Study On Hardware Redundancy Rate Based On Guaranteed Cost

Reliable control is an important control method of linear system. The traditional reliable control take the possibility of failure into consideration in the process of controller design. No matter whether component failure, the closed-loop system can maintain a specific performance index. But reliable control also have many shortcomings, such as increased control energy, declined system performance, slow output response speed.This paper is based on the problems existing in the reliable control.By increasing the hardware of the system’s "important" components, we ensure that the system was reliable operation and maintain a specific performance index, which is known as hardware redundancy.First, for a class of linear systems, the state feedback controllers are presented based on a condition for the existence of guaranteed cost state feedback controllers. This paper analyses the relationship between actuator gain error of each channel and guaranteed cost for closed-loop systems with state feedback controllers. Concepts of tolerate interval, tolerate factor of actuator gain error and hardware redundancy rate are presented. Considering mathematical model of actuator gain error, an algorithm is given to determine the tolerate interval, the tolerate factor and the hardware redundancy rate via optimization problems with linear matrix inequality(LMI) constraints. A numerical example is also given to illustrate the design procedures and their effectiveness.Second, for a class of closed-loop linear systems with dynamic output-feedback D-guaranteed cost controllers, hardware redundancy mode is proposed for sensor-signal gain error.Considering mathematical model of sensor-signal gain error, we present concepts of sensor-signal gain-error tolerate interval, tolerate factor and hardware redundancy rate.An algorithm is given to determine the tolerate interval, the tolerate factor and the hardware redundancy rate via optimization problems with LMI constraints. Engineers can design the sensor hardware redundancy according to the hardware redundancy rate of each sensor channel. An example of a plane’s landing process is also given to illustrate the effectiveness of the proposed method.Third, For a class of singular systems,the problem of reliable guaranteed cost control is studied. Based on LMI, a sufficient and essential condition of existing guaranteed cost control is given for singular systems without actuator faults. Considering mathematical model of actuator continuous faults, we present a sufficient condition of existing reliable guaranteed cost control. Design method of reliable guaranteed cost control is proposed by solving LMI. The closed-loop singular systems with reliable guaranteed cost control is quadratically stable and the performance index is bounded regardless of actuator faults. A numerical example is also given to illustrate the effectiveness of the proposed method.