Research For Reliable H_∞Control And Acceptant Range Based On A Class Of Linear Systems

By the reason of the difference of the project practical units’ stability, the errors which areled by the system variable simplification makes it very difficult to transform and obtain thepractical models of the industrial process as controller modeling. Furthermore, in the long termoperation system various hardware aging results in the uncertainty of the models and the partsystem fault also leads to the unpredictability of the system operating result. Robust reliable H_∞control solves some problems successfully in the practical engineering field. Therefore, therobust reliable H_∞control theory has been accepted and researched widely.In the first part, on the base of consulting a large number of domestic and foreign literature,this dissertation introduces the development and current situation of control theory, considersthe system source of the uncertainty and the fault and analyses the problems to be solved suchas the conservatism of the reliable H_∞control existing, the design cost increase and the systemperformance decrease. The mathematics knowledge is expounded which is used in the controlfield and some related lemmas is proved. This dissertation gathers together all the H_∞controltheories in order to prepare for the latter certification.In the next part, this dissertation expounds the state feedback controller and gives thesufficient and necessary proof of the linear inequality. And then, it designs a robust statefeedback controller and a robust reliable H_∞state feedback control which is simulatednumerically to the uncertain system. According to the features of the system, this dissertationraises the conservatism of the robust reliable control and the problems which should be solvedin the linear system. This dissertation also summarizes the problems in which the energyconsumption of the controllers designed is too large and it is not convenient to use thecontrollers designed in the actual project. Otherwise, it doesn’t mean that the system is whollyparalysis when there is system fault, but it is due to the component aging of the system itselfwhich leads to the system signal fluctuation in most cases.In the last part, according to the above problems, through a class of linear system H_∞indexand the features of the state feedback H_∞controller signal fluctuation with disc pole constraint,for the each channel’ fault of the actuator, this dissertation raises the idea of gain fluctuationacceptant range, which is to say that it considers and calculates the range of the hardwaremaximum capability when there is gain fluctuation in the hardware with the premise of theunconverted origin system. At the same time, this dissertation provides the approach to solvethe allocative system optimization problem through the hardware redundancy in case of not togain the control energy. By comparing the condition in which there is gain fluctuation with theother one in which there isn’t gain fluctuation and according to the acceptant range of each fault channel’s gain fluctuation, it can enable designers to see the importance of each channel toclosed-loop system which we can base to enhance the hardware redundancy rate of this channel.In this way, we will strengthen the reliability of the system hardware design.The idea of gain fluctuation acceptant range which is raise by this dissertation can solvethe conservatism of the H_∞performance index optimization algorithm which is used by themajority designers for the system fault. And it can improve the reliability of system operationthe through the concept of the hardware redundancy which is given. This gain fluctuationacceptant range algorithm which is combining with the actual operation tightly is the best wayto be used to judge artificially the uncertainty. This algorithm puts forward my own design ideato the robust reliable control theory involved in the practical engineering and it also developsthe content of the reliable control theory.