Fuzzy Model-based Control Research Articles

Fuzzy Scheduler Fault-Tolerant Control for Wind Energy Conversion Systems

In this paper, a new fuzzy scheduler fault-tolerant control method is proposed for nonlinear systems subject to sensor faults, parameter uncertainties, wind disturbance, and state variables unavailable for measurements. An algorithm based on the reconfiguration mechanism is then investigated for detection, isolation, and accommodation of sensor faults. The Takagi-Sugeno fuzzy model is employed to represent the nonlinear wind energy conversion system, and then a model-based fuzzy scheduler controller design uses the concept of general-distributed compensation. Sufficient stability conditions are expressed in terms of linear matrix inequalities, which can be solved very efficiently using convex optimization techniques. The proposed algorithm maximizes the produced power and minimizes the voltage ripple and is able to maintain stability of the system during sensor faults, wind disturbance, and parameter uncertainties. The design procedures are applied to a dynamics model of the typical wind energy conversion system to illustrate the effectiveness of the proposed control technique.

An interval-valued fuzzy controller for complex dynamical systems with application to a 3-PSP parallel robot

In this paper, we present a novel interval-valued fuzzy model-based controller for handling the effects of uncertainty in controlling a complex dynamical system. Theoretically, model-based controllers may be the ideal control mechanisms; however, they are highly sensitive to model uncertainties and lack robustness. These controllers are also computationally intensive, rendering them unusable for many real-world applications. In this work, we incorporate an interval fuzzy logic paradigm into a computed-torque controller for a 3-PSP parallel robot. This paradigm aims to handle the uncertainties in the robot model. The proposed approach benefits from algebraic operations on type-I fuzzy numbers to enhance its capability in dealing with uncertainty. The simulations prove the superiority of the proposed controller in the presence of uncertainty. Furthermore, comparisons with a competing type-I reduced controller as well as a PD controller show this superiority to be more pronounced especially when noise level is remarkably high. Moreover, the designed controller satisfies the computational complexity constraints for real-time implementation.

Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

This paper investigates the stability of fuzzy-model-based (FMB) control system, formed by a T–S fuzzy model and a fuzzy controller connected in a close loop, based on a fuzzy-Lyapunov function. A general FMB control system that the T–S fuzzy model and fuzzy controller not sharing the same premise membership functions and/or the same number of fuzzy rules is considered. A membership-function-dependent stability analysis approach is proposed to consider the membership functions of both the T–S fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities. As the stability conditions are membership-function dependent, they are dedicated to the FMB control system with the specified membership functions under consideration. It is thus the membership-function-dependent stability conditions are more relaxed compared to the existing membership-function-independent stability conditions. A fuzzy-Lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work. In this paper, this criterion is not required and thus the stability conditions can be further relaxed. Some simulation examples are given to demonstrate the merits of the proposed approach.

델타 연산자를 이용한 관측기 기반 출력 궤환 퍼지 제어기의 디지털 재설계

본 논문은 미리 설계된 타카기-수게노 퍼지 모델 기반 아날로그 제어기를 상태 정합의 의미에서 등가인 샘플치 제어기로 효율적으로 변환하기 위해, 관측기 기반 출력 궤환 퍼지 제어기에 대한 지능형 디지털 재설계 기법을 제안한다. 아날로그 제어 시스템과 샘플치 제어 시스템 사이의 점근적 연관성을 위해 델타 연산자를 사용한다. 지능형 디지털 재설계 문제는 정합될 선형 연산자 간의 놈의 거리를 최소화하는 문제로 생각한다. 제어기 설계 조건은 선형행렬부등식의 형태로 유도되며, 디지털 재설계시 관측기와 제어기에 대한 분리 설계 조건이 만족함을 보인다. This paper addresses an intelligent digital redesign (IDR) technique for observer-based output-feedback control systems, in order to efficiently convert a pre-designed Takagi-Sugeno fuzzy model-based analog controller into a sampled-data one in the sense of state matching. A delta operator is used to get an asymptotic relation between the analog and the sampled-data control systems. The IDR problem is viewed as a minimization problem of the norm distances between linear operator to be matched. The condition is represented as linear matrix inequalities, and the separation principle on the IDR is shown.

