A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

Robust nonlinear variable selective control for networked systems

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi–Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H₂ performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.     

Sensor fault tolerant control of nonlinear Takagi–Sugeno systems. Application to vehicle lateral dynamics

This paper presents a new scheme for sensor fault tolerant control for nonlinear systems based on the Takagi–Sugeno modeling. First, a structured residual generator aimed at detecting and isolating sensor faults is designed. A bank of observers controlled either by only one system output or a set of outputs is then implemented, leading to a set of state estimates. The parallel distributed compensation structure is adopted to design the fault tolerant controller. The novelty in this paper is that the estimated state used in the controller is a weighted state vector obtained from all the estimated states provided by the different observers. The weighting functions depend on the residual vector signals delivered by the residual generator. They are designed to avoid crisp switches in the control law. Indeed, the interesting feature of the proposed approach is to avoid the commonly used switching strategy. For each residual component, the greater its magnitude is, the less the weight affected to the corresponding state estimate is. Consequently, the controller only uses estimations computed on the basis of healthy measurements. The closed‐loop stability is studied with the Lyapunov theory, and the obtained conditions are expressed as a set of linear matrix inequalities. The proposed residual generation and fault tolerant controller are applied to a vehicle lateral dynamics affected by sensor faults. Copyright © 2015 John Wiley & Sons, Ltd.     

Dual asynchronous control for T-S fuzzy semi-Markov jump systems: A finite-time design

This paper addresses the control problem of Takagi–Sugeno fuzzy semi-Markov jump systems (TFSMJSs) under the finite-time analysis and synthesis framework. Due to the commonly used networked communication structure, the semi-Markovian jumping modes and fuzzy premise variables cannot always perfectly match for system and controller among the whole system operation. More precisely, both asynchronous phenomena in fuzzy membership and jumping mode are taken into account, and then, mode-dependent finite-time controllers are developed with these features. By utilizing stochastic analysis and Lyapunov–Krasovskii stability theory, sufficient criteria are first established for the closed-loop system in the context of mean-square sense. Furthermore, feedback controller gains are captured by the matrix technique and parallel distributed compensation (PDC)-related arguments. Eventually, a simulation example of an unmanned marine vehicle (UMV) is utilized to demonstrate the validity of the developed results.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

离散系统鲁棒稳定的简化条件及其反馈控制方法

给出了一种离散系统鲁棒稳定性的分析方法。通过对离散系统不确定部分不同表达式的研究，提出一种系统鲁棒稳定判别不等式。为解决系统鲁棒稳定性的实际计算问题，给出了离散系统鲁棒稳定性的另一种描述，井由此描述和不等式恒等变形，得到新的鲁棒稳定性判据。该判据结构筒单，很容易判定系统的鲁棒性。在此基础上，给出了系统鲁棒反馈控制的设计方法。     

Output feedback controller design of Takagi–Sugeno fuzzy systems

This paper presents new systematic design methods of two types of output feedback controllers for Takagi–Sugeno (T–S) fuzzy systems, one of which is constructed with a fuzzy regulator and a fuzzy observer, while the other is an output direct feedback controller. In order to use the structural information in the rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition (SFP) is employed to the premise variables of fuzzy systems. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The concept of parallel distributed compensation (PDC) is employed to design fuzzy regulators and fuzzy observers from the T–S fuzzy models. New stability analysis and design methods of output direct feedback controllers are also presented. The output feedback controllers design and simulation results for a nonlinear mass-spring-damper mechanical system show that these methods are effective.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.     

CLUSTERED BASED TAKAGI‐SUGENO NEURO‐FUZZY MODELING OF A MULTIVARIABLE NONLINEAR DYNAMIC SYSTEM

This research frame work investigates the application of a clustered based Neuro‐fuzzy system to nonlinear dynamic system modeling from a set of input‐output training patterns. It is concentrated on the modeling via Takagi‐Sugeno (T‐S) modeling technique and the employment of fuzzy clustering to generate suitable initial membership functions. Hence, such created initial memberships are then employed to construct suitable T‐S sub‐models. Furthermore, the T‐S fuzzy models have been validated and checked through the use of some standard model validation techniques (like the correlation functions). Compared to other well‐known approximation techniques such as artificial neural networks, fuzzy systems provide a more transparent representation of the system under study, which is mainly due to the possible linguistic interpretation in the form of rules. Such intelligent modeling scheme is very useful once making complicated systems linguistically transparent in terms of fuzzy if‐then rules. The developed T‐S Fuzzy modeling system has been then applied to model a nonlinear antenna dynamic system with two coupled inputs and outputs. Validation results have resulted in a very close antenna sub‐models of the original nonlinear antenna system. The suggested technique is very useful for development transparent linear control systems even for highly nonlinear dynamic systems.     

基于模糊模型的不确定非线性系统鲁棒D 镇定

针对 T- S模糊模型描述的不确定非线性系统 ,应用二次 D-稳定概念 ,对给定复平面上的某一D域提出模糊系统全局鲁棒 D-稳定的充分条件 ,基于并行分布补偿 (PDC)技术 ,各局部状态反馈镇定控制器设计归结于解一组耦合线性矩阵不等式 (L MI) ,全局控制器通过隶属度函数由各局部控制器混合而成 ,并以此保证整个系统的鲁棒 D-稳定性。最后用质量弹簧阻尼系统给出了仿真示例。     

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

The fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.     

A robust constrained control approach for flexible air‐breathing hypersonic vehicles

This article investigates the robust adaptive control system design for the longitudinal dynamics of a flexible air‐breathing hypersonic vehicle (FAHV) subject to parametric uncertainties and control input constraints. A combination of back‐stepping and nonlinear disturbance observer (NDO) is utilized for exploiting an adaptive output‐feedback controller to provide robust tracking of velocity and altitude reference trajectories in the presence of flexible effects and system uncertainties. The dynamic surface control is introduced to solve the problem of “explosion of terms.” A new NDO is developed to guarantee the proposed controller's disturbance attenuation ability and to performance robustness against uncertain aerodynamic coefficients. To deal with the problem of actuator saturation, a novel auxiliary system is exploited to compensate the desired control laws. The stability of the presented NDO and controller is analyzed. Simulation results are given to demonstrate the effectiveness of the presented control strategy.     

Improvement of Takagi‐Sugeno fuzzy model for the estimation of nonlinear functions

Two new and efficient approaches are presented to improve the local and global estimation of the Takagi‐Sugeno (T‐S) fuzzy model. The main aim is to obtain high function approximation accuracy and fast convergence. The main problem is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. The approaches developed here can be considered as generalized versions of T‐S method with optimized performance. The first uses the minimum norm approach to search for an exact optimum solution at the expense of increasing complexity and computational cost. The second is a simple and less computational method, based on weighting of parameters. Illustrative examples are chosen to evaluate the potential, simplicity and remarkable performance of the proposed methods and the high accuracy obtained in comparison with the original T‐S model. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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。     

Designing of non-fragile robust model predictive control for constrained uncertain systems and its application in process control

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.     

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.     

Relaxed fuzzy control synthesis of nonlinear networked systems under unreliable communication links

This paper proposes relaxed conditions for control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links. To widen the applicability of the fuzzy control approach under network environments, a novel fuzzy controller, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the multi-steps-past normalized fuzzy weighting functions, is provided to make much more use of the information of the underlying system. Moreover, a new kind of slack variable approach is also developed and thus the algebraic properties of these multi-instant normalized fuzzy weighting functions are collected into some augmented matrices. As a result, the conservatism of control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links can be significantly reduced. Two illustrative examples are presented to demonstrate the effectiveness of the theoretical development.