Controller design for electric power steering system using T-S fuzzy model approach

Pressure ripples in electric power steering （EPS） systems can be caused by the phase lag between the driver s steering torque and steer angle, the nonlinear frictions, and the disturbances from road and sensor noise especially during high-frequency maneuvers. This paper investigates the use of the robust fuzzy control method for actively reducing pressure ripples for EPS systems. Remarkable progress on steering maneuverability is achieved. The EPS dynamics is described with an eight-order nonlinear state-space model and approximated by a Takagi-Sugeno （T-S） fuzzy model with time-varying delays and external disturbances. A stabilization approach is then presented for nonlinear time-delay systems through fuzzy state feedback controller in parallel distributed compensation （PDC） structure. The closed-loop stability conditions of EPS system with the fuzzy controller are parameterized in terms of the linear matrix inequality （LMI） problem. Simulations and experiments using the proposed robust fuzzy controller and traditional PID controller have been carried out for EPS systems. Both the simulation and experiment results show that the proposed fuzzy controller can reduce the torque ripples and allow us to have a good steering feeling and stable driving.     

Parameter-dependent Lyapunov functional for systems with multiple time delays

The separation of the Lyapunov matrices and system matrices plays an important role when one use sparameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between the terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.     

Sliding Mode Control for T-S Fuzzy Systems

A sliding mode control scheme for a class of complex nonlinear systems with T-S fuzzy models is proposed in this paper. It is shown that, by using the concept of extreme matrices to determine the upper bound information of the interactions of the fuzzy subsystems, a simple, yet constructive sliding mode control scheme can be developed to guarantee the asymptotic stability and robustness of the closed-loop system. Simulation results are presented in support of the proposed scheme.     

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.     

A stability criterion for singular systems with two additive time-varying delay components

The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities (LMIs). Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.     

Relaxed delay-dependent stabilization criteria for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov functions

This paper presents delay-dependent stability analysis and controller synthesis methods for discrete-time Takagi-Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, the delay-dependent stabilization criteria are derived for the switching fuzzy system based on the piecewise Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered in each subregion, and accordingly the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, a design example is given to show the validity of the proposed method.     

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.     

Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach

A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. The T-S fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability. Finally, the error caused by fuzzy modeling is considered and the input-tostate stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to-state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.     

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.     

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H_∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H_∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.     

T-S模糊系统的基于观测器的H∞控制设计

研究了T-S(Takagi-Sugeno)模糊系统H∞控制设计问题.放宽了Kim E等的T-S模糊 系统可二次稳定的条件.给出了T-S模糊系统新的观测器设计方法.然后给出了T-S模糊系统 基于观测器的H∞控制存在的两个新的充分条件.新方法不但简单,而且充分考虑了模糊子系统 间的相互作用.最后通过例子,应用LMI技术,说明了本文给出的T-S模糊系统的基于观测器 的H∞控制器的设计方法简便易行.     

一类T-S模糊控制系统的稳定性分析及设计

研究了一类输入采用双交叠模糊分划的T-S模糊控制系统稳定性分析及控制器设计问题.基于分段模糊Lyapunov函数,提出了一个新的判定开环T-S模糊系统稳定性的充分条件,该方法只需在各个模糊区间里满足模糊Lyapunov方法中的条件,其保守性比公共Lyapunov函数法和分段Lyapunov函数法的保守性更低.运用并行分布补偿法(PDC)进一步探讨了闭环T-S模糊控制系统的稳定性分析问题并设计了模糊控制器.最后,一个仿真示例说明了本文方法的有效性.     

Approaches to quadratic stability conditions and H/sub /spl infin// control designs for T-S fuzzy systems

In this paper, the problems of quadratic stability conditions and H/sub /spl infin// control designs for Takagi-Sugeno (T-S) fuzzy systems have been studied. First, a new quadratic stability condition, which is more simple than that in a previous paper, has been proposed. Second, two new sufficient conditions in the terms of linear matrix inequalities (LMIs) which guarantee the existence of the state feedback H/sub /spl infin// control for the T-S fuzzy systems have been proposed. The conditions are not only simple but also consider the interactions among the fuzzy subsystems. Finally, based on the LMIs, the H/sub /spl infin// controller designing methods for the T-S fuzzy systems have been given.     