Stability analysis of nonlinear-function fuzzy-model-based control systems

This paper presents the stability analysis of nonlinear-function fuzzy-model-based (FMB) control systems. A fuzzy model with nonlinear function terms is proposed to represent nonlinear plants. A fuzzy controller with the nonlinear function terms is then proposed to close the feedback loop. The nonlinear function terms enhance the capability of fuzzy modelling and feedback compensation. Following the linear-matrix-inequality (LMI) based stability analysis approach for the traditional FMB control systems, it will lead to stability conditions involving the nonlinear terms for the proposed nonlinear-function FMB control systems. As a result, the stability conditions will have an infinite number of LMIs, which make it impractical to find a feasible solution numerically using convex programming techniques. A stability analysis approach is proposed to obtain effective LMI-based stability conditions for the proposed nonlinear-function FMB control systems. Simulation examples are given to illustrate the merits of the proposed fuzzy control approach.

Design of optimized fuzzy model-based controller for nonlinear systems using hybrid intelligent strategies

This paper introduces three hybrid methods for the generation and optimization of rules and membership functions of a fuzzy logic controller for nonlinear systems. The proposed methods overcome the deficiency of a systematic approach for optimal design of fuzzy controllers. An optimally designed fuzzy logic controller should have the least number of fuzzy variables and fuzzy rules and the best possible configuration of fuzzy rules in the rule table. The first strategy of this paper is a two-phase optimization problem: in the first phase, the number of fuzzy variables and their arrangement in the rule table are optimized by a genetic algorithm; in the second phase, the parameters of the membership functions are optimized via extended Kalman filtering. The second strategy tries to achieve the goals of the first method all in one phase by modifying the chromosome structure of the genetic algorithm. Then in the next step, a local search algorithm is utilized to improve the obtained results. The third strategy is similar to the second strategy in structure. However, along with optimizing the number of fuzzy variables and membership parameters, the number of fuzzy rules is also optimized. The first and second strategies are obliged to use every possible combination of fuzzy variables in the rule table; however, the third strategy is capable of distinguishing between useful and useless fuzzy rules in the rule table. The introduced strategies are applied to an automotive cruise control system. The results of the simulations show the effectiveness of the proposed methods and the superiority of the latter approaches over the former ones.

Robust speed control method for permanent magnet synchronous motor

This study develops a Takagi–Sugeno (T–S) fuzzy model-based robust controller which can precisely track a reference trajectory by cancelling out the effects of unknown external noises and parameter uncertainties on a surface-mounted permanent magnet synchronous motor (SPMSM). Furthermore, the speed tracking control algorithm demands the load torque information, so a simple load torque observer is used to estimate it. The stability of the proposed controller and the load torque observer is mathematically studied. The proposed control scheme is executed on a PMSM drive using a digital signal processor (TMS320F28335). Finally, the simulation and experimental results are presented to verify that the proposed methodology achieves a better robust performance, a less steady-state error and a faster dynamic response than the non-linear control method in the presence of unknown external noises and SPMSM parameter uncertainties.

T–S fuzzy control for dithered nonlinear singularly perturbed systems with multiple time delays

This paper is concerned with the stability problem of nonlinear multiple time-delay singularly perturbed (NDSP) systems. To overcome the effect of modeling error between the reduced-order model of the NDSP plant and Takagi–Sugeno (T–S) fuzzy models, a robustness design of model-based fuzzy control is proposed in this study. A stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of NDSP systems. According to this criterion, a model-based fuzzy controller is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NDSP system. If the designed fuzzy controller cannot stabilize the NDSP system, a high-frequency signal, commonly referred to as dither, is simultaneously introduced to stabilize it. Based on the relaxed method, the NDSP system can be stabilized by regulating appropriately the parameters of dither. If the dither’s frequency is high enough, the output of the dithered reduced system and that of its corresponding mathematical model – the relaxed reduced system – can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered reduced system based on the one of the relaxed reduced system.

