# Fuzzy Controller Design: Theory and Applications (Automation and Control Engineering)

No matter how many inputs to the FC are, the FC should these applications can be viewed in the framework of possess at least one input variable e1 that corresponds to the mechatronic systems. Selected papers are given in the end of this paper. Many excellent works are unfortunately According to Fig. In addition, this survey paper is not able to cover all involves the sequence of operations a , b and c : categories of industrial applications of fuzzy logic control in detail. Industrial applica- reference input the set point , the control error — is converted tions of control systems with Mamdani fuzzy controllers into fuzzy representation.

Next, Section 3 is focused on of crisp information. Applications of adaptive and predictive fuzzy control control the given process. The principles to evaluate and dealing with supervision and optimization, i.

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Control systems with Mamdani fuzzy controllers understandable and usable by the actuator in order to be capable of controlling the process. All three modules are assisted adequate databases. In structures. However, it can be used on the supervisory level, for addition, the design of such control systems suffers from the lack example in adaptive control system structures. Nowadays fuzzy of systematic approaches.

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## IJCAS International Journal of Control, Automation, and Systems

Therefore much research attention has control is no longer only used to directly express the knowledge on been devoted to the stability analysis. Actual trends make use of the CP or, in other words, to do model-free fuzzy control. These FCs of FCSs into the stability theory of conventional nonlinear are usually used as direct closed-loop controllers. The manufacturing area is related to robotics.

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Mamdani FCs [—]. Problems and practical issues related to suspension calculates the control signal action directly to control a system. The control of hybrid electric vehicles The second approach is viewed as gain scheduling [,]. Other applications are reported in [,—]. Hence they [,,—] or neural networks [29,—], and robust require high quality servo systems that ensure both stabilization FCs [29,93,—]. The same problem is in case of complex control systems where the actuators can be viewed as local control 2.

Sliding mode fuzzy control systems with high needs as the performance is concerned. Servo systems are widely used in mechatronics applications charac- It is well acknowledged that sliding mode control exhibits terized by tight coupling of different implementation techniques robustness properties []. So a natural direction is to embed this including hydraulics, mechanics, electro-mechanics, electronics property in fuzzy control. This will lead to the alleviation of the and software [73—75].

One of complementing the advantages of both ones. Fuzzy control has recently been applied to a variety layers [—]. The results outlined in these areas [94—] can be connected well to those dedicated to servo systems. These approaches ensure the convenient treatment of FCS 2. PI-, PD- and PID-fuzzy control stability analysis and design in the framework of the well developed methods dedicated to sliding mode control. The CS performance indices 2. On the tages over the one-degree-of-freedom ones [—]. But, the other hand, conventional fuzzy control is known for its ability to main drawback of 2-DOF controllers is that although they ensure cope with nonlinearities and uncertainties.

Introduction of the regulation, the reduction of overshoot is paid by slower set- dynamic fuzzy controller structures with the aim of control point responses because the 2-DOF structures can be reduced to system performance improvement leads to PI-, PD- or PID-fuzzy feedforward controllers with set-point weighting. Stable design of model-based fuzzy control systems controlled process P s is included to the generic 2-DOF control system structures presented in Fig. Similar structures signal input vector, y t is the output vector, and can be formulated under the form of state-feedback control systems to be treated in the following sections.

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- Fuzzy Controller Design Theory And Applications Automation And Control Engineering?

This brings a twofold advantage. Second, the controller itself The local linear models of the process can be considered as a fuzzy system. This idea is known as parallel are supposed to be observable and controllable. In discrete T-S distributed compensation [18]. Popular approaches employ quadratic, piecewise quadratic, values.

Hence the TP model transforma- algorithms embedded in well acknowledged software tools. They include the cascade control systems should be determined. The type of the convex 3. Therefore the design can be based One of the current trends in fuzzy control is to derive less on the manipulation of the convex hull beside the manipulation of conservative conditions to prove the stability and the performance the LMIs. The fuzzy partitions are the combinations of Based on the core theory of the TP model transformation that is the products of rather simple arguments expressed as membership coming from the singular value decomposition SVD methods functions.

In real-world applications one particular case concerns [] the TP model transformation is capable of reducing the fuzzy modelling of nonlinear systems under the form of TP fuzzy complexity of TP structured functions like T-S fuzzy models or B- systems. The expression of TP fuzzy systems can be understood in spline models and so on. The multilinear generalizations of the SVD terms of operations on multi-dimensional arrays [].

The HOSVD has been dynamic system model, given over a bounded domain, into the TP developed since the existing framework of vector and matrix model form, including polytopic or T-S fuzzy model forms. Use is made of higher-order tensors to of parameter independent constant system models under the describe the transformations in the same way as the matrices form of linear time-invariant LTI systems. This transformation of describe linear transformations between vector spaces. LPV models is uniform in both theoretical and algorithmic Making use of the TP model transformation, different optimi- execution and it considers different optimization constraints.

