Research And Plication Of Adaptive Control For Pure Feedback Nonlinear Systems With Input Constraint

In industrial control systems and practical engineering applications,there is no linear object in the strict sense.Nonlinear phenomena such as friction,saturation,dead time and time delay greatly increase the difficulty of system controller design.Traditional linear control theory has been difficult to solve today's complex and variable nonlinear problems.In recent years,with the continuous in-depth study of nonlinear system control,many control methods have emerged,such as feedback linearization,inversion control,fuzzy logic control and so on,which promote the development of control theory and technology.However,in many practical nonlinear systems,it is necessary to consider the effects of parameter uncertainty,non-affine structure,saturated input and other constraints,as well as the steady-state and transient performance of the system to meet the control requirements,which makes the design of system controller more difficult.Aiming at this challenging problem,this paper takes the input constrained pure feedback nonlinear system as the control object,and discusses the design of system controller in detail.The main work of this paper is as follows(1)An adaptive control scheme based on backstepping control is proposed for a class of pure feedback nonlinear systems with non-affine input constraints and unknown parameters.Compared with strict feedback system,pure feedback system is more general and can describe more practical application systems.However,due to the non-affine structure in control input and system state,it is impossible to design the controller of the system directly.Therefore,based on the method of increasing integral,the auxiliary integral system is introduced and combined with the new coordinate transformation,the original dimensional non affine system is extended to dimensional affine system,which effectively solves the non-affine problem of the system,and then a new adaptive control scheme is proposed through the inversion control method.The designed adaptive law can quickly and accurately approximate the unknown parameters in the system.(2)A new adaptive control scheme with preset performance is proposed for a class of pure feedback nonlinear systems with saturated input constraints and internal disturbances.The saturated input signal of the system is a kind of unsmooth signal,which greatly affects the stability of the system.Therefore,a class of smooth nonlinear functions is introduced to approximate the saturated input signal of the system by combining with bounded error.Different from the increasing integral method,this part adopts the mean value theorem for the non-affine structure in the pure feedback system,so that the state variables and control inputs of the system are transformed into affine relations.Then,a new class of adaptive controller is designed by using the theory of preset performance control,fuzzy logic control and backstepping control,and the stability analysis of the controller is given by using Lyapunov stability theory.It is proved that all signals in the closed-loop system are uniformly bounded.(3)The designed system controller is applied to nonlinear systems such as flexible single link manipulator and Brusselator chemical reaction system for simulation verification.The simulation results show that the designed system controllers have good tracking performance,the adaptive law of the system can quickly and accurately approximate the unknown parameters in the system,and the dynamic performance and steady-state performance of the system controller are guaranteed under the preset performance control.Finally,the design scheme is compared with other schemes,and the results show that the controller designed in this paper is better than other schemes in system performance and adaptive control effect.