THE GENETIC DESIGN OF HYBRID FUZZY CONTROLLERS

In this study, we introduce a comprehensive design methodology of hybrid fuzzy controllers (HFCs). The hybrid facet of the proposed architecture of the controller manifests in the form of a convex combination of a standard proportional integral derivative (PID) controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithms) and an autotuning algorithm based on estimation modes. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. Numerical studies are presented and a detailed comparative analysis is included as well.     

Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression

Proportional and derivative kick i.e., a large change in control action of a proportional plus integral plus derivative (PID) controller due to a sudden change in reference set-point is generally undesired in process industry. Therefore, the structure of conventional parallel PID controller is modified to integral minus proportional derivative (I-PD) controller. In this paper, three hybrid fuzzy IPD controllers such as a fuzzy I-fuzzy PD (FI-FPD) controller and its hybrid combinations with its conventional counterpart such as fuzzy I-PD (FI-PD) and I-fuzzy PD (I-FPD) are presented in view of above industrial problem. These controllers are based upon the counterpart conventional I-PD controller and contains analytical formulae. Computer simulations are carried out to evaluate the performance of hybrid fuzzy controllers along with conventional I-PD and PID controllers for set-point tracking and disturbance rejection for an induction motor in closed loop using LabVIEW? environment. The gains of conventional and hybrid fuzzy controllers are tuned using genetic algorithm (GA) for minimum overshoot and settling time. It has been observed that hybrid fuzzy controllers along with the conventional I-PD controller significantly remove the kick from the control action in reference set-point tracking. However, in disturbance rejection, I-PD and FI-PD controllers fail to eliminate the kick from the control signal. In contrast, FI-FPD and I-FPD controllers considerably reduced spikes from the control action in disturbance rejection. Among the conventional and hybrid fuzzy IPD controllers, FI-FPD demonstrates much better set-point tracking and disturbance rejection response with spike free control action.     

Modelling and motion control of a mechatronic system using BGM with intelligent controllers

In this research paper, a mechatronics system such as a pan tilt platform (PTP) has been considered for motion control under intelligent controllers. A proportional-derivative (PD) controller is considered for comparison of results obtained from fuzzy and hybrid controllers. The trajectory following performance of the mechatronics system is found against these controllers. The results of simulations show that hybrid fuzzy controller reduce the tracking error effectively in lesser settling time. The intelligent controllers require knowledge base of error and derivative of error to compensate the PTP dynamics. The intelligent controllers have similar trends as the PD controllers and compensated both electrical and mechanical dynamics. The PD controller requires position measurement. The intelligent controllers have knowledge base consisting of position and velocity data. Thus intelligent controllers have position measurement along with knowledge base for position control system. The best results were achieved with hybrid fuzzy controllers. They meet the desired specifications.     

A general technique for deriving analytical structure of fuzzy controllers using arbitrary trapezoidal input fuzzy sets and Zadeh AND operator

Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more effective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input fuzzy sets. Many fuzzy controllers use arbitrary trapezoidal/triangular input fuzzy sets that are asymmetric. At present, there exists no technique capable of deriving the analytical structure of these fuzzy controllers. Extending our original technique, we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller, Mamdani type or TS type, that employs the arbitrary trapezoidal input fuzzy sets and Zadeh fuzzy AND operator. The new technique contains our original technique as a special case. Given the importance of PID control, we focus on Mamdani fuzzy PI and PD controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy PI/PD controllers. The controllers use two arbitrary trapezoidal fuzzy sets for each input variable, four arbitrary singleton output fuzzy sets, four fuzzy rules, Zadeh fuzzy AND operator, and the centroid defuzzifier. This configuration is more general and complicated than the Mamdani fuzzy PI/PD controllers in the current literature. It actually contains them as special cases. We call this configuration the generalized fuzzy PI/PD controller.     

Design and analysis of region-wise linear fuzzy controllers

In this paper, a methodology to reduce the complexity of a robust controller based on fuzzy if-then rules is proposed. The motivation and the design of this complexity-reduced fuzzy controller are presented. This fuzzy controller with the triangular membership functions and fuzzy partition methods used here leads to a region-wise linear fuzzy controller (RLFC). The properties of the region-wise linear fuzzy controllers are discussed and the reasons why they in general perform better than the PD controllers are also provided. And the simulation results based on a second order plant are included to show that the region-wise linear fuzzy controller outperforms the PD controller. We also show that the region-wise linear fuzzy controller and original fuzzy controller have similar performances.     