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model‐based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS‐based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

Robust Maximum Power Tracking Control of Uncertain Photovoltaic Systems: A Unified T-S Fuzzy Model-Based Approach

This paper presents a unified T-S fuzzy model-based maximum power control approach to enhance the efficiency and robustness of the solar photovoltaic (PV) power generation. First, the maximum-power-voltage-based control scheme and direct maximum power control scheme are introduced for the maximum power point tracking (MPPT). By using T-S fuzzy model representation, the two MPPT control schemes are formulated to an output tracking control problem in a unified form. Then, the T-S fuzzy observer and controller are developed to achieve asymptotic MPPT for uncertain PV power systems, where the controller and observer gains are able to be separately solved from novel linear matrix inequality formulation. Furthermore, the MPPT robustness is also discussed in the presence of rapidly changing atmosphere and external disturbances. Different from the traditional MPPT approaches, the proposed T-S fuzzy controller does not require searching the maximum power operational point and using coordinate transformation. All the buck, boost, or buck-boost converters can be used to achieve MPPT in the same control method. Finally, the satisfactory performance is shown from the simulation and experimental results.

Fuzzy Gain Scheduled Multivariable Control of Nonlinear System Using PSO Based PID

In this paper, Particle swarm optimization (PSO) is utilized to optimize the coefficients of decoupling controllers for a nonlinear process. The optimization criteria considered is the Integral Square Error (ISE) to minimize the tracking error. The controller is tuned at chosen operating points, which are selected to cover the nonlinear range of the process. The optimal PID controller parameters are gain scheduled using Sugeno Fuzzy Gain scheduler. Fuzzy gain scheduling is a special form of model-based fuzzy control that uses linguistic rule fuzzy reasoning to determine the controller parameter transition policy for a dynamic plant subject to large changes in the operating state. The effectiveness of the proposed control scheme has been demonstrated by conducting simulation studies on a Continuous Stirred Tank Reactor (CSTR) which exhibits dynamic nonlinearity.

T–S fuzzy model-based tracking control of a one-dimensional manipulator actuated by pneumatic artificial muscles

Pneumatic artificial muscle (PAM) has highly nonlinear and time-varying behavior due to gas compression and nonlinear elasticity of the bladder containers. Hence, it is difficult to achieve excellent tracking performance when using classical control methods. This study proposes a Takagi–Sugeno (T–S) fuzzy model-based control for improving control performance. The proposed approach decomposes the model of a nonlinear system into a set of linear subsystems. This allows, the T–S fuzzy model-based controller to use simple linear control techniques providing a systematic framework for the design of a state feedback controller. Stability analysis is carried out using Lyapunov direct method. The powerful LMI Toolbox in MATLAB is employed to solve linear matrix inequalities (LMIs) to obtain the controller gains. Experimental results verified that the proposed controller can achieve excellent tracking performance under different disturbances.

LMI-Based Stability Analysis for Fuzzy-Model-Based Control Systems Using Artificial T–S Fuzzy Model

This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.

T–S fuzzy model-based impulsive control for chaotic systems and its application

Abstract This paper provides the impulsive control for chaotic systems based on Takagi–Sugeno (T–S) model. A less conservative impulsive control scheme for chaotic systems based on their T–S fuzzy model is presented. Then the proposed impulsive control scheme is successfully applied to stabilize Lorenz system and the numerical simulation illustrates the effectiveness of our results.

Extruder Melt Temperature Control With Fuzzy Logic

AbstractIn polymer extrusion, the delivery of a melt which is homogenous in composition and temperature is paramount for achieving high quality extruded products. However, advancements in process control are required to reduce temperature variations across the melt flow which can result in poor product quality. The majority of thermal monitoring methods provide only low accuracy point/bulk melt temperature measurements and cause poor controller performance. Furthermore, the most common conventional proportional-integral-derivative controllers seem to be incapable of performing well over the nonlinear operating region. This paper presents a model-based fuzzy control approach to reduce the die melt temperature variations across the melt flow while achieving desired average die melt temperature. Simulation results confirm the efficacy of the proposed controller.

