Fixed-time Tracking Control Of Nonlinear Systems Based On Auto Disturbance Rejection Control

With the rapid development of control system theory,the actual control system model becomes more and more complex.There are non-model dynamics,unknown nonlinear and disturbance in the system as the result of external interference,difficulty in obtaining system parameters accurately.Active disturbance rejection control(ADRC)plays a crucial role in uncertain nonlinear systems because of its excellent ability in controller robustness and uncertainty reduction.Although the research on ADRC has achieved fruitful results and been widely used in many fields,there are still some problems to be solved.In practical applications,the initial value of the system is often difficult to obtain accurately,which makes the convergence time of the system difficult to estimate.However,fixedtime control has been widely concerned in recent years because its convergence time is only related to the design parameters.Based on Lyapunov theory,homogeneous theory and fixed-time stability theory,this paper takes nonlinear systems and extended state observer(ESO)as research objects.The fixed-time control problem of nonlinear systems with different constraints and structures is studied deeply in this paper.The main work arrangements are as follows:A fixed-time tracking controller based on active disturbance rejection is designed for second-order uncertain nonlinear systems with external disturbances.In this control,internal uncertainty and external disturbance are regarded as total disturbance,and the total disturbance is extended to a new system state based on the idea of ADRC.By constructing a fixed-time extended state observer(FTESO),the total disturbance of the system is estimated,and the observation error of the observer is guaranteed to converge within fixed-time.The fixed-time tracking controller is designed based on backstepping step method.Based on Lyapunov stability theory,homogeneity theory and fixed-time stability theory,the stability of the system is analyzed and the upper bound of stability time and convergence domain are given.A fixed-time anti-saturation tracking controller based on active disturbance rejection technology is designed for high order uncertain nonlinear systems with external disturbance and input saturation.The high-order FTESO considers the internal uncertainty and the external disturbance as the total disturbance,and designs an fixed-time antisaturation controller based on the backstepping method.The controller can obtain the desired anti-saturation performance by adjusting the anti-saturation gain.Based on Lyapunov stability theory,homogeneity theory and fixed-time stability theory analysis,the stability time upper bound and error convergence domain of fixed-time are given.For high order uncertain nonlinear systems with external perturbations and output constraints,a fixed-time output constraint tracking controller based on active disturbance rejection technology is designed.Firstly,the improved high-order FTESO is designed to estimate the uncertainty and external disturbance in the higher-order state.Compared with the previous FTESO,its gain parameters are less conservative.An output constraint tracker with fixed-time is designed by means of barrier Lyapunov function(BLF)and backstepping method,ensuring that the output of system is always within the constraint range.The stability time upper bound and convergence domain of tracking error are given.