Research On Control Of Upper Trianglar Underactuated Nonlinear Systems

The upper triangular underactuated nonlinear system,also known as the feedforward underactuated nonlinear system,is widely used in various fields such as robotics,construction,transportation,and aerospace.The underactuated nonlinear system is a kind of mechanical system whose number of control inputs is less than the degree of system freedom.According to the form of its state equation,it can be divided into feedforward specification type,feedback specification type and non-triangular specification type.This paper first uses the Lagrangian method to model the dynamics of nonlinear systems.According to the characteristics of dynamics,mechanical systems can be divided into several common types,including fully driven mechanical systems,underactuated mechanical systems,smooth mechanical systems,and Non-complete mechanical system.Among them,the model characteristics of the underactuated mechanical system are mainly discussed,and the Lagrange equation is used to model the dynamics of some typical feedforward underactuated nonlinear systems,including the pendulum system and the oscillating system.The transformation organizes it into a feedforward specification.The idea of nested saturation control is a classical stability control idea for a feedforward nonlinear cascade system,which is skillfully combined with the system structure characteristics of the feedforward system.Based on the idea of nested saturation,many control schemes for feedforward systems have been derived.Most control schemes need to rely on certain a priori conditions,such as requiring nonlinear systems to be known,or system states with certain boundary conditions,or The system can be linearized,or certain states of the system need to meet a certain rate of growth.Based on the traditional nested saturation control method,this paper introduces the dynamic saturation factor,designs its online logic switching idea,discusses the stability control problem of the feedforward underactuated system without a priori condition,and gives the mathematic analysis.Finally,based on the designed control scheme and GoogolTech hardware equipment,the simulation and physical experiments are carried out for the sway system and the swinging system,and the characteristics and deficiencies of the controller proposed in this paper are discussed.