Analysis Of A Class Of Delta Operator Systems Subject To Actuator Saturation

As everyone knows, almost all systems have saturation in the physical world which makes the control system more difficult to study. In the face of saturated nonlinear problems, most people study the performance of control system under ideal conditions.However, in the practical system, if the saturation phenomenon is ignored, the error between the output value and the theoretical value will be increased, and the performance of the system will be reduced. In recent years, although the research on actuator saturation control system has made great progress, the results of the actuator saturation and actuator failures in delta domain are very rare.This paper further studies the problem of estimating the domain of attraction for delta operator systems with actuator saturation. By using some new control strategies, the conservative of estimating the domain of attraction for delta operator system is reduced,and the convergence rate of the system is improved. The semi-global stability of delta operator system, and the problem of fault-tolerant control for delta operator system with actuator saturation have been studied. The stability condition of the system is obtained.Some numerical simulations are carried out. The research results are as follows:Firstly, the stability of actuator saturation control system has been studied based on the delta operator method. By improving the sampling step of system reasonably, the conservation of estimating the domain of attraction for delta operator systems has been reduced. Ellipsoid sets are used to describe the invariant set of delta operator system with actuator saturation. The shape of reference set is used to estimate the domain of attraction of the delta operator system with actuator saturation. We use Lyapunov function to obtain the stabilization condition of delta operator system. Finally, numerical simulation is carried out to verify the effectiveness of the proposed method.Secondly, we propose some new methods to study the speed of convergence of delta operator systems with actuator saturation. At the same time, linear matrix inequalities are used to calculate the ellipsoid sets. The new control strategy is proposed to improve the convergence rate of the system. Finally, numerical simulation is carried out to verify theeffectiveness of the proposed method.Thirdly, we study the problem of semi-global stability for delta operator systems with actuator saturation in null controllable region by designing new controllers. The concept of null controllable region is first introduced for delta operator system. Linear matrix inequalities are used to calculate ellipsoid sets of delta operator system with actuator saturation. In order to further expand the the domain of attraction for delta operator system with actuator saturation, we design a series of switching controllers to guarantee the semiglobal stability of delta operator system in a given region. Finally, numerical simulation is carried out to verify the effectiveness of the proposed method.Finally, we propose some new methods to study the problem of delta operator system.We firstly design the mathematical model of fault-tolerance control system with delta operator method. The fault-tolerant controller is designed by analyzing the expressions of the saturation term and the fault term. Ellipsoid sets are used to describe the invariant sets of delta operator system. Linear matrix inequalities are used to calculate ellipsoid sets of delta operator system with actuator saturation. The convex hull sets are used to describe the saturated nonlinear item. Finally, numerical simulation is carried out to verify the effectiveness of the proposed method.