An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.     

An approach to improve active disturbance rejection control

ABSTRACT

In order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.     

A simplified version of mamdani's fuzzy controller: the natural logic controller

This paper proposes the natural logic controller (NLC) that it comes through a very important simplification of the Mamdani's fuzzy controller (MFC) allowing easy-design for single-input-single-output (SISO) regulation problems. Usually, fuzzy controllers are built with two classical signals of process: The error and its rate of change. They use a moderate number of fuzzy subsets and fuzzy rules. The main features of the NLC approach are that use the minimal fuzzy partition (only two fuzzy subsets per variable) and it use the minimal fuzzy rule base (only two rules). The nonlinear resulting fuzzy controller is the simplest one with an analytically well-defined, input-output mapping and accepting a linear approximation at origin. It allows easy extension to more than two signals of process. Some properties of nonlinear mapping of NLC are analyzed and some results are also presents on testing stability when NLC is used on a linear process. A special attention is addressed to the two inputs NLC case, where stability can be tested using the circle criterion. Finally, two application examples are discussed in details.     

An approach to adaptive control of fuzzy dynamic systems

This paper discusses adaptive control for a class of fuzzy dynamic models. The adaptive control law is first designed in each local region and then constructed in the global domain. It is shown that the resulting fuzzy adaptive control system is globally stable. Robustness issues of the adaptive control system are also addressed. A simulation example is given for demonstration of the application of the approach     

A general approach to rule aggregation in fuzzy logic control

We look at the representation and aggregation of individual rules in the fuzzy logic control system. Two extreme paradigms for rule representation are introduced, the Mamdani model and the logical model. We look at the characteristics of these approaches. We then combine these two approaches to get a general model for the representation of rules. From this general formulation we obtain two soft classes of rules aggregation, or-like and and-like aggregations.     

模糊控制规则优化方法研究

模糊控制规则的选择是模糊控制器设计的关键问题之一,在现有应用遗传算法优化模糊控制规则的方法进行研究的基础上,以模糊控制规则的完整性和一致性为出发点,提出了一种用遗传算法来优化模糊控制规则的改进算法,具体给出了遗传算法设计中的各种函数和算子的确定,并将优化过的规则用于设计模糊控制器,进行仿真研究,取得了令人满意的效果。     

Four wheel steering control by fuzzy approach

This study introduces a fuzzy four-wheel steering control design method for automotive vehicles. After the analysis of some stability aspects of the vehicle lateral motion, including front steering angle variations, the representation of vehicle nonlinear model by Takagi-Sugeno (T-S) fuzzy model is presented. Next, based on the fuzzy model, a fuzzy controller is developed to improve the stability of the vehicle. Sufficient conditions for stability and stabilization of the T-S fuzzy model using fuzzy feedback controllers is given. To demonstrate the effectiveness of the proposed fuzzy controller, simulation results are given showing the performance improvements of the vehicle in terms of the stability and the maneuverability in critical situations.     

A multiple Lyapunov function approach to stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.     

A new approach to fuzzy modeling and control of discrete-time systems

We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new representation, designated the hyperbolic model, combines the advantages of fuzzy system theory and classical control theory. On the one hand, the hyperbolic model is easily derived from a set of Mamdani-type fuzzy rules. On the other hand, classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of Mamdani-type fuzzy rules. Thus, this new approach combines the best of two worlds. It enables linguistic interpretability of both the model and the controller, and guarantees closed-loop stability and robustness.     

Fault tolerant control using a fuzzy predictive approach

This paper proposes the application of fault-tolerant control (FTC) using fuzzy predictive control. The FTC approach is based on two steps, fault detection and isolation (FDI) and fault accommodation. The fault detection is performed by a model-based approach using fuzzy modeling and fault isolation uses a fuzzy decision making approach. The information obtained on the FDI step is used to select the model to be used in fault accommodation, in a model predictive control (MPC) scheme. The fault accommodation is performed with one fuzzy model for each identified fault. The FTC scheme is used to accommodate the faults of two systems a container gantry crane and three tank benchmark system. The fuzzy FTC scheme proposed in this paper was able to detect, isolate and accommodate correctly the considered faults of both systems.     

A novel approach for multistage inference fuzzy control

This paper presents a methodology to the design of a multistage inference fuzzy controller in which the consequence in an inference stage is passed to the next stage as fact, and so forth. A new general method which is based on a performance index of the control system is used to generate fuzzy rule bases for the multistage inference. This proposed method can reduce the design cycle time. In order to reduce the computation time, a method for precomputing the match-degrees of fuzzy values is adopted. Thus, the number of operations that must be carried out at execution time can be significantly reduced. The new method has been applied to two applications, a two-trailer-and-truck system and a three-trailer-and-truck system. The simulation studies showed that the proposed method is feasible.     