Numerical simulation for Fuzzy-PID controllers and helping EP reproduction with PSO hybrid algorithm

Many Fuzzy-PID controller schemes used in industry today are based on some sort of simplified fuzzy reasoning methods and PID parameters. We present a design for Fuzzy-PID controllers using a novel PSO-EP-based hybrid algorithm. We succeed in making mathematical calculations and in encouraging EP reproduction with PSO. The main advantage of our design is that the integration of the PSO-EP-based hybrid algorithm structure generates new parameters for the Fuzzy-PID control schemes. The proposed algorithm is an improved variant of PSO, a relatively recently introduced stochastic optimization strategy for Fuzzy-PID controllers that is investigated in this study. The function of Fuzzy-PID controllers is illustrated by means of a model of the induction motor control system and a higher-order numerical model.     

Study of Learning Fuzzy Controllers

This paper compares two types of learning fuzzy controllers, the self-organizing fuzzy (SOF) controller and the hybrid self-organizing fuzzy proportional–integral–derivative (SOF-PID) controller. The SOF is an extension of the rule-based fuzzy controller, with additional rule creation and rule modification mechanisms. The hybrid SOF-PID comprises the SOF as a learning supervisory controller readjusting the proportional gain of the PID controller at the actuator section, when the system is on line. The structures of the SOF controller and the hybrid SOF-PID controller are studied. The performances of the SOF controller and the hybrid SOF-PID controller are compared by applying them to a two-link non-linear revolute-joint robot arm. For the path tracking experiments, the hybrid SOF-PID controller followed the required path more closely and smoothly than the SOF controller. The results of the experiments for the SOF controller and the hybrid SOF-PID controller are also compared with those obtained with a conventional PID controller, using the same values supplied at the setpoint.     

Fuzzy controllers: synthesis and equivalences

It has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. In particular, any given linear control can be achieved with a fuzzy controller for a given accuracy. The aim of this paper is to show how to automatically build this fuzzy controller. The proposed design methodology is detailed for the synthesis of a Sugeno or Mamdani type fuzzy controller precisely equivalent to a given PI controller. The main idea is to equate the output of the fuzzy controller with the output of the PI controller at some particular input values, called modal values. The rule base and the distribution of the membership functions can thus be deduced. The analytic expression of the output of the generated fuzzy controller is then established. For Sugeno-type fuzzy controllers, precise equivalence is directly obtained. For Mamdani-type fuzzy controllers, the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values. The usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed     

Stability analysis and synthesis for an affine fuzzy control systemvia LMI and ILMI: a continuous case

A new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper. The method suggested is based on the numerical convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities (LMIs). The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In the synthesis, the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner. Fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains. Continuous iterative LMI (ILMI) approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system     

Development of genetic fuzzy logic controllers for complex production systems

Complex production systems can produce more than one part type. For these systems, production rate and priority of production for each part type is determined by production controllers. In this paper, genetic fuzzy logic control (GFLC) methodology is used to develop two production control architectures namely “genetic distributed fuzzy” (GDF), and “genetic supervisory fuzzy” (GSF) controllers. Previously these controllers have been applied to single-part-type production systems. In the new approach the GDF and GSF controllers are developed to control complex production systems. The methodology is illustrated and evaluated using two test cases; two-part-type production line and re-entrant production systems. Genetic algorithm is used to tune the membership functions of input variables of GSF or GDF controllers. The objective function of the GSF controller minimizes the production cost based on work-in-process (WIP) and backlog costs, while surplus minimization is considered by GDF controller. The results show that GDF and GSF controllers can improve the performance of production systems. GSF controllers decrease the WIP level and its variations. GDF controllers show their abilities in reducing the backlog level but generally, production cost for GDF controller is greater than GSF controller.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

GA-fuzzy control of smart base isolated benchmark building using supervisory control technique