Fuzzy Model-based Servo Control for Discrete-Time Nonlinear Systems with Constraints

AbstractThis paper presents servo control for discrete-time nonlinear systems with constraints on inputs and states using the fuzzy model-based control approach. Firstly, the nonlinear error system is constructed based on error vector between state and the target point by utilizing the input difference between current input and cancellation input. Secondly, the error system is exactly converted into a Takagi-Sugeno fuzzy model utilizing sector nonlinearity approach. Finally, the fuzzy servo controller is designed by simultaneously solving servo controller design condition and the constraint conditions on inputs and states. The design conditions are given in the form of LMI. Servo control with constraints on inputs and states is achieved by the designed servo controller. Design examples illustrate the utility of this approach.

Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach

This study investigates the systems stability of fuzzy-model-based (FMB) control systems. Based on the T-S fuzzy model representing the non-linear system, a fuzzy controller using grid-point (GP) technique is proposed to close the feedback loop. A GP is defined as the sub-operating domain of the non-linear system. For each GP, a corresponding GP fuzzy controller is employed to control the system. As the non-linearity in each GP is lower compared to that of the full operating domain, it is in favour of yielding relaxed stability analysis result using the GP control technique of which the nature of the membership functions and operating domain are taken into account. Furthermore, unlike most of the fuzzy control approaches, the proposed one can be applied to FMB control systems subject to imperfect premise matching that the fuzzy model and fuzzy controller do not share the same premise membership functions. As a result, some simple membership functions can be employed for the fuzzy controllers to lower the implementation cost. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived to guarantee the system stability and facilitate the controller synthesis. Simulation examples are given to demonstrate the merits of the proposed FMB control scheme using the proposed GP technique.

SOS-Based Stability Analysis of Polynomial Fuzzy-Model-Based Control Systems Via Polynomial Membership Functions

This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been reported in the form of SOS-based stability conditions. Lack of information on the relations between membership functions and premise variables, in the existing stability analysis approaches, causes conservatism of their results. In this paper, to derive relaxed stability conditions for polynomial FMB control systems, membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis. Considering a polynomial FMB control system and based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived, where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller. Each product term is approximated by a polynomial. In order to obtain better approximation, the operating domain of membership functions is partitioned to subregions. Then, SOS-based stability conditions for all subregions are derived. Unlike some published stability-analysis approaches, the proposed one can be employed for stability analysis of polynomial fuzzy-control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions. The solution of the SOS-based stability conditions can be found numerically using SOSTOOLS, which is a free third-party MATLAB Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.

FUZZY LOGIC-BASED INVERSE DYNAMIC MODELLING OF ROBOT MANIPULATORS

This paper presents the design and implementation of a systematic fuzzy modelling methodology for the inverse dynamic modelling of robot manipulators. The fuzzy logic modelling methodology is motivated in part by the difficulties encountered in the modelling of complex nonlinear uncertain systems, and by the objective of developing an efficient dynamic model for the real-time model-based control. The methodology is applied to build the fuzzy logic-based inverse dynamic model of a prototyped wire-actuated parallel manipulator with uncertain dynamics. The developed inverse dynamics has been used in a fuzzy model-based adaptive robust controller for the tracking control of the parallel manipulator.

Model-Based Multi-input, Multi-output Supervisory Semi-active Nonlinear Fuzzy Controller

Abstract: The authors recently proposed a new multi-input, single-output (MISO) semi-active fuzzy controller for vibration control of seismically excited small-scale buildings. In this article, the previously proposed MISO control system is advanced to a multi-input, multi-output (MIMO) control system through integration of a set of model-based fuzzy controllers that are formulated in terms of linear matrix inequalities (LMIs) such that the global asymptotical stability is guaranteed and the performance on transient responses is also satisfied. The set of model-based fuzzy controllers is divided into two groups: lower level controllers and a higher level coordinator. The lower level fuzzy controllers are designed using acceleration and drift responses; while velocity information is used for the higher level controller. To demonstrate the effectiveness of the proposed approach, an eight-story building structure employing magnetorheological (MR) dampers is studied. It is demonstrated from comparison of the uncontrolled and semi-active controlled responses that the proposed design framework is effective in vibration reduction of a building structure equipped with MR dampers.