Fuzzy control of nonlinear systems using rule adjustment

This book presents a systematic framework targeting at fuzzy modeling and fuzzy control of nonlinear systems with uncertainties. The book is organized into three major parts incorporating 13 chapters. The first part contains four chapters focusing on the modeling of nonlinear dynamical systems by using fuzzy logic. The second part includes five chapters in which fuzzy inference and control techniques are addressed. The final part consists of four chapters, which covers several advanced topics in fuzzy control ranging from controller and filter design to chaotification of fuzzy systems and feedforward fuzzy control of nonlinear systems via Fourier integrals. One of the major contributions of this book is that it presents the latest original research developments in the field. It provides rich examples and references, too. It is a valuable resource for those researchers and practitioners interested in expanding their knowledge from fuzzy logic and applications to nonlinear dynamical systems.

We show how frequency domain design procedures can be effectively used in nonlinear fuzzy control systems. For this purpose, theoretical justifications of the approach discussed here are provided to show that solid notions from nonlinear system and control theory can be successfully applied in the fuzzy control domain. The methodology proposed is very simple, but powerful, effective and practical. In addition, it supports systematic control system design and stability analysis in the frequency domain for systems described by mathematical, linguistic or experimental models. Several case studies are included to illustrate the usefulness of frequency response in conventional fuzzy control systems analysis and design.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

This paper investigates the dissipative interval type-2 (IT2) fuzzy control issue for a group of uncertain nonlinear systems subject to randomly occurring sensor saturation and quantization. By utilizing the both lower and upper membership functions with relevant tradeoff moduli, uncertainties, which exist in the considered systems, can be captured effectively. During the design of the IT2 fuzzy controller, we take the actuator failure into consideration. Considering the randomicities for the occurrences of sensor saturation and quantization, two separate Bernoulli stochastic distributed courses are utilized to construct the corresponding complicated transmission route. In term of Lyapunov stability theory, sufficient criteria to design dissipative IT2 fuzzy controller are presented to assure the stochastic stability with strict dissipativity of resulting closed-loop systems. Finally, illustrative example verifies the effectiveness and merits of the control strategy proposed in this paper.

The objective of this study is to enhance the responsiveness and precision of control systems through the acceleration of evolutionary programming in the optimization of nonlinear fuzzy control systems. Nonlinear systems are ubiquitous in engineering practice, presenting significant challenges due to their complexity and uncertainty for traditional control methodologies. Fuzzy control, an intelligent control approach rooted in empirical rules, possesses the capability to navigate uncertain and nonlinear issues. However, conventional fuzzy controllers struggle to achieve optimal control performance when confronted with highly complex nonlinear systems. Consequently, this paper introduces the application of accelerated evolutionary programming (RGA) for the optimization of fuzzy controllers, aiming to augment their performance in nonlinear systems. By merging genetic algorithms with a fuzzy adaptive PID controller, the optimized fuzzy controller is better equipped to adapt to the dynamic changes of nonlinear systems, offering robust and efficient control strategies. The results of simulation experiments demonstrate a marked improvement in response time, stability, and error reduction with the fuzzy control system based on RGA optimization. This study offers novel insights and methodologies for the further optimization of control within nonlinear systems, while providing theoretical support for the practical applications of complex systems.

The present paper utilizes covariance matrix adaptation (CMA), an evolution strategy, in conjunction with H∞-based robust control law to design a stable adaptive fuzzy controller for a class of non-linear systems. The objective of the design is to develop a self-adaptive optimal/near optimal fuzzy controller, with guaranteed stability and satisfactory robust transient performance. The global search capability of CMA and H∞-based tuning, that provide a fast adaptation utilizing local search method, is employed in tandem with this proposed design methodology. The hybrid control strategy is implemented for benchmark simulation case study, and the results demonstrate the usefulness of the proposed approach.

The antilock braking system (ABS) is designed to optimize braking effectiveness and maintain steerability; however, the ABS performance will be degraded in the case of severe road conditions. In this study, a self-learning fuzzy sliding-mode control (SLFSMC) design method is proposed for ABS. The SLFSMC ABS will modulate the brake torque for optimum braking. The SLFSMC system is comprised of a fuzzy controller and a robust controller. The fuzzy controller is designed to mimic an ideal controller and the robust controller is designed to compensate for the approximation error between the ideal controller and the fuzzy controller. The tuning algorithms of the controller are derived in the Lyapunov sense; thus, the stability of the system can be guaranteed. Also, the derivation of the proposed SLFSMC ABS does not need to use a vehicle-braking model. Simulations are performed to demonstrate the effectiveness of the proposed SLFSMC ABS in adapting to changes for various road conditions.