The effectiveness of a supervisory fuzzy control technique for reduction of seismic response of a smart base isolation system is investigated in this study. To this end, a first generation, base isolated, benchmark building is employed for numerical simulation. The benchmark structure under consideration has eight stories and an irregular plan. Furthermore it is equipped with low damping elastomeric bearings and magnetorheological (MR) dampers for seismic protection. The proposed control technique employs a hierarchical structure of fuzzy logic controllers (FLC) consisting of two lower-level controllers (sub-FLC) and a higher-level supervisory controller. One sub-FLC has been optimized for near-fault earthquakes and the other sub-FLC is well-suited for far-fault earthquakes. These sub-FLCs are optimized by use of a multi-objective genetic algorithm. Four objectives, i.e. reduction of peak superstructure acceleration, peak isolation system deformation, RMS superstructure acceleration and RMS isolation system deformation are used in a multi-objective optimization process. When an earthquake is applied to the benchmark building, each of the sub-FLCs provides different command voltages for the semi-active controllers and the supervisory fuzzy controller appropriately combines the two command voltages based on a fuzzy inference system in real time. Results from numerical simulations demonstrate that isolation system deformation as well as superstructure responses can be effectively reduced using the proposed supervisory fuzzy control technique in comparison with a sample clipped optimal controller.     

A systematic approach for fine-tuning of fuzzy controllers applied to WWTPs

A systematic approach for fine-tuning fuzzy controllers has been developed and evaluated for an aeration control system implemented in a WWTP. The challenge with the application of fuzzy controllers to WWTPs is simply that they contain many parameters, which need to be adjusted for different WWTP applications. To this end, a methodology based on model simulations is used that employs three statistical methods: (i) Monte-Carlo procedure: to find proper initial conditions, (ii) Identifiability analysis: to find an identifiable parameter subset of the fuzzy controller and (iii) minimization algorithm: to fine-tune the identifiable parameter subset of the controller. Indeed, the initial location found by Monte-Carlo simulations provided better results than using trial and error approach when identifying parameters of the fuzzy controller. The identifiable subset was reduced to 4 parameters from a total of 33, which improved the quality of the optimization of the control system by a minimization algorithm. Overall the systematic approach considerably improved the performance of the control system as measured by the Integral Absolute Error (deviation between the set-point and the controlled variable) of the controllers. Moreover, the methodology overcomes the dependency of the initial parameter space issue typical of local identifiability analysis. All in all this systematic approach is expected to facilitate the design and application of fuzzy controllers in particular to WWTPs compared to the time-consuming and tedious trial and error approach currently used in practice.     

Adaptive fuzzy model based inverse controller design using BB-BC optimization algorithm

The use of inverse system model as a controller might be an efficient way in controlling non-linear systems. It is also a known fact that fuzzy logic modeling is a powerful tool in representing nonlinear systems. Therefore, inverse fuzzy model can be used as a controller for controlling nonlinear plants. In this context, firstly, a new fuzzy model based inverse controller design methodology is presented in this study. The design methodology introduced here is based on a recursive optimization procedure that searches for an optimal inverse model control signal at every sampling time. Since the task of optimization should be accomplished in between two sampling periods the use of a fast optimization algorithm becomes essential. For this reason, Big Bang-Big Crunch (BB-BC) optimization algorithm is used due to its low computational time and high global convergence properties. Even though, inverse model controllers may produce perfect control while operating in an open loop fashion, this open loop control would not be sufficient in the case of modeling mismatches or disturbances that might occur over the system. In order to overcome this problem, secondly, an on-line adaptation mechanism via BB-BC optimization algorithm is introduced in addition to BB-BC optimization based fuzzy model inverse controller. The adaptation mechanism is used to update the related parameters of the model while minimizing the absolute value of the instantaneous error between the system and model outputs. In this manner, the system output is somehow fed back, the overall control form can be considered as a closed-loop system. The new fuzzy model based inverse control scheme with the new online adaptation mechanism has been implemented and tested on the two real time processes; namely, heat transfer and pH processes and very satisfactory results has been reported.     

