A Nonlinear Control Design For A Class Of Underactuated Systems

The underactuated systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled.The major character is that the dimension of input space is less than that of output space.Because fewer actuators are utilized,the mechanical design and manufacture of under-actuated systems become more simplified than that of the full-actuated systems.More,the cost as well as the system weight could be reduced.Thanks to these benefits,a lot of practical systems are designed to be under-actuated,such as robotics,aerospace systems,marine systems,flexible systems,mobile systems,and locomotive systems and so on.Although the underactuated nature brings much convenience to system design and manufacture,it creates a great challenge for the control of the systems.For these reason,underactuated systems have become a research focus in the field of control theory.In this dissertation,the control problems of a class of underactuated mechanical systems are studied.This paper uses the example of non-holonomic underactuated mechanical systems to illustrate the control scheme of such systems.The content of the research includes the following:First,the definition and characteristics of the underactuated system are introduced,includeing many applications in actual life.In the case of overhead crane,this paper illustrates the underactuated characteristics bring convenient on the design and manufacture.At the same time,and also brings a great challenge for the control.Furthermore,this paper expounds the research status quo of the underactuated system.Second,this chaper give the underactuated system the construction method of mathematical mode by using Lagrange dynamics method,and analyzes the structural characteristics of the model.With 2D overhead crane and 2-DOF underactuated planar closed-chain robotic system as the research object,it illustrates the deducing process of the mathematical model.Third,in view of 2D overhead crane system under the external disturbance,the finite time positioning and eliminate swinging control problems are reasearched.Transform overhead crane system into the chained system.Based on terminal sliding mode control technology and the crane path planning,we put forward the finite time controller of the positioning and eliminate swinging problem.At the same time,using the method adding a power integrator,the finite time positioning and eliminate swinging control problems are discussed further.And the stability of designed controller is proved.The simulation results verify the effectiveness of the proposed control plan.Fourth,in view of the character of unknown parameters and having external disturbance of the 2-DOF underactuated robotic closed-chain system,we design the adaptive fuzzy control based on differential flat and make it meet the H_?tracking performance.Finally,the Matlab simulation results show that the influence of fuzzy approximation and external disturbance on the tracking error is attenuated to an arbitrarily desired level by the proposed method.Finally,combining with the results in this paper,we make a brief summary,and give the applied research prospect of the control strategy of the under-actuated mechanical system,and pointed out the direction for further study.