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.     

A fuzzy reinforcement learning approach to power control in wireless transmitters.

We address the issue of power-controlled shared channel access in wireless networks supporting packetized data traffic. We formulate this problem using the dynamic programming framework and present a new distributed fuzzy reinforcement learning algorithm (ACFRL-2) capable of adequately solving a class of problems to which the power control problem belongs. Our experimental results show that the algorithm converges almost deterministically to a neighborhood of optimal parameter values, as opposed to a very noisy stochastic convergence of earlier algorithms. The main tradeoff facing a transmitter is to balance its current power level with future backlog in the presence of stochastically changing interference. Simulation experiments demonstrate that the ACFRL-2 algorithm achieves significant performance gains over the standard power control approach used in CDMA2000. Such a large improvement is explained by the fact that ACFRL-2 allows transmitters to learn implicit coordination policies, which back off under stressful channel conditions as opposed to engaging in escalating "power wars."     

A new approach to adaptive fuzzy control: the controller outputerror method

The controller output error method (COEM) is introduced and applied to the design of adaptive fuzzy control systems. The method employs a gradient descent algorithm to minimize a cost function which is based on the error at the controller output. This contrasts with more conventional methods which use the error at the plant output. The cost function is minimized by adapting some or all of the parameters of the fuzzy controller. The proposed adaptive fuzzy controller is applied to the adaptive control of a nonlinear plant and is shown to be capable of providing good overall system performance.     

An approach to fuzzy control of nonlinear systems: stability anddesign issues

Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called “parallel distributed compensation” is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart     

Consistent proportional delay differentiation: A fuzzy control approach

Proportional delay differentiation (PDD) is an important service model for providing relative differentiated services on the Internet. It aims to maintain pre-specified packet queueing-delay ratios between different classes of traffic at each hop. Existing rate-allocation approaches for PDD services assume the average queueing delay of a class is inversely proportional to its service rate. This assumption is not necessarily valid when the system is not heavily loaded. To provide consistent PDD services under various load conditions, in this paper, we propose a novel rate-allocation approach that applies fuzzy control theory to capture the nonlinear relationship between the queueing delay and the service rate. In the approach, a class’s service rate is adjusted according to a set of fuzzy control rules defined over its error (the difference between the target delay ratio and the achieved one), the change of error, and the change of service rate. We prove that the fuzzy control system is stable and the service rate of a class converges to its equilibrium point at steady state. Simulation results demonstrate that, in comparison with other rate-allocation approaches, the fuzzy control approach is able to provide consistent PDD services under wide range load conditions. It is also shown robust under various system conditions, including with multiple classes, changing target delay ratios, changing load conditions, and different traffic patterns.     

Control-affine fuzzy neural network approach for nonlinear process control

An internal model control strategy employing a fuzzy neural network is proposed for SISO nonlinear process. The control-affine model is identified from both steady state and transient data using back-propagation. The inverse of the process is obtained through algebraic inversion of the process model. The resulting model is easier to interpret than models obtained from the standard neural network approaches. The proposed approach is applied to the tasks of modelling and control of a continuous stirred tank reactor and a pH neutralization process which are not inherently control-affine. The results show a significant performance improvement over a conventional PID controller. In addition, an additional neural network which models the discrepancy between a control-affine model and real process dynamics is added, and is shown to lead to further improvement in the closed-loop performance.     

A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems

This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature. A rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases. In comparison with conventional conditions, the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design. The latter design work is quite hard for T-S fuzzy control systems. Based on the LMI-based conditions derived, one can easily synthesize controllers for stabilizing T-S fuzzy control systems. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.     

How to improve computer advisory services

There are an increasing number of active computer users who are not computer professionals and so require continuous guidance in order to effectively employ computer facilities. In universities such guidance is provided by a formal advisory service. While advisory services play a vital role for university users, there are numerous problems which can detract from their effectiveness. This paper identifies many of these problems, and recommends ways of overcoming them. These suggestions are largely based on the results of a research project carried out for the past four years at the University of Liverpool. Topics considered are: (i) the assessment of various methods for organizing advisory services; (ii) the specific needs of inexpert users and strategies for effectively advising them; (iii) problems of the comprehension of computing information; (iv) guidelines for good advisory communication; (v) methods for improving the professional status of the advisory function.