T-S模糊控制系统的稳定性分析及系统化设计

研究了输入采用双交叠模糊分划的模糊控制系统的性质,提出了一个新的判定T—S模 糊控制系统稳定的充分条件.该条件只需在各最大交叠规则组内分别寻找公共的正定矩阵，减 小了以往稳定性判定方法的局限性和难度.运用并行分布补偿法(PDC)进一步探讨了闭环T-S 模糊控制系统的稳定性分析和模糊控制器系统化设计方法.通过两个例子的仿真研究验证了本 文方法的有效性.     

Stability and asynchronous stabilization for a class of discrete-time switched nonlinear systems with stable and unstable subsystems

The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained.     

输入采用一般模糊划分的T-S模糊控制系统稳定性分析

通过定义一种对输入空间的一般模糊划分(General fuzzy partition, GFP), 研究了输入采用GFP的T-S模糊系统的性质, 以充分利用规则前件变量的结构信息. 通过构造连续分段光滑Lyapunov函数, 提出了新的T-S模糊控制系统的稳定性条件. 该条件同时考虑了各局部子系统之间的相互关系, 降低了现有稳定性条件的保守性和求解难度. 通过严格证明和数值示例, 比较了所得稳定性条件之间的保守性关系及其与以往充分条件之间的关系. 对运用并行分布补偿(Parallel distributed compensation, PDC)和线性矩阵不等式(Linear matrix inequalities, LMI)方法所设计的T-S模糊控制系统进行计算机仿真研究, 结果验证了所得稳定性条件的有效性和优越性.     

T-S模糊系统的局部稳定

讨论了T-S模糊系统的局部稳定性及控制器设计问题．给出连续T-S模糊系统局部稳定的定义,利用非二次Lyapunov函数和线性矩阵不等式（LMI）方法得到连续T-S模糊系统局部稳定的充分条件,并给出了基于LMI的局部镇定控制器设计方法．该方法不同于已有的全局稳定控制器设计方法,为判别模糊系统的稳定提供了新的选择．最后通过数值算例演示了控制器的设计方法。并证明了该方法的可行性。     

T-S模糊系统输出反馈控制器的稳定性分析与设计

输出反馈控制是T-S模糊控制系统设计的一种重要方法．本文提出了一类由模糊状态观测器和模糊调节器构成的输出反馈控制器稳定性分析和解析设计的新方法．为了减小稳定性分析的保守性和难度,本文充分利用了模糊规则前件变量模糊隶属度函数的结构信息,对前件变量采用标准模糊分划的T-S模糊系统输出反馈控制器进行了研究,获得了一些新的稳定性条件．然后采用平行分布补偿法(PDC)和线性矩阵不等式方法(LMI),研究了该类输出反馈控制器的解析设计方法．通过一个非线性质量块-弹簧-阻尼器系统输出反馈控制器的设计和计算机仿真,验证了本文方法的有效性．     

基于分段模糊Lyapunov方法的离散模糊系统分析与设计

研究了基于分段模糊Lyapunov函数的离散T-S模糊控制系统稳定性分析及控制器设计问题．首先,在定义离散型分段模糊Lyapunov函数的基础上,提出了一个新的判定开环离散T-S模糊系统稳定性的充分条件．该条件仅需在每个最大交叠规则组内分别满足模糊Lyapunov方法中的条件,从而降低了公共Lyapunov方法和模糊Lyapunov方法的保守性和难度．然后,利用并行分布补偿方法对闭环系统的稳定性进行了分析并设计了模糊控制器．最后,一个仿真示例说明了本文方法的有效性和优越性．