Font Size: a A A

Research On Interval Observer And Its Control System

Posted on:2017-05-31Degree:DoctorType:Dissertation
Country:ChinaCandidate:Z W HeFull Text:PDF
GTID:1108330503985106Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
In recent decades, observer design and its research in the control system has gradually become an important research topic in control theory. This scheme has been extensively applied in many relevant areas, such as system monitoring, process identification, fault detection and so on. However, all the information for the model of actual system is frequently not available, or these measurements are not completely reliable due to existing exogenous disturbances and noises. Therefore, considering reasonable intervals instead of relying on single point measurements, a novel method for designing observer is presented with the interval-observer-based framework. Compared with the classical observer design requirement of observer error dynamic state converging to zero, interval observer is only designed to ensure the observer error dynamic state positive, which can be gained by designing observer error dynamic state matrix for Metzler matrix. Based on its advantages and relevance both in theoretical research and practical application, interval observer design will be further studied in this dissertation. The main contribution and innovation of this dissertation are summarized as follows:1. For a class of linear continues-time system, Luenberger interval observer is designed. The characteristics of this method is firstly to gain a positive representation for linear system by elementary transformation, and then to design a Luenberger interval observer for positive system. Such a methodology of interval observer design guarantees the existence of observer gain. Unlike the existing methods for designing interval observer, this thesis attempts to design a class of interval observer for linear discrete-time system via the comparison principle of positive system; such a design method can effectively solve the problem of existence of observer gain.2. Based on the existing results for interval observer, to successfully design an interval observer is to rely on the existence of observer gain satisfying error dynamic system matrix for Metzler matrix. To address this problem, a condition for the existence of interval observer gain is firstly obtained and presented in terms of linear matrix inequalities(LMIs) for Metzler matrix; also, it is stated that the condition is less conservative by discussing L2-gain performance of nonlinear systems.3. The problem of design interval observer for linear parameter-varying(LPV) system is considered. First, the time-varying interval observer system and gain scheduled controller are designed. Second, according to the polytopic structure of linear parameter-varying system, the stabilizing condition is presented in terms of LMIs. Compared with the result of interval observer design about an affine structure of LPV system, which only gives observer gain to satisfy Metzler matrix, but the method proposed in this thesis can obtain both observer gain and gain scheduled controller by solving LMIs. Finally, a simple numerical example is given to illustrate the efficiency of the proposed method.4. Based on average dwell time control scheme, the problem of interval observer design is discussed, and also a new method for state estimation of nonlinear switched system is presented. Meanwhile, based on the interval observer, the problem for designing feedback controller is realized under the condition of nonlinear terms satisfying Lipschitz case.
Keywords/Search Tags:Interval observer, Error dynamic system, Metzler matrix, Linear parametervarying system, Nonlinear switched system, L2-gain performance, Asymptotic stability
PDF Full Text Request
Related items