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.     

Genetic fuzzy system for data-driven soft sensors design

This paper proposes a new method for soft sensors (SS) design for industrial applications based on a Takagi–Sugeno (T–S) fuzzy model. The learning of the T–S model is performed from input/output data to approximate unknown nonlinear processes by a coevolationary genetic algorithm (GA). The proposed method is an automatic tool for SS design since it does not require any prior knowledge concerning the structure (e.g. the number of rules) and the database (e.g. antecedent fuzzy sets) of the T–S fuzzy model, and concerning the selection of the adequate input variables and their respective time delays for the prediction setting. The GA approach is composed by five hierarchical levels and has the global goal of maximizing the prediction accuracy. The first level consists in the selection of the set of input variables and respective delays for the T–S fuzzy model. The second level considers the encoding of the membership functions. The individual rules are defined at the third level, the population of the set of rules is treated in fourth level, and a population of fuzzy systems is handled at the fifth level. To validate and demonstrate the performance and effectiveness of the proposed algorithm, it is applied on two prediction problems. The first is the Box–Jenkins benchmark problem, and the second is the estimation of the flour concentration in the effluent of a real-world wastewater treatment system. Simulation results are presented showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily with appropriate input variables and delay selection and a reasonable number of rules. The proposed methodology is able to design all the parts of the T–S fuzzy prediction model. Moreover, presented comparison results indicate that the proposed method outperforms other previously proposed methods for the design of prediction models, including methods previously proposed for the design of T–S models.     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.     

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi–Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T–S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T–S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.     

Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching

This paper investigates the stability analysis and performance design of nonlinear systems. To facilitate the stability analysis, the Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear plant. Under the imperfect premise matching in which T–S fuzzy model and fuzzy controller do not share the same membership functions, a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant. However, the nice characteristic given by the perfect premise matching, leading to conservative stability conditions, vanishes. In this paper, under the imperfect premise matching, information of membership functions of the fuzzy model and controller are considered in stability analysis. With the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based stability conditions are derived using Lyapunov-based approach. Furthermore, LMI-based performance conditions are provided to guarantee system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.      

Robustness design of nonlinear dynamic systems via fuzzy linearcontrol

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H^∞ robustness performance. First, the Takagi and Sugeno fuzzy linear model (1985) is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H^∞ performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H^∞ scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H^∞ control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method     

基于T-S模型的非线性时滞系统非脆弱保性能模糊控制

针对一类用T-S模糊模型描述的非线性时滞系统,采用状态反馈的并行分布补偿方法,研究其保守性较小的非脆弱保性能模糊控制问题,使闭环系统在控制器存在加性摄动的情况下,其闭环性能指标值低于确定的上界.利用线性矩阵不等式处理方法,导出了非脆弱保性能模糊控制律的存在条件,通过建立和求解一个线性矩阵不等式问题,给出了非脆弱保性能模糊控制律的设计方法.仿真结果表明了所提出方法的有效性.     

Fuzzy path tracking control for automatic steering of vehicles

In this paper, the path tracking (PT) control for automatic steering of vehicles is studied. The Takagi–Sugeno (T–S) fuzzy model of vehicle obtained from a nonlinear model is considered and a fuzzy controller is designed. The stability analysis is discussed using Lyapunov’s approach combined with the linear matrix inequalities (LMI) approach. Finally, simulation results are given to demonstrate the controller’s effectiveness.     

Fault-tolerant control of three-pole active magnetic bearing

Active magnetic bearings have many advantages over conventional bearings due to contactless operation and adjustable force dynamics. However, one of the obstacles associated with these bearings is failure modes, which may result in destructive rotor dynamic behaviour. One of the important failure modes is electric power outage which may be due to failure of power amplifier, coil or electric wiring. In the present work, a fault tolerant controller has been designed for three-pole magnetic bearings to provide unaltered performance in the event of fault occurrence. The controller has been designed by incorporating the nonlinear fuzzy logic control. The present design of fuzzy logic controller is done by reducing the number of rules of its rule base. Simulations have been carried out to test the performance of the controller for different failure conditions. The designed controller is able to stabilize the rotor for large deviations from the origin even in the presence of failure. The controller is found to be robust as it provides satisfactory operation in the presence of uncertainties.     