The paper describes the development of two different type-2 adaptive fuzzy logic controllers and their use for the control of a non linear system that is characterized by the presence of bifurcations and parameter uncertainty. Although a type-2 fuzzy logic controller is able to handle the non linearities and the uncertainties present in a system, its robustness and effectiveness can be increased by the use of an opportune adaptive algorithm. A simulation study was conducted to compare the behavior of adaptive controllers with that of simple type-1 and type-2 fuzzy logic controllers. The system to be controlled, used for the simulation, is a continuous bioreactor for the treatment of mixed wastes in which a culture of Pseudomonas Putida is carried out while phenol and glucose are carbon and energy sources. From simulations results it can be seen that both adaptive controllers, but in particular the self tuning controller, have a better performance being able to eliminate oscillations that are present with basic fuzzy controllers.

This study considers the tracking control problem of the nonstrict-feedback nonlinear system with unknown backlash-like hysteresis, and a finite-time adaptive fuzzy control scheme is developed to address this problem. More precisely, the fuzzy systems are employed to approximate the unknown nonlinearities, and the design difficulties caused by the nonlower triangular structure are also overcome by using the property of fuzzy systems. Besides, the effect of unknown hysteresis input is compensated by approximating an intermediate variable. With the aid of finite-time stability theory, the proposed control algorithm could guarantee that the tracking error converges to a smaller region. Finally, a simulation example is provided to further verify the above theoretical results.

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

A new stable Adaptive Interval Type-2 Fuzzy Proportional Integral Sliding Mode Controller (AI2FPISMC) is introduced here to control a class of nonlinear systems. The proposed method is based on interval type-2 fuzzy logic system (IT2FLS) whose antecedent and consequent membership functions are interval type-2 fuzzy sets. IT2FLS is utilized to approximate unknown nonlinear functions. To achieve high performance, optimizing membership functions (MFs) of interval type-2 fuzzy sets (IT2FS) is required. Genetic algorithm (GA) is a parallel search optimization method; that here contributes to optimize the MFs. In order to cope with the chattering of sliding mode controller, PI control law is proposed and Lyapunov analysis is utilized to prove asymptotic stability of the proposed approach. The adaptation laws are derived using Lyapunov approach. Two nonlinear system simulation examples are presented to verify the effectiveness of the proposed method, and their results confirm the optimization merits.

There are two main drawbacks in fuzzy control: 1) the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters; and 2) the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur. In this paper we illustrate these two problems on a two-link flexible robot testbed by: 1) developing, implementing, and evaluating a fuzzy controller for the robotic mechanism, and 2) illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system. Next, we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule-base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed, and automatically tune the fuzzy controller so that it can adapt to variations in the payload. >

In this study, we strive to combine the advantages of fuzzy logic control (FLC), genetic algorithms (GA), H∞ tracking control schemes, smooth control and adaptive laws to design an adaptive fuzzy sliding model controller for the rapid and efficient stabilization of complex and nonlinear systems. First, we utilize a reference model and a fuzzy model (both involving FLC rules) to describe and well-approximate an uncertain, nonlinear plant. The FLC rules and the consequent parameter are decided on via GA. A boundary-layer function is introduced into these updated laws to cover modeling errors and to guarantee that the state errors converge into a specified error bound. After this, a H∞ tracking problem is characterized. We solve an eigenvalue problem (EVP), and derive a modified adaptive neural network controller (MANNC) to simultaneously stabilize and control the system and achieve H∞ control performance. Furthermore, a stability criterion is derived utilizing Lyapunov’s direct method to ensure the stability of the nonlinear system. Finally, the control methodology is demonstrated via a numerical simulation.

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

A PI-like fuzzy controller is designed and implemented for the inverted pendulum system. First, the proposed fuzzy controller adopts the step response phase trajectories to derive the corresponding linguistic control rules of such a system, then applies the relationship between input and output signals in a proportional integral controller to convert the relationship of linguistic control rules to a decision table. At the same time, the membership function's shape is mapped and tuned with constant proportional gain and constant integral gain. Finally, the fuzzy controller of the inverted pendulum system is accomplished by the designed decision table and the determined membership function. By using the Single Board Fuzzy Controller, made by Togai InfraLogic Inc., the proposed methods are proved.