Study On Control Theory For Nonlinear Systems With Input Uncertainty

The first step of designing control system is to build the mathematical model of controlled plant.Due to the complexity of actual physical system,the mathematical model is the presence of unmolded dynamics or neglected system features.Besides,the controlled object is also affected by parameter uncertainties and external disturbances.The complex uncertainty make the control system design much more difficult,but conventional methods for uncertain nonlinear systems rarely take the input uncertainty into consideration,and gradually cannot be applied to the guidance and control systems,such as hypersonic vehicle,maneuvering target interceptor,etc.This paper mainly studies two kinds of nonlinear systems,one kind is uncertain control gain,which may cause unknown control direction of nonlinear system,the other is input disturbance,or matched and unmatched disturbance.The main contents and contributions of this paper are as follows:Super-Twisting sliding mode control for nonlinear systems with unknown control gain is studied.Firstly,Super-Twisting sliding mode control for first-order nonlinear systems with uncertain control gain is designed.The relationship between parameters of controller and bound of uncertainty is build,and the obtained upper bound of convergence time is more precision.An adaptive Super-Twisting sliding mode control law for second-order nonlinear systems with unknown control gain is proposed,where the adaptive law is designed based on Lyapunov method.The proposed method improves the control precision of nonlinear system with wide range of control gain uncertainty,this kind of second-order sliding mode control could effectively reduce chattering,and is applied to guidance law with impact angle constraints for maneuvering target.The switching control strategy for nonlinear systems with unknown time-varying control directions is studied.Firstly,conventional design method is analyzed and compared,including Nussbaum function,monitoring function,etc.Based on conventional sliding mode control and Lyapunov condition,the convergence condition for situation,where the direction of controller is not same with plant,is built.We hold that this situation cannot directly affect the convergence.Differential Lyapunov function is employed to design the switching strategy,not identify control direction of plant.This research provides a new way for systems with unknown control direction.Nonsingular terminal sliding mode control for nonlinear systems with multiple input disturbances is studied.Aiming at nonlinear systems with time-varying unmatched multi-input disturbance,Lyapunov method is employed to design extended nonlinear disturbance observer,which is used to estimate disturbance and its changing rate.The MIMO system is separated into fast time-varying inner loop and slow time-varying outer loop,novel sliding mode surface and nonsingular terminal sliding mode controller with disturbance compensation are designed respectively.The proposed method is useful to improve control precision of nonlinear systems with unmatched multi-input disturbance,and is applied to controlled design for reentry gliding vehicles.Fast convergent nonsingular terminal sliding mode control for nonlinear system with input disturbance is studied.In view of the non-strictly convergence of conventional nonsingular terminal sliding mode control,exponential-type sliding mode surface and fast convergent nonsingular terminal sliding mode controller are designed,based on Lyapunov method.The proposed method can effectively achieve global convergence,and is applied to control system design for reentry gliding vehicle,guidance law design with impact angle constraints for intercepting maneuvering target.Disturbance observer is employed to compensate unknown acceleration of target,and results demonstrate that both the rapidity and precision can be improved.Gauss pseudospectral robust predictive control for constrained nonlinear systems with uncertainties is studied.The Min-Max problem in finite-time horizon for nonlinear systems with uncertainties is designed,then Gauss pseudospectral method is employed to transform it into a discretized nonlinear programming problem.Based on Legendre-Gauss orthogonal polynomial,a new set of collocation points and also receding horizon optimization strategy are proposed.The proposed method could strictly fulfill constraints and improve the speed of solution.The application in integrated guidance and control system for interceptor demonstrates that the proposed method could achieve the ability of rapid response to maneuvering target,and the complexity of conventional integrated method is reduced.