Constraint Nonlinear Control And Its Application In Train Traction System

Constraints are ubiquitous in physical systems.These constraints will have different effect on the system,such as:physical stoppages,saturation,as well as performance and safety specifications.If the system is running in violation of the constraints,it is very likely to result in performance degradation.In severe cases,it can even endanger or damage the system.This paper is based on the study of high-speed train control system.First of all,for a class of nonlinear uncertain systems,the controller design problems with state constraints or input constraints are studied.Then the research results are applied to the actual train control system.The main research work is summarized as follows:In order to stabilize a class of uncertain nonlinear strict-feedback systems with full state constraints,an adaptive backstepping control method is proposed.A Symmetric Barrier Lyapunov Function is introduced in each step of backstepping control algorithm to ensure that all states do not violate the constraints.In this way,a new type of adaptive backstepping control algorithm is investigated.The main advantage is less adaptive parameters under the state constraints.By making use of Lyapunov analysis,the tracking error,the adaptation law and the control input can be proved bounded,at the same time the state constraints are not violated.According to the principle of dynamics,the single-point dynamic model of the train is constructed,and its uncertainties properties are analyzed qualitatively.The above state-constrained control method for a general nonlinear system is applied to this actual train system to realize the control of the train under the constraint of speed.Due to only take the high-speed train speed constraints into account,it belongs to the part of the state constraints.Similar to the method given by the full state constraint,a controller design method using Barrier Lyapunov Functions for constrained states and the rest of states use quadratic function controller design methods.In this way,a backstepping adaptive controller is designed under speed constraints.The stability of the system and the convergence of the error of velocity and displacement of high-speed train are given in this paper.The simulation example proves the validity of the proposed algorithm.Through backstepping design procedure,a new adaptive controller is designed for a class of strict-feedback nonlinear systems with input saturation.The controller consists of a backstepping controller and a robust adaptive controller.The adaptive law is got from Lyapunov function and Barbalat lemma.In order to settle the problem of actuator saturation,an input constraints error dynamic enlargement method is adopted.By making use of Lyapunov analysis,the tracking error,the adaptation law and the control input can be proved bounded,at the same time the state constraints are not violated.Due to the output is limited in the train traction and braking process,applying the above control method under input constraints for a general nonlinear system to this train control system.The saturated backstepping adaptive controller of the train is designed.In a limited time,the tracking error of the train can be converged to the expected accuracy range.And the article gives the theoretical proof of the global stability of the system.The simulation example proves the validity of the proposed algorithm.