Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems

In this paper, we propose an adaptive fuzzy controller for a class of nonlinear SISO time-delay systems. The plant model structure is represented by a Takagi–Sugeno (T–S) type fuzzy system. The T–S fuzzy model parameters are adjusted online. The proposed algorithm utilizes the sliding surface to adjust online the parameters of T–S fuzzy model. The controller is based on adjustable T–S fuzzy parameters model and sliding mode theory. The stability analysis of the closed-loop system is based on the Lyapunov approach. The plant state follows asymptotically any bounded reference signal. Two examples have been used to check performances of the proposed fuzzy adaptive control scheme.     

Guaranteed‐cost fuzzy controller design for a self‐sustaining bicycle with practical constraints

This study presents a guaranteed‐cost fuzzy controller for a self‐sustaining bicycle. First, the nonlinear dynamics of the bicycle are exactly transformed into a T‐S fuzzy system with model uncertainty. The guaranteed‐cost fuzzy controller is then designed for the transformed T‐S fuzzy system. For practical considerations, the input/state constraints are also satisfied in the design. The main contribution of this study is the guaranteed‐cost control design for a T‐S fuzzy system with model uncertainty and input/state constraints. Finally, simulation results show the validity of the proposed controller design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

State-feedback stabilisation for fuzzy bilinear uncertain system with disturbance via fuzzy control approach

This article presents a fuzzy control scheme for a class of Takagi–Sugeno (T–S) fuzzy uncertain bilinear system with disturbance (FUBSD). First, the T–S FUBSD is established and based on the parallel distributed compensation method, the overall robust H _∞ fuzzy controller is proposed to globally stabilise the T–S FUBSD. Then, some sufficient conditions are derived to guarantee the robust stabilisability of the overall fuzzy control system via linear matrix inequalities. Finally, a numerical example is utilised to demonstrate the validity and effectiveness of the proposed control scheme.     

Robust fuzzy control of nonlinear stochastic delay systems with impulsive effects

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Non-fragile guaranteed cost fuzzy control for nonlinear first-order hyperbolic partial differential equation systems

This paper concerns the non-fragile guaranteed cost control for nonlinear first-order hyperbolic partial differential equations (PDEs), and the case of hyperbolic PDE systems with parameter uncertainties is also addressed. A Takagi–Sugeno (T–S) fuzzy hyperbolic PDE model is presented to exactly represent the nonlinear hyperbolic PDE system. Then, the state-feedback non-fragile controller distributed in space is designed by the parallel distributed compensation (PDC) method, and some sufficient conditions are derived in terms of spatial differential linear matrix inequalities (SDLMIs) such that the T–S fuzzy hyperbolic PDE system is asymptotically stable and the cost function keeps an upper bound. Moreover, for the nonlinear hyperbolic PDE system with parameter uncertainties, using the above-design approach, the robust non-fragile guaranteed cost control scheme is obtained. Furthermore, the finite-difference method is employed to solve the SDLMIs. Finally, a nonlinear hyperbolic PDE system is presented to illustrate the effectiveness and advantage of the developed design methodology.     

Analysis of stability and robust stability of polynomial fuzzy model-based control systems using a sum-of-squares approach

The well known Takagi–Sugeno (T–S) fuzzy model can be extended in different ways including the polynomial fuzzy model, whose consequent parts are polynomial sub-systems. Compared with the traditional T–S fuzzy model, the polynomial fuzzy model can represent a nonlinear system more accurately with a smaller number of fuzzy logic rules. It is worth emphasizing that the stability analysis and controller design of polynomial fuzzy model-based (PFMB) control systems are not based on the linear matrix inequalities but the recently developed sum-of-squares decompositions. In this paper, based on an existing result for traditional fuzzy control systems, we propose a new stability condition for the stability analysis of PFMB control systems. Furthermore, the stability of PFMB control systems with parameter uncertainties is investigated. The popular inverted pendulum and an unstable nonlinear system are employed to demonstrate the quality of the proposed stability conditions.     

Multiple fuzzy model-based temperature predictive control for HVAC systems

In this paper, a multiple model predictive control (MMPC) strategy based on Takagi–Sugeno (T–S) fuzzy models for temperature control of air-handling unit (AHU) in heating, ventilating, and air-conditioning (HVAC) systems is presented. The overall control system is constructed by a hierarchical two-level structure. The higher level is a fuzzy partition based on AHU operating range to schedule the fuzzy weights of local models in lower level, while the lower level is composed of a set of T–S models based on the relation of manipulated inputs and system outputs correspond to the higher level. Following this divide-and-conquer strategy, the complex nonlinear AHU system is divided into a set of T–S models through a fuzzy satisfactory clustering (FSC) methodology and the global system is a fuzzy integrated linear varying parameter (LPV) model. A hierarchical MMPC strategy is developed using parallel distribution compensation (PDC) method, in which different predictive controllers are designed for different T–S fuzzy rules and the global controller output is integrated by the local controller outputs through their fuzzy weights. Simulation and real process testing results show that the proposed MMPC approach is effective in HVAC system control applications.     

