Design And Stability Analysis Of Time-delay Reset Control Systems

In the actual control system,the time-delay phenomenon exists widely,which not only reduces the control performance of the system,but also sometimes leads to the instability of the system,making the system out of control.The stability analysis of time-delay systems has caused extensive research.Reset control can effectively overcome the limitations of linear feedback control design and improve system performance.Reset control is an important branch of control theory.It promotes the further improvement of control system theory,extends the applicability of the basic concepts and methods of control theory,and also presents more challenging theoretical issues.Compared with the classical linear control theory,the advantage of the reset control is that it can overcome the linear basis constraints with a very simple strategy,and the time lag is one of the main sources of this restriction.Therefore,The study of the performance of the reset control system with time-delay has great practical significance.Therefore,this paper makes a preliminary study of the stability of the time-delay reset control system,combines the reset control theory and the Lyapunov stability theory to obtain the corresponding stability criteria,and uses numerical simulation examples to verify the stability conclusions.The main research work of this paper is as follows:1.The stability of time-delay reset control system with time-dependent reset law is studied.By using the method of converting the time-delay reset control system into a sampling system,a new Lyapunov-Krasovskii functional is constructed and a triple-integral term is introduced to obtain a time-delay reset control system with less conservation stability criteria.Compared with most of the conclusions in the existing literature,the stability criterion obtained in this paper does not require the stability of the base system,so it is less conservative.2.This paper also studies the L2 gain performance problem of the reset control system with output time-varying delay under disturbance.Since the reset control system is a special hybrid control system,this paper uses the theoretical results of the hybrid control system to construct a set of augmented Lyapunov-Krasovskii functionals combined with the Newton-Leibniz formula and the integral inequality method.The delay-dependent stability criterion is also used to reduce the conservativeness of the stability criterion using the segmented Lyapunov function method.Finally,it is proved that the reset control can improve the L2 gain performance of the control system and enhance the system's anti-jamming performance ability.3.This paper aims at the influence of the time lag of the single-DOF remote operating system communication link on the system,and uses the reset control to overcome the limitation of the linear basis and designs a suitable reset controller.A mathematical model of the teleoperation system was established,and the stability of the teleoperation system with communication delay was analyzed based on the previous research results.Finally,a simulation study was performed under different time delays for both free motion and contact motion.It is verified that the reset control has better control performance for the teleoperation system with communication delay,which makes the system have smaller overshoot in the case of faster position tracking performance.