Research On Robust Control And Fault Diagnosis For Affine T-S Fuzzy Systems

With the scales and complexities of modern control systems are increasing,the con-trolled object or process often is difficult to obtain a desired mathematical model,because of its nonlinear,random disturbances and uncertainties.For such control systems,it is difficult to get satisfactory control effects by using the conventional control theory.How-ever,the fuzzy control techniques can represent linguistic terms and provide different control scheme according to the different status of controlled subjects.Since then,the fuzzy control techniques can guarantee a better control effect for the controlled object subjected to nonlinear,time-varying and multi-parameter decoupling.In particular,T-S fuzzy model is based on using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions.T-S fuzzy models have been shown to be universal function approximators in the sense that they are able to approximate any smooth nonlinear functions to any degree of accuracy in any convex compact region.As a result,a number of significant analysis results and synthesis methods are obtained by taking full advantage of linear control the-ory.However,due to the inherent nonlinearities of T-S fuzzy systems,there are still many problems to be solved.On the basis of the previous work,this dissertation further studies some problems of T-S fuzzy systems,such as,robust performance analysis,controller design and fault diagnosis.Affine T-S fuzzy models are constructed to represent a class of nonlinear sys-tems with strong nonlinearities.Compared with linear T-S fuzzy models,affine T-S fuzzy models have much improved function approximation capabilities and interpretation capa-bilities,and then lead to less conservative controller design conditions.A novel matrix decoupling technique is proposed for continuous-time affine T-S fuzzy systems,which re-moves the structure constraint on the Lyapunov matrix in the existing results.By choosing system outputs as the fuzzy premise variables,affine T-S fuzzy models are used to rep-resent a class of nonlinear systems with states are not fully measurable.In contrast to the existing results,the proposed approach avoids the heavy computational burden due to the mismatched regions between the plant and controller.For the affine T-S fuzzy systems with finite frequency disturbance inputs,a new H? controller synthesis method in finite frequency is proposed.For the uncertain affine T-S fuzzy large-scale systems with unknown interconnections,by a cyclic-small-gain condition,the decentralized state feedback controller and decentralized dynamic output feedback controller are designed respectively,and the influence of measurement errors on membership functions is consid-ered.Further,in a multiple-model scheme,the fault diagnosis problem is discussed for a class of state-feedback T-S fuzzy control systems with local nonlinear parts and unknown membership functions.Parts of the developed theories are applied to the controller de-sign and fault diagnosis of the pendulum model,double-inverted pendulums model and the reentry phase of a NSV.Simulation examples illustrate the advantages and effective-ness of proposed approaches.The main contents are outlined as follows:In Chapters 1-2,the development and main research methods of fuzzy control are analyzed and summarized,and some preliminaries about the considered problems are given.In Chapter 3,the stability analysis and controller design problems for affine T-S fuzzy systems are investigated.It is the first time to present the stability analysis con-ditions based on matrix decoupling techniques.By introducing slack matrices,the con-troller design conditions are obtained in the formulation of LMI.In contrast to the existing methods,the proposed method can remove the constraint on Lyapunov matrices and pro-vide less conservative design conditions.Numerical examples illustrate the effectiveness and merits of the proposed method.In Chapter 4,the problem of H? controller synthesis in finite frequency for a class of continuous-time affine T-S fuzzy systems is investigated.Based on a piecewise Lyapunov function combined with S-procedure and matrix decoupling techniques,a new controller design method has been proposed which makes full use of the frequency information of disturbances to reduce design conservatism.The controller design conditions are obtained in the formulation of LMIs.In contrast to the controller design in full frequency,the proposed method can guarantee a better disturbance attenuation under known disturbance frequency ranges.Finally,numerical examples are used to illustrate the effectiveness and superiority of the proposed method.In Chapter 5,the decentralized state feedback control problem for uncertain affine T-S fuzzy large-scale systems with unknown interconnections is investigated.First,based on the structural information encoded in the fuzzy rules,the state-space of each sub-system is partitioned into operating and interpolation regions.Then,a decentralized piecewise state feedback controller is designed,and a cyclic-small-gain condition is in-troduced to address the unknown interconnections such that the resulting closed-loop sys-tem is asymptotically stable with disturbance attenuation.By constructing a piecewise Lyapunov function combined with S-procedure and introducing extra slack variables,a decentralized piecewise state feedback controller design method is derived in the formu-lation of LMIs.In contrast to the existing methods,the proposed method can avoid the matching conditions between the interconnections and control inputs,and remove the equality constraints on Lyapunov matrices and controller gains.Finally,an example is given to illustrate the effectiveness and merits of the proposed method.In Chapter 6,the decentralized dynamic output feedback control problem for affine T-S fuzzy large-scale systems with measurement errors is investigated.First,based on the structural information encoded in the fuzzy rules,the output space of each subsystem is partitioned into operating and interpolation regions.Then,a decentralized piecewise dynamic output feedback controller is designed,and a cyclic-small-gain condition is in-troduced to address the unknown interconnections such that the resulting closed-loop sys-tem is asymptotically stable with disturbance attenuation.By constructing S-procedure with fully considering the measurement error information and introducing extra slack variables,a decentralized piecewise dynamic output feedback controller design method is derived with satisfying an L? performance.In contrast to the result without considering measurement errors,the proposed method can guarantee a better steady performance in presence of measurement errors.Finally,an example is given to illustrate the effectiveness of the proposed method.In Chapter 7,the fault diagnosis problem for T-S fuzzy systems with local nonlinear parts and unknown membership functions is investigated.First,a state feedback controller is designed,such that the closed-loop system is stable and satisfied some prescribed H?performances in normal case and faulty cases.In a multiple-model scheme,a bank of fault detection and isolation observers are constructed,each of which is based on a T-S model that describes the system in the presence of a particular fault.By introducing a switching technique,the presented fault detection and isolation scheme utilizes the online switch-ing ability,which can guarantee that one of the fault detection and isolation observers can track the current system state,such that the corresponding residual signal converges exponentially to zero.Therefore,the proposed fault detection and isolation scheme can detect and isolate the fault whenever it occurs.Further,for the T-S fuzzy control systems with actuator faults,combine with the proposed fault detection and isolation scheme and adaptive technique,an adaptive fault estimation observer design method is proposed,such that the obtained fault estimation errors converge exponentially to zero.Finally,examples are given to illustrate the effectiveness and merits of the proposed method.Finally,the results of the dissertation are summarized and further research topics are pointed out.