Multivariable gain-scheduled fuzzy logic control of an exothermic reactor

Fuzzy logic control frequently exhibits superior performance to classical linear controllers even for ‘hard’, mathematically well defined plants, as described in this paper. The case-study of a highly nonlinear exothermic continuous stirred tank reactor, which poses a multivariable control problem with two interacting loops and open-loop instability, is used. The behaviour of the fuzzy logic controller is compared with that of a PID controller. A smooth, easily tuneable gain-schedule is designed to handle offset-like problems with a fuzzy controller. It is analytically shown that such a gain-schedule is the simpler, intuitive equivalent of a manipulation of the corresponding fuzzy membership functions. The fuzzy controller structure chosen is a parsimonious one, with the choice of Gaussian bell-shaped membership functions generating a smooth input/output surface with nontrivial inferencing spanning the entire input space. This provides a clear, non-heuristic reason to select Gaussian over triangular shapes for membership functions. The gain-scheduled fuzzy controller shows excellent control performance, significantly outperforming the PID controllers in both servo and regulatory modes. The disturbance rejection behaviour of the modified fuzzy controller is observed to be particularly good.     

A type-2 fuzzy logic controller design for buck and boost DC–DC converters

Conventional (type-1) fuzzy logic controllers have been commonly used in various power converter applications. Generally, in these controllers, the experience and knowledge of human experts are needed to decide parameters associated with the rule base and membership functions. The rule base and the membership function parameters may often mean different things to different experts. This may cause rule uncertainty problems. Consequently, the performance of the controlled system, which is controlled with type-1 fuzzy logic controller, is undesirably affected. In this study, a type-2 fuzzy logic controller is proposed for the control of buck and boost DC–DC converters. To examine and analysis the effects of the proposed controller on the system performance, both converters are also controlled using the PI controller and conventional fuzzy logic controller. The settling time, the overshoot, the steady state error and the transient response of the converters under the load and input voltage changes are used as the performance criteria for the evaluation of the controller performance. Simulation results show that buck and boost converters controlled by type-2 fuzzy logic controller have better performance than the buck and boost converters controlled by type-1 fuzzy logic controller and PI controller.     

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.     

输入采用广义梯形隶属函数的两维最简模糊控制器结构分析

总结了应用最为广泛的三角形和梯形隶属函数的共同特点, 明确定义了一种将以上两种隶属函数作为特例的广义梯形 (Generalized trapezoid-shaped, GTS) 隶属函数, 推导了输入变量采用 GTS 隶属函数的 I 类和 II 类两维最简模糊控制器的解析式. 基于此, 深入研究了模糊控制器的解析结构, 并证明了这两类模糊控制器等价于一种变结构的非线性 (或线性) PI 控制器与相应的非线性 (或定常) 控制偏置之和, 并且在其输入论域上是单调递增、连续且有界的. 最后, 将该类控制器应用于倒立摆控制系统, 通过仿真证明了其有效性, 同时揭示了此类控制器是一种更一般化的模糊控制器.     

The adaptive control of nonlinear systems using the Sugeno-type offuzzy logic

An adaptive fuzzy controller is synthesized from a collection of fuzzy IF-THEN rules. The parameters of the membership functions characterizing the linguistic terms in the fuzzy IF-THEN rules are changed according to some adaptive laws for the purpose of controlling a plant to track a reference trajectory. In the paper, a direct adaptive fuzzy control design method is developed for the general higher order nonlinear continuous systems. We use the Sugeno-type of the fuzzy logic system to approximate the controller. It is proved that the closed-loop system using this adaptive fuzzy controller is globally stable in the sense that all signals involved are bounded. Finally, we apply the method of direct adaptive fuzzy controllers to control an unstable system     

采用非线性规则和不均匀分布的输入输出隶属函数时典型模糊控制器的结构分析

针对两输入 (e,Δe)一输出 (Δu)的典型模糊控制器, 其输入变量采用三角形、全交迭、对称、不均匀分布的隶属函数, 输出变量采用对称、不均匀分布的单点隶属函数, 当采用非线性控制规则和Sum Product推理方法时, 推导了输出的解析表达式, 分析了其结构特性和极限特性, 证明了此类模糊控制器具有通用逼近性, 并讨论了典型模糊控制系统的局部稳定性.     

Intuit before tuning: Type-1 and type-2 fuzzy logic controllers

Although a considerable amount of effort has been put in to show that fuzzy logic controllers have exceptional capabilities of dealing with uncertainty, there are still noteworthy concerns, e.g., the design of fuzzy logic controllers is an arduous task due to the lack of closed-form input–output relationships which is a limitation to interpretability of these controllers. The role of design parameters in fuzzy logic controllers, such as position, shape, and height of membership functions, is not straightforward. Motivated by the fact that the availability of an interpretable relationship from input to output will simplify the design procedure of fuzzy logic controllers, the main aims in this work are derive fuzzy mappings for both type-1 and interval type-2 fuzzy logic controllers, analyse them, and eventually benefit from such a nonlinear mapping to design fuzzy logic controllers. Thereafter, simulation and real-time experimental results support the presented theoretical findings.     