Hybrid state-space fuzzy model-based controller with dual-ratesampling for digital control of chaotic systems

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit     

Design of adaptive fuzzy logic controller based on linguistic-hedgeconcepts and genetic algorithms

In this paper, we propose a novel fuzzy logic controller, called linguistic hedge fuzzy logic controller, to simplify the membership function constructions and the rule developments. The design methodology of linguistic hedge fuzzy logic controller is a hybrid model based on the concepts of the linguistic hedges and the genetic algorithms. The linguistic hedge operators are used to adjust the shape of the system membership functions dynamically, and ran speed up the control result to fit the system demand. The genetic algorithms are adopted to search the optimal linguistic hedge combination in the linguistic hedge module, According to the proposed methodology, the linguistic hedge fuzzy logic controller has the following advantages: 1) it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables; 2) it is sufficient to adopt a fewer number of rules for inference; 3) the rules are developed intuitionally without heavily depending on the endeavor of experts; 4) the linguistic hedge module associated with the genetic algorithm enables it to be adaptive; 5) it performs better than the conventional fuzzy logic controllers do; and 6) it can be realized with low design complexity and small hardware overhead. Furthermore, the proposed approach has been applied to design three well-known nonlinear systems. The simulation and experimental results demonstrate the effectiveness of this design.     

A Hybrid Approach for Design of Stable Adaptive Fuzzy Controllers Employing Lyapunov Theory and Particle Swarm Optimization

This paper proposes a new approach for designing stable adaptive fuzzy controllers, which employs a hybridization of a conventional Lyapunov-theory-based approach and a particle swarm optimization (PSO) based stochastic optimization approach. The objective is to design a self-adaptive fuzzy controller, optimizing both its structures and free parameters, such that the designed controller can guarantee desired stability and can simultaneously provide satisfactory performance. The design methodology for the controller simultaneously utilizes the good features of PSO (capable of providing good global search capability, required to provide a high degree of automation) and Lyapunov-based tuning (providing fast adaptation utilizing a local search method). Three different variants of the hybrid controller are proposed in this paper. These variants are implemented for benchmark simulation case studies and real-life experimentation, and their results demonstrate the usefulness of the proposed approach.     

New methodology for analytical and optimal design of fuzzy PIDcontrollers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation     

Evolutionary design of discrete controllers for hybrid mechatronic systems

This paper investigates the issue of evolutionary design of controllers for hybrid mechatronic systems. Finite State Automaton (FSA) is selected as the representation for a discrete controller due to its interpretability, fast execution speed and natural extension to a statechart, which is very popular in industrial applications. A case study of a two-tank system is used to demonstrate that the proposed evolutionary approach can lead to a successful design of an FSA controller for the hybrid mechatronic system, represented by a hybrid bond graph. Generalisation of the evolved FSA controller to unknown control targets is also tested. Further, a comparison with another type of controller, a lookahead controller, is conducted, with advantages and disadvantages of each discussed. The comparison sheds light on which type of controller representation is a better choice to use in various stages of the evolutionary design of controllers for hybrid mechatronic systems. Finally, some important future research directions are pointed out, leading to the major work of the succeeding part of the research.     

Neuro-fuzzy techniques to optimize an FPGA embedded controller for robot navigation

This paper describes how low-cost embedded controllers for robot navigation can be obtained by using a small number of if-then rules (exploiting the connection in cascade of rule bases) that apply Takagi–Sugeno fuzzy inference method and employ fuzzy sets represented by normalized triangular functions. The rules comprise heuristic and fuzzy knowledge together with numerical data obtained from a geometric analysis of the control problem that considers the kinematic and dynamic constraints of the robot. Numerical data allow tuning the fuzzy symbols used in the rules to optimize the controller performance. From the implementation point of view, very few computational and memory resources are required: standard logical, addition, and multiplication operations and a few data that can be represented by integer values. This is illustrated with the design of a controller for the safe navigation of an autonomous car-like robot among possible obstacles toward a goal configuration. Implementation results of an FPGA embedded system based on a general-purpose soft processor confirm that percentage reduction in clock cycles is drastic thanks to applying the proposed neuro-fuzzy techniques. Simulation and experimental results obtained with the robot confirm the efficiency of the controller designed. Design methodology has been supported by the CAD tools of the environment Xfuzzy 3 and by the Embedded System Tools from Xilinx.