Thus, the transformation replaces the that the LMI-based control design frameworks can be applied usual analytical conversions. They are mostly vertexes of a polytopic structure. In conclusion, the T-S fuzzy model originally is a fuzzy! In other words, the TP model transformation is to be used and executed before utilizing the LMI design, i. A short presentation of the applications of TP model transfor- mation, well connected to T-S FCSs, is presented in [] and accompanied by a temperature control application.

An attractive control design method accompanied by application is given [,] to stabilize parameter varying nonlinear state-space models. It is based on two numerical steps. In the second step LMIs are Fig. Changing the side slopes of a group of membership functions. The modal solved under the PDC framework. The advantages of this method are twofold.

First, the understanding of the process and of the controller, and has access controller can be derived automatically, regardless of analytic to all input and usually also to all output signals. The supervisory derivations. These four items will be discussed below. That controller does not change the controller design technique. The results show that both numerical parameters of the underlying FC, but it chooses every time the best methods, the TP model transformation and the LMIs, can be control signal based on a performance measure expressed in terms accomplished numerically without analytical derivations, leading of an objective function.

The goal is to minimize the objective to fast controller designs. A case study regarding the TP model transformation behaviour in real-world applications is discussed in [] with focus on the 4. Adaptation of the size of the membership functions single pendulum gantry system.

A generalization of the double fuzzy summation results to multiple summations with a TP The supervisor can change the size of the membership functions structure is emphasized in []. This is meant to replace the well of the fuzzy sets corresponding to the linguistic terms of the FC, accepted common structure in many fuzzy models. A simulated e. The toolbox is applied to linguistic variables of the fuzzy controller. The triangular several benchmark systems and to the real-time control of the membership functions of the linguistic terms LT1, Lt2, LT3 and liquid levels in a three tank system [].

LT4 were chosen in Fig. An excellent application of the TP model transformation deals Likewise, the spread s of Gaussian fuzzy sets can be adapted. An example of this is a controller for the cruise control of model transformation with PDC design framework. It shows the a car []. If the car goes uphill or downhill the cruise system controls the throttle in such a way that the car keeps its velocity, if the driver 4.

By then, There are many formations for the FC in FCSs similarly to the the car will accelerate until it returns to the desired speed. An adaptive FC has one extra component, a supervisory can lead to too fast or too slow acceleration and overshoot. In [] the system is described as in Fig.

The FC calculates the throttle opening, passes it on to the actuator which applies it to the vehicle. If the throttle opening is too slow or too fast, i. An adaptive fuzzy controller with a supervisory system. Structure of fuzzy parking system. Logical scheme of an adaptive fuzzy system for cruise control.

EAV is the error average value, UAV is the average value of the throttle opening, Verr is the maximum value of the error []. Table 1 Parking garages and the prediction quality of the adapted fuzzy system. The error average value and its PG3 0. If the car accelerates too slow this means, for PG6 0. Time information concerns the time of Usually this is done in combination with a data clustering method. Together with the weather information evenly distributed over the whole data space, but occur in groups.

This parking garage, and the time people need to enter the parking enables one to work with a minimal number of fuzzy sets whose garage, as many of them have narrow passages and long waiting membership functions are well positioned to deal with the data.

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Overviews on data-driven clustering to a different positioning of the membership functions and methods for adaptive fuzzy control are given in [,]. After repositioning and resizing []. The the prediction quality changed as described in Table 1. Adaptation of the rule base instead of a black box neural network. The combination of a neural network learning system and a readable fuzzy rule base is perfect A third adaptation method option is to change the rule weights for automotive industry. If an due to the well accepted functional equivalence between certain action was unsuccessful the weights of the involved rules are classes of fuzzy systems and certain architectures of neural decreased.

Rules that after some time have rule weight 0 are not networks []. Neuro-fuzzy control is in fact fuzzy control that involved anymore and will be removed. Of course the capabilities and parallel processing brought by the neural net- quality of this method highly depends on the performance works. ANFIS [] is the most popular approach with this regard. One should always Industrial applications of adaptive fuzzy control can be found in check which rules were removed, in some cases these rules batch processes [—], robotics [58,,—], aircrafts concern exception cases and should be reintroduced by hand.

This [—] or servo systems and electrical drives [—]. A neural-fuzzy-based 4.

## Fuzzy Controller Design: Theory and Applications (Automation and Control Engineering)

Adaptation of the link values force model for controlling band sawing process in the framework of an intelligent adaptive control and monitoring system is given in A fourth adaptation method is to change the link values. This is []. An adaptive control solution for a ventilating and air- derived from neural networks and is actually not natural for fuzzy conditioning HVAC system is proposed in [].

It means the following. Consider a rule base with two Topics of interest in adaptive fuzzy control include robust inputs X1 and X2 and one output Y, and three fuzzy sets P, Z, and N, adaptive control, the combination with sliding mode control and on each input domain. One can translate the fuzzy system to a the inclusion of derivative-free optimization techniques to neural network as described in Fig.