模糊控制的系统化设计和稳定性分析

给出了一种模糊控制系统的系统化设计方法,它采用一组局部T-S模糊模型来表 示模糊系统,对每个局部模型,利用状态反馈进行控制器设计,最后给出了全局模糊系统的稳 定性分析.通过对一个典型的非线性球-棒控制系统的仿真研究,表明该方法是有效的,它的 性能指标优于现有文献的结果.     

H ∞ control of a suspension with a magnetorheological damper

This research work presents an H _∞ controller based on a Takagi–Sugeno (T–S) fuzzy model for a two-degrees-of-freedom (2-DOF) one-quarter-vehicle semi-active suspension with a magnetorheological damper where the actuator dynamics are included in the control synthesis. These dynamics enclose nonlinear damper phenomena, avoided in many other studies, and that can improve the suspension system by means of a more accurate model. The objective is to obtain a semi-active suspension that considerably improves the passive suspension efficiency based on some frequency domain performance criteria. The advantage of having the T–S system as a reference is that each piecewise linear system can be exposed to the well-known control theory. Besides, the proposed solution is compared with the recent reported work to highlight its advantages. A case of study is included and simulation work supports the results. The methodology applied herein can be extended to a half-vehicle model, and to the four wheels to have a global chassis control in order to maximise passenger comfort and vehicle stability.     

H∞ fuzzy control design of discrete‐time nonlinear active fault‐tolerant control systems

This paper is concerned with the problem of H_∞ fuzzy controller synthesis for a class of discrete‐time nonlinear active fault‐tolerant control systems (AFTCSs) in a stochastic setting. The Takagi and Sugeno (T–S) fuzzy model is employed to exactly represent a nonlinear AFTCS. For this AFTCS, two random processes with Markovian transition characteristics are introduced to model the failure process of system components and the fault detection and isolation (FDI) decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the state of the failure process. A non‐parallel distributed compensation (non‐PDC) scheme is adopted for the design of the fault‐tolerant control laws. The resulting closed‐loop fuzzy system is the one with two Markovian jump parameters. Based on a stochastic fuzzy Lyapunov function (FLF), sufficient conditions for the stochastic stability and H_∞ disturbance attenuation of the closed‐loop fuzzy system are first derived. A linear matrix inequality (LMI) approach to the fuzzy control design is then developed. Moreover, a suboptimal fault‐tolerant H_∞ fuzzy controller is given in the sense of minimizing the level of disturbance attenuation. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2008 John Wiley & Sons, Ltd.     

Stable indirect adaptive switching control for fuzzy dynamical systems based on T–S multiple models

A new indirect adaptive switching fuzzy control method for fuzzy dynamical systems, based on Takagi–Sugeno (T–S) multiple models is proposed in this article. Motivated by the fact that indirect adaptive control techniques suffer from poor transient response, especially when the initialisation of the estimation model is highly inaccurate and the region of uncertainty for the plant parameters is very large, we present a fuzzy control method that utilises the advantages of multiple models strategy. The dynamical system is expressed using the T–S method in order to cope with the nonlinearities. T–S adaptive multiple models of the system to be controlled are constructed using different initial estimations for the parameters while one feedback linearisation controller corresponds to each model according to a specified reference model. The controller to be applied is determined at every time instant by the model which best approximates the plant using a switching rule with a suitable performance index. Lyapunov stability theory is used in order to obtain the adaptive law for the multiple models parameters, ensuring the asymptotic stability of the system while a modification in this law keeps the control input away from singularities. Also, by introducing the next best controller logic, we avoid possible infeasibilities in the control signal. Simulation results are presented, indicating the effectiveness and the advantages of the proposed method.     

离散型模糊系统的稳定线性监督控制设计

在对现有的T-S型模糊系统的稳定性结果进行 分析的基础上,研究了状态空间形式下离散型模糊系统在子空间上的线性分解,基于该线性 分解设计一线性监督控制器使模糊闭环系统稳定,从而用简单的线性系统理论完成了对复杂 非线性系统的控制．仿真结果证明了该线性监督控制器的有效性．     

电压畸变条件下三相三线有源电力滤波器的T–S模糊H∞控制

有源电力滤波器(APF)是解决电力系统谐波治理的有效方法, 由于电源电压存在畸变影响了APF的补偿参考电流的检测精度并影响补偿的效果. 本文采用T–S模糊控制的方法对三相三线APF进行建模, 将电源电压的畸变成分作为理想情况的干扰, 在保性能的前提下给定性能指标, 实现T–S模糊H∞控制性能. 在满足稳定性的要求条件下, 设计的T–S模糊H∞状态反馈控制器使APF在电源电压畸变的情况下, 将电源电流补偿为正弦特性, 满足了APF谐波综合补偿的控制要求. 仿真结果验证了所建T–S模糊模型的有效性, 展示出所设计的H∞控制器的有效性能. 补偿电流可以准确的检测, 在电源电压非正弦条件下可以进行有效的控制.