State Observers Design Based On Robust Control Of Uncertain Sampled-data Systems

Considering the parameter uncertainties and extermal disturbance of sampled-data systems,the problems of state observers design based on robust control for the sampled-data systems with uncertainties were studied.In pratical control systems,it's necessary to use observer for state informations unable or uneasy to be observed because of noises.For the uncertain sampled-data systems based on observers the following contents are discussed:First,the guaranteed cost controller of a class of uncertain sampled-data systems was studied based on the state observers.A class of sufficient conditions for the guaranteed cost controller of the sampled-data systems was given via solving a class of LMI constrains.The guaranteed cost controller law and state observer gain were derived.Then,the system performances were improved.Second,the observer results of Luenberger observers have big errors when unknown disturbances exist.Based on the properties that intergral link is able to sustain disturbances and improve the steady performances,error intergral of output between the practical syatem and the observer system was used.Proportional-integral observer was designed to enhance the ability of sustaining disturbance with observer.By virtue of robust control theory and linear matrix inequality (LMI) method,proportional-integral state observers based on robust H₂/H_∞controller of a class of sampled-data systems were designed.At the same time,a class of sufficient conditions was obtained and smaller conservative solution approach of robust H 2performance index and state observer gains which contained proportion,integral and controller were given . Compared with Luenberger observer ,proportional integral observer which was designed in this paper has more surperiority. Third,an improved method was designed based on proportional intergral observer to have fast reaction errors and enhance responses.Not only error intergral of output between the practical syatem and the observer system was used,but also proportional was used. Robust hybid H₂/H_∞controller of a class of sampled-data systems based on the improved state observer was reseached.Compared with proportional intergral observer , the improved observer has more ability of sustaining disturbances,but the proportional link which was added in the errors between the practical syatems and the observer systems made solution more complex.Fourth,robust control of uncertain sampled-data systems with poles constraint based on proportional integral observer and the improved proportional integral observer was researched.By means of linear matrix inequation (LMI) method,the poles were allocated in the special regions to enhance the observer ability and performances of the systems.