which is a linear function of system tracking error vector and a time-dependent monotonous function. Simulations are performed on a third-order non-linear model with external disturbances and parameter variations. The performance of the sliding mode controller with the proposed design methodology is compared both with a conventional sliding mode controller and with another sliding mode controller that also uses an additive term in the control law to minimize the reaching time. The simulation results have shown that the proposed method has improved the robustness and the transient response with respect to related sliding mode controllers.
Onat, C.; Kucukdemiral, I.B.; Sivrioglu, S.; Yuksek, I.; Cansever, G.
doi: 10.1177/0142331208090630pmid: N/A
There always exists a conflict between ride comfort and suspension deflection performances during the vibration control of suspension systems. Active suspension control systems, which are designed by linear methods, can only serve as a trade-off between these conflicting performance criteria. Both performance objectives can only be accomplished at the same time by using a nonlinear controller. This paper addresses the non-linear induced L2 control of an active suspension system, which contains non-linear spring and damper elements. The design method is based on the linear parameter varying (LPV) model of the system. The proposed method utilizes the bilinear damping characteristic, stiffening spring characteristic when the suspension deflection approaches the structural limits, mass variations and parameter-dependent weighting filters. Simulation studies both in time and frequency domain demonstrate that the active suspension system controlled by the proposed method always guarantees an agreement between acceleration (comfort) and suspension deflection magnitudes together with a high ride performance.
Efe, Mehmet Önder; Debiasi, Marco; Peng Yan, ; Özbay, Hitay; Samimy, Mohammad
doi: 10.1177/0142331208090964pmid: N/A
This paper presents a simple yet effective one-step-ahead predictor based on an adaptive linear element (ADALINE). Several tuning schemes are studied to see whether the obtained model is consistent. The process under investigation is a subsonic cavity flow system. The experimental data obtained from the system is post-processed to obtain a useful predictor. The contribution of the paper is to demonstrate that despite the spectral richness of the observed data, a simple model with various tuning schemes can help to a satisfactory extent. Seven algorithms are studied, including the least mean squares (LMS), recursive least squares (RLS), modified Kaczmarz's algorithm (MK), stochastic approximation algorithm (SA), gradient descent (GD), Levenberg—Marquardt optimization technique (LM) and sliding mode-based tuning (SM). The model and its properties are discussed comparatively.
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