The Research Of Control Design On Feedforward Nonlinear Systems

Recently,the dynamic/static gain control design method attracted extensive attention of researchers,and was applied to study feedforward nonlinear systems.By using the dynamic/static gain control design method,the problem of designing controllers can be converted into that of designing a parameter,and the designed controllers have a simple structure.Compared with the forwarding method,the dynamic/static gain control design method is simpler.It is well known that the forwarding method and the saturated control method are powerful tools to design the stability controllers for the feedforward systems.The feedforward nonlinear systems without time delay have been studied by using the dynamic/static gain control design method in some existing papers.Since the time delay phenomenon is always inevitable,and the computer control technology is widely used,how to study the global asymptotic stabilization of delayed feedforward nonlinear systems,and the sampling data state feedback stabilization of feedforward systems without delay by using the dynamic/static gain control design method are the main research contents of this dissertation.In chapter 2,it is solved the problem of global stabilization for the feedforward nonlinear systems with distributed delays in both state and input.This dissertation for the first time uses the dynamic gain control design method to study such distributed delays problem.This dissertation presents a skillful nonlinear transformation,by which the feedforward nonlinear systems with distributed delays in both state and input are converted into new feedforward nonlinear systems with only state distributed delays.Then,another appropriate state transformation is introduced for the new systems,and the control design problem can be converted into the problem of designing a dynamic parameter.At last,the dynamic parameter can be determined by estimating the nonlinear terms,and the state feedback controller and output feedback controller are thus constructed such that the feedforward nonlinear systems are globally asymptotic stability at the origin.In chapter 3,it is solved the problem of global stabilization for the feedforward nonlinear systems with discrete delays and continuous delays in both state and input variables,and the involved nonlinear terms satisfy function gain growth conditions.In general,the study of such nonlinear terms is more difficult than that of nonlinear terms satisfying the linear growth condition,and it is an important and challenging work to study such feedforward nonlinear systems.With the help of Newton-Leibniz formula,it is introduced a novel nonlinear transformation,and the feedforward nonlinear systems with state and input delays can be converted into the new systems essentially with state delays.Then,the estimate of nonlinear terms is given through a lot of elaborate mathematical calculation,and a state feedback controller and a Lyapunov functional are delicately constructed in the process of the estimate.In chapter 4,for feedforward nonlinear systems with discrete and distributed delays in both state and input variables,by applying a model transformation,a design scheme of delay-free state feedback controllers are provided in chapter 4.The designed controller has a simple form.The closed-loop systems consisting of the feedforward nonlinear systems and the controllers,achieve globally asymptotic stability.In chapter 5,by using the static gain control design method,it is constructed a sampling data state feedback controller for the feedforward systems satisfying the linear growth condition.The problem of designing state feedback controller can be converted into the problem of finding a constant parameter L.In theory,a large enough L can be always found such that the sampling data controller globally asymptotically stabilizes the given systems.However,when a large L is chosen,the control gain of the designed controller will get much lower,and this reduces the practical control effect.Hence,under the condition that the resulting closed-loop systems can achieve stability,the parameter L should be picked out as small as possible.