Study Of Robust ControlApproach For Nonlinear Systems Based On T-S Fuzzy Models

In the practical industrial process control, controlled objects whose structure iscomplicated increasingly, generally express characteristics of uncertainties, time-delays,nonlinearities, because of characteristics of the structure themselves and phenomena of thesignal transmission and measurement insensitivity. The traditional control theory is difficultto solve problems of the modeling and analysis of such complex systems, which brings outgreat difficulties for the design of control systems. Therefore, it has very important theoreticaland practical significance to research nonlinear systems with time-delay and uncertain, whichis also a hotspot problem in research of current control field.Fuzzy systems based on T-S model can approximate nonlinear systems with anyaccuracy, where analysis and synthesis methods in the linear control theory can be applied to.It can make the roles that external disturbances and parameter variations on the control effectgreatly weakened, and the system robustness is enhanced. So the research upon fuzzy systemsbased on T-S model has important practical significance.The stability analysis and design problems of robustL2L and H state feedbackcontrollers about continuous and discrete fuzzy systems are further studied, based on a T-Slinear model and a T-S bilinear model, according to Lyapunov stability theory and the robustcontrol theory, combined with the linear matrix inequality technique in the paper. The thesisconsists of the following aspects:Firstly, for a class of continuous uncertain nonlinear systems with time-delay both instates and inputs, a T-S linear model is established. A global controller is designed byintroducing a Moon inequality based on the Lyapunov function method, which can ensurethat the closed-loop T-S fuzzy systems are asymptotically robust stable and meet certainperformance constraints. Then in view of many nonlinear processes in real systemspresenting some phenomena about the product of control variables and state variables, a T-Sbilinear model is set up for a class of delay nonlinear systems. Considering that certain usefulterms which are ignored in previous derivation processes may lead to some conserativesituations, sufficient conditions are given for the existence of admissible robustL2L andH controllers by introducing free-weighting matrices. Free-weighting matrices introducedare to solve the situation that the constraint condition of the derivatives of time-delay is lessthan1.Secondly, the stability analysis and design problems of robustl2l and H controllers are studied about a class of discrete time-delay nonlinear fuzzy systems with uncertain based on a T-S linear model and a T-S bilinear model. By using the paralleldistributed compensation algorithm, sufficient conditions of existed local controllers aregiven, and global controllers are designed by using the linear matrix inequality technique. Asimulation is provided to demonstrate that designed controllers based on the T-S fuzzy modelcan meet control requirements.Finally, the T-S fuzzy robust control method is applied to the continuous stirring tankreactor in industry, simulation results are provided to demonstrate the effectiveness of theproposed design scheme, which can be applied to other chemical industrial reactions.