Design of high performance linear feedback laws for operation that extends into the nonlinear region of AMB systems

Existing active magnetic bearings (AMBs) operate in the linear region of the magnetic material flux density, which limits the utilization of the bearing capacity. In order to increase the utilization of the bearing capacity and enhance the performance of the AMB system, this paper develops a method for designing high performance linear feedback laws. The resulting feedback laws allow the AMB to operate in its nonlinear region and hence improve the closed-loop performance. We first establish an approximate nonlinear AMB current force response model, and place this nonlinear curve inside a sector formed by two piecewise linear lines. Based on the linear line segments in these two piecewise linear lines, we determine the maximum disturbance that can be tolerated by solving an optimization problem with linear matrix inequality (LMI) constraints. For a given level of disturbance under the maximum tolerable disturbance, we formulate and solve the problem of designing the linear feedback that achieves the highest level of disturbance rejection as another LMI problem. Both $L_2$ disturbances and $L_\infty$ disturbances are considered. Finally, we illustrate our design by both simulation and experimental results.     

Reliable LQ fuzzy control for continuous-time nonlinear systems with actuator faults

This paper deals with the reliable linear quadratic (LQ) fuzzy control problem for continuous-time nonlinear systems with actuator faults. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear system. By using multiple Lyapunov functions, an improved linear matrix inequality (LMI) method for the design of reliable LQ fuzzy controllers is investigated, which reduces the conservatism of using a single Lyapunov function. The different upper bounds on the LQ performance cost function for the normal and different actuator fault cases are provided. A suboptimal reliable LQ fuzzy controller is given by means of an LMI optimization procedure, which can not only guarantee the stability of the closed-loop overall fuzzy system for all cases, but also provide an optimized upper bound on a weighted average LQ performance cost function. Finally, numerical simulations on the chaotic Lorenz system are given to illustrate the application of the proposed design method.     

基于LMI的一类非线性多时滞系统的模糊H∞滤波器设计

This paper develops fuzzy H1 filter for state estimation approach for nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. We design a stable fuzzy H1 filter based on the Takagi-Sugeno (T-S) fuzzy model, which assures asymptotic stability and a prescribed H1 index for the filtering error system. Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem. The LMI problem can be efficiently solved with global convergence using the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the proposed method.     

基于LMI的模糊控制器设计方法

针对Ｔ－Ｓ模糊模型,提出同时满足稳定条件和控制受约束的模糊控制器的线性矩阵不等式设计方法。将稳定性及控制约束转化为满足Ｌｙａｐｕｎｏｖ稳定的凸优化问题,并提出了ＬＭＩ的模糊系统控制器设计和稳定性分析的系统框架。倒立摆的模糊控制器设计实例表明了设计方法的有效性。     

Mixed H2/H∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed H₂/H_∞ fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H₂/H_∞ controller is developed to achieve the suboptimal H₂ control performance with a desired H_∞ disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H₂/H_∞ control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method     

不确定时滞系统的模糊保成本控制

研究一类用T－S模糊模型描述的不确定时滞系统的鲁棒保成本控制问题，提出了系统存在保成本控制律的充分条件，基于LMI给出了系统设计状态反馈模糊保成本控制器的新方法，仿真结果证明了该方法的有效性。     

Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.     

鲁棒极点配置约束下的模糊控制系统设计

针对一类利用T-S模糊模型近似描述的不确定非线性系统,给出了一种具有鲁棒极点配置功能的模糊控制器和模糊状态观测器的设计方法.首先,利用并行分配补偿(PDC)设计思想和基于线性矩阵不等式(LMI)的鲁棒极点配置理论,得到了使整个闭环系统全局渐近稳定并满足希望的动态性能的充分条件.然后将这些条件转化为标准的LMI问题.最后将该设计方法应用于倒立摆的平衡控制中,验证了本方法的有效性.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Fuzzy control of an ANFIS model representing a nonlinear liquid-level system

This paper aims to serve two main objectives; one is to demonstrate the modelling capabilities of a neuro-fuzzy approach, namely ANFIS (adaptive-network based fuzzy inference system) to a nonlinear system; and the other is to design a fuzzy controller to control such a system. The nonlinear system, which is a liquid-level system, is represented first by its mathematical model and then by ANFIS architecture. The ANFIS model is formed by means of input–output data set taken from the mathematical model. Then a PID-type fuzzy controller, which linguistically approximates the classical three-term compensation, was designed to control the system represented by both its mathematical and ANFIS models in order to perform an agreement comparison between them. It is shown that the ANFIS architecture can model a nonlinear system very accurately by means of input–output pairs obtained either from the actual system or its mathematical model. It is also shown that such a system can be controlled effectively by a fuzzy controller.     

非线性系统广义模糊跟踪控制

研究一种给定 H∞ 模型参考跟踪特性的非线性系统的 T-S 广义模糊跟踪控制问题. 通过把一般的模糊模型等价变换到广义模糊模型, 引入了松弛变量, 并基于线性矩阵不等式 (LMI) 给出了新的 H∞ 跟踪控制器设计方法. 控制器参数在一组线性矩阵不等式中同时得到求解, 避免了原有方法分步求解的困难, 方法简单易行且具有鲁棒性. 两个算例表明了结论的有效性.