Experimental Comparison Research on Active Vibration Control for Flexible Piezoelectric Manipulator Using Fuzzy Controller

Space manipulators are flexible structures. Vibration problem will be unavoidable due to motion or external disturbance excitation. Model based control methods will not maintain the required accuracy because of the existence of nonlinear factors and parameter uncertainties. To solve these problems, fuzzy logic control laws with different membership function groups are adopted to suppress vibrations of a flexible smart manipulator using collocated piezoelectric sensor/actuator pair. Also, dual-mode controllers combining fuzzy logic and proportional integral control are designed, for suppressing the lower amplitude vibration near the equilibrium point significantly. Experimental comparison research is conducted, using fuzzy control algorithms and the dual-mode controllers with different membership functions. The experimental results show that the adopted fuzzy control algorithms can substantially suppress the larger amplitude vibration; and the dual-mode controllers can also damp out the lower amplitude vibration significantly. The experimental results demonstrate that the proposed fuzzy controllers and dual-mode controllers can suppress vibration effectively, and the optimal placement is feasible.     

Steady-state error of a system with fuzzy controller

We consider the problem of control error of a fuzzy system with feedback. The system consists of a plant, linear or nonlinear, fuzzy controller, and feedback loop. As controller we use both PD and PI fuzzy type controllers. We apply different t-norm and co-norm: logic, algebraic, Yager, Hamacher, bounded, drastic, etc. in the process of fuzzy reasoning. Triangular shape of membership functions is supposed, but we generalize the results obtained. Steady-state error of a system is calculated. We have obtained very interesting results. The steady-state error is identical for pairs of triangular t- and co-norms.     

FUZZY SCHEDULING OF REGIONAL QFT CONTROLLERS

A novel optimization-based controller synthesis method is developed for nonlinear dynamic systems with structured parametric uncertainty. Fuzzy logic is used to smoothly schedule independently designed regional robust controllers over the plant's operational envelope. These linear controllers are synthesized using established conventional control design techniques, e.g., quantitative feedback theory. The resulting full envelope nonlinear dynamic controller handles complex dynamic systems which cannot otherwise be addressed by simple fuzzy logic control (FLC). An analytical representation of the membership functions of FLC allows the optimization to chose the location parameters of the regional controllers. The scheduled controller's valid region of operation is maximized, thus efficiently achieving full envelope operation, while guaranteeing pre-specified tracking performance. © 1997 by John Wiley & Sons, Ltd. This paper was produced under the auspices of the US Government and it is therefore not subject to copyright in the US.     

Design of a multilevel fuzzy controller for nonlinear systems and stability analysis

In this paper, a multilevel fuzzy control (MLFC) system is developed and implemented to deal with the real-world nonlinear plants with intrinsic uncertainties and time-varying parameters. The proposed fuzzy control strategy has a hierarchical structure with an adaptation mechanism embedded in the lower level to tune the output membership functions (MFs) of the first layer fuzzy controller and can be used to control a system with an input-output monotonic relationship or a piecewise monotonic relationship. The stability of the closed-loop system under the proposed MLFC is theoretically proven. Simulations are carried out by applying the proposed multilevel fuzzy control (MLFC) to a uncertain nonlinear plants, and it is shown that much better system performances are achieved compared with conventional fuzzy logic controllers (FLC), even in presence of disturbance and noise.     

Design of a fuzzy logic controller for a jet engine fuel system

The design, implementation and evaluation of two types of fuzzy logic controllers (FLC) are presented. The system under consideration is the control of fuel delivery in a jet engine test bench. Two methods of designing FLCs were experimented with. The first method included the development of a tool that inputs the rules, membership functions, and outputs the appropriate consequences. The second method was based on bivariante curve development and scaling. The evaluations of the proposed controllers were performed with an existing proportional–integral (PI) controller. Both of the design methodologies were proven to be superior in comparison with the conventional controller currently utilized for the control of combustion pressure on jet engines.     

Fuzzy logic controller design for spacecraft proximity operations

A Genetic Algorithms (GAs) based method is presented in this paper for concurrent design of rule sets and membership functions for a fuzzy logic controllers to be used in spacecraft proximity operations. The heuristic nature of fuzzy logic makes GAs a natural candidate for logic design in which both rule sets and membership functions are optimized simultaneously. The employment of GAs natural genetic operations provides a means to search in a complex system space that is difficult to described mathematically. A one-dimensional controller for spacecraft proximity operations is implemented for examination in detail. The expension of the algorithm for a 6 DOP controller is discussed.     