According to [,], the are needed in industrial applications due to the complicated logarithms and exponentials are needed in this scheme to cope expression of the objective function with several possible local with several neural network properties. Several fuzzy rule interpolation techniques data pairs and train the network. Fuzzy model-based predictive control because the neural network has adapted the link values. This rule is hard to interpret but will probably describe the situation exactly. One illustrative industrial application of fuzzy model-based This method is, for example, used in a system with many predictive control is presented in [].

There was an initial rule of the future process output. Use is made of the fact that if you have base describing the logical relation between the sensors and the a fuzzy model, you can test assumed future situations by putting driving situation. Test data were generated by driving the car with data into the model. It is possible to compare the outcomes of a video camera several days in all kinds of situations. The test data different control inputs and take the best to proceed with. The were categorized to several driving situations.

After translating the results presented in [] involve a fuzzy model of a chemical rule base to a neural network all rule weights, the positions of the plant under the form of the following six fuzzy rules: membership functions and the link weights were adapted which resulted in a much improved fuzzy rule base.

It then calculates which parameters force the output to reach the reference trajectory in the best way and uses these parameters in the next control step. Other industrial applications of fuzzy model- Fig. A neural network translation from a fuzzy rule base. The authors thank Prof. Robert - adaptive and predictive control systems. The authors would also like to thank the colleagues and friends Although the literature makes a distinction between model- Prof.

Stefan Preitl, Prof. Peter Baranyi, Prof. Marius L.

## Intelligent Adaptive Fuzzy Control

Tomescu for their fruitful co- fuzzy control outlined in [] is needed. This is the way that enables systematic analyses of the structural properties of the FCSs such as stability, References controllability, parametric sensitivity and robustness. Zadeh, Fuzzy sets, Information and Control 8 3 — Mamdani, Applications of fuzzy algorithms for control of a simple dynamic and it represents one of the perspectives of fuzzy control.

Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy A lot of industrial applications of fuzzy control are known and logic controller, International Journal of Man—Machine Studies 7 1 1— This paper has highlighted just part of them. It [4] W. Kickert, H. Van Nauta Lemke, Application of a fuzzy logic controller in a contains both mathematics and concrete applications thus warm water plant, Automatica 12 4 — Ostergaard, Fuzzy logic control of a heat exchanger process, in: M. Gupta, emphasizing the concrete connection between the industrial G.

Saridis, B. Gaines Eds. The presentation of rather real-time [7] C. In this context the popularity of [8] C. Driankov, H. Hellendoorn, M. There are several challenges which deserve more study when [10] W. Yager, D. Mendel, Fuzzy logic systems for engineering: a tutorial, in: Proceedings of to certain narrow applications, the IEEE 83, vol. Palm, D. Passino, S. Tanaka, H. Michels, F. Klawonn, R.

Kruse, A. Zhang, D. Kluska, Analytical Methods in Fuzzy Modeling and Control, Springer-Verlag, - the need for low-cost fuzzy controllers from the points of view of Berlin, Heidelberg, Verbruggen, An overview on fuzzy modelling for control, Control controllers, Engineering Practice 4 11 — Mitra, Y. Kaynak, K. Erbatur, M. Ertugrul, The fusion of computationally intelligent processes [—]. Sala, T.

Guerra, R. Sets and Systems 3 — Sugeno, T. Taniguchi, On improvement of stability conditions for continuous publications. Tian, C. Peng, Delay-dependent stability analysis and synthesis of uncertain T- viewed as a guarantee that future successful applications will be S fuzzy systems with time-varying delay, Fuzzy Sets and Systems 4 constructed. Precup, S. Preitl, I. Rudas, M. Tomescu, J. Tar, Design and experiments [62] N. Schouten, M. Salman, N. Mechatronics 13 1 22— Mohan, A. Bravo, A. Mirzaei, M. Moallem, B. Mirzaeian, B. Fahimi, Design of an optimal fuzzy fuzzy systems using interval arithmetic, Fuzzy Sets and Systems 3 controller for antilock braking systems, in: Proceedings of IEEE Confer- — Borne, M.

Benrejeb, On the representation and the stability study of large scale [65] Z. Zhao, Z. Yu, Z. S 55— Sakly, B. Zahra, M. Benrejeb, Stability analysis of continuous PI-like fuzzy — Moon, K. Portugal, , pp. Haber, V. Zhao, E. Collins Jr. Onat, M. Habiballa, V. Eftekhari, L. Marjanovic, P. Angelov, Design and performance of a rule-based — Galichet, L. Foulloy, Integrating expert knowledge into industrial control — Lygouras, V.

Kodogiannis, T. Pachidis, K. Tarchanidis, C. Koukourlis, [40] R. Haber, J. Alique, A. Alique, J. Uribe-Etxebarria, Embedded Variable structure TITO fuzzy-logic controller implementation for a solar air- fuzzy-control system for machining processes: results of a case study, Compu- conditioning system, Applied Energy 85 4 — Maidi, M. Diaf, J. First Published Imprint CRC Press. Pages pages. Export Citation. Get Citation. Kovacic, Z. View abstract. Welcome to CRCPress.

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