For A Class Linear System Regional Reliable Control Pole Placement

Reliable control includes the sensor and actuator faults into the controller design process toensure stability and performance of the closed-loop system. For a class of linear systems, thispaper presents an approach Linear Matrix Inequality (LMI) based to design a state-feedbackrobust reliable controller. A more practical continuous model of sensor and actuator failures thandiscrete model is considered, this paper presents the sufficient condition for existence of the statefeedback robust reliable controller in disk, the sufficient condition for existence of the reliablecontroller in maxed region and the necessary and sufficient conditions of poles in the centrifugalsector region. Base on the studies above, this paper has put forward the concept of gain errortolerate interval for the each actuator channel. By using mathematical model of gain error withsingle actuator channel, this paper presents the algorithm of the actuator gain error tolerateinterval in disk pole placement.First, continuous model of actuator failures is considered, this paper presents the sufficientcondition for existence of the state feedback robust reliable controller. By solving the LMI,determine the parameter matrix of the robust reliable controller. The robust reliable controllergiven, not only can keep poles of the uncertain closed-loop system in expected disk, but also canagainst the influence of actuator failures for the disk poles.Second, this paper not only gives the necessary and sufficient conditions of poles in thecentrifugal sector region, but also presents an LMI (Linear Matrix Inequality) based approach todesign a state-feedback reliable controller for mixed region. A more practical continuous modelof actuator failures than discrete model is considered, we present the sufficient condition forexistence of the state feedback reliable controller. By solving the LMI, determine the parametermatrix of the robust reliable controller. The reliable controller given can keep from the influenceof actuator faults and achieve pole placement in the mixed region.At last, base on the studies above, for a class of linear systems with relation to the diskregion pole placement, this paper has put forward the concept of gain error tolerate interval forthe each actuator channel. By using mathematical model of gain error with single actuatorchannel, we present the algorithm of the actuator gain error tolerate interval in disk poleplacement. The importance degree can be seen by designer about influence of each channel,according to the gain error tolerate interval. The designer can enhance the hardware redundancyrate of the actuator channel according to the importance degree. This paper has providedimportant theory evidence for the design of actuator channel hardware redundancy in the diskregion pole placement.For the theoretical studies above, some numerical and practical examples are given to showthe effectiveness and the feasibility of the obtained results.