Design of fuzzy controllers with adaptive rule insertion

In this paper, an approach of designing adaptive fuzzy controllers is presented to systematically develop efficient and effective rules for fuzzy controllers. The proposed fuzzy controllers are first designed with two basic fuzzy if-then rules. Then according to the design requirements of the fuzzy control system, new fuzzy if-then rules are inserted into the rule-base structure of the fuzzy controller. Initially the inserted fuzzy rules are redundant in the sense that the resultant input-output mapping of the fuzzy rules remains intact. After that the parameters of the membership functions for the fuzzy sets of the newly added fuzzy rules are trained on-line to minimize predefined cost functions. Thus, efficient fuzzy controllers can be systematically designed. Simulations for linear, nonlinear, and delayed systems are provided to show the effectiveness of the proposed approach.     

Simultaneous design of membership functions and rule sets for fuzzycontrollers using genetic algorithms

This paper examines the applicability of genetic algorithms (GA's) in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions; however, the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology. When GA's have been used to develop both, it has been done serially, e.g., design the membership functions and then use them in the design of the rule set. This, however, means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently. GA's are fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. This new method has been applied to two problems, a cart controller and a truck controller. Beyond the development of these controllers, we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules     

Real-time control of a water-gas shift reactor by a model-based fuzzy gain scheduling technique

A model-based fuzzy gain scheduling technique is proposed. Fuzzy gain scheduling is a form of variable gain scheduling which involves implementing several linear controllers over a partitioned process space. A higher-level rule-based controller determines which local controller is executed. Unlike conventional gain scheduling, a controller with fuzzy gain scheduling uses fuzzy logic to dynamically interpolate controller parameters near region boundaries based on known local controller parameters. Model-based fuzzy gain scheduling (MFGS) was applied to PID controllers to control a laboratory-scale water-gas shift reactor. The experimental results were compared with those obtained by PID with standard fuzzy gain scheduling, PID with conventional gain scheduling, simple PID and a nonlinear model predictive control (NMPC) strategy. The MFGS technique performed comparably to the NMPC method. It exhibited excellent control behaviour over the desired operating space, which spanned a wide temperature range. The other three PID-based techniques were adequate only within a limited range of the same operating space. Due to the simple algorithm involved, the MFGS technique provides a low cost alternative to other computationally intensive control algorithms such as NMPC.     

Application of covariance matrix adaptation–evolution strategy to optimal control of hepatitis B infection

To avoid the cirrhosis and liver cancer, antiviral treatment for chronic hepatitis is necessary. In the literature, several mathematical models have been used to describe the dynamics of viral infections. In addition, several control strategies have been reported in the literature to deal with optimal antiviral therapy problem of infectious diseases. In this paper, three controller structures with optimized parameters using covariance matrix adaptation–evolution strategy algorithm are proposed for optimal control of basic hepatitis B virus (HBV) infection dynamical system. The first structure is an optimized neural-type sigmoid-based closed-loop controller, which is a nonlinear feedback controller. The second structure is an optimized open-loop time-based fuzzy controller in which the control input is approximated using the mixture of Gaussian membership functions. Finally, an optimized closed-loop fuzzy controller is used as the third control structure. After designing the controllers, some parameters of the HBV infection model are considered to be unknown and the robustness of the controllers is studied. Experimental results show that the optimized neural-type sigmoid-based closed-loop controller has the best performance in terms of healthy hepatocytes and free HBVs concentration among the investigated controllers and the optimized closed-loop fuzzy controller is the best in terms of minimum mean control input signal that is the drug usage. Concerning the robustness, the optimized neural-type sigmoid-based closed-loop controller has the best performance.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach

In this paper, a novel fuzzy logic controller called linguistic-hedge fuzzy logic controller in a mixed-signal circuit design is discussed. The linguistic-hedge fuzzy logic controller has the following advantages: 1) it needs only three simple-shape membership functions for characterizing each variable prior to the linguistic-hedge modifications; 2) it is sufficient to adopt nine rules for inference; 3) the rules are developed intuitively without heavy dependence on the endeavors of experts; 4) it performs better than conventional fuzzy logic controllers; and 5) it can be realized with a lower design complexity and a smaller hardware overhead as compared with the controllers that required more than nine rules. In this implementation, a current-mode approach is adopted in designing the signal processing portions to simplify the circuit complexity; digital circuits are adopted to implement the programmable units. This design was fabricated with a TSMC 0.35 /spl mu/m single-polysilicon-quadruple-metal CMOS process. In this chip, the LHFLC processes two input variables and one output variable. Each variable is specified using three membership functions. Nine inference rules, scheduled in a rule table with a dimension of 3 /spl times/ 3, define the relationship implications between these three variables. Under a supply voltage of 3.3 V, the measurement results show that the measured control surface and the control goal are consistent. The speed of inference operation goes up to 0.5M FLIPS that is fast enough for the control application of the cart-pole balance system. The cart-pole balance system experimental results show that this chip works with nine inference rules. Furthermore, by performing some off-chip modifications, such as shifting and scaling on the input signals and output signal of this design, according to the specifications defined by the controlled plants, this design is suitable for many control applications.