Decoupling And Asymptotic Output Tracking Problems For Nonlinear Differential-algebraic Time-delay Systems

In practical projects such as ecological engineering,electrical network analysis,economics,and computer-aided design,there are almost all nonlinear factors,time-delay and uncertainties,and some of these control systems are mixed by differential equations and algebraic equations.Therefore,the mathematical model of the entire system can be expressed as the form of nonlinear differential-algebraic systems,which is the extension of the description of the complex systems by the differential systems.The theory and application of nonlinear differential-algebraic systems have become a hot research field in the control community at home and abroad in recent years.Due to the complexity and diversity of the nonlinear differential-algebraic time-delay system itself,as well as the effects of time-delay and interference,the research on nonlinear differential-algebraic systems becomes one of the hot topics in control theory research.This thesis considers input-output decoupling,disturbance decoupling control and asymptotic output tracking of a class of nonlinear differential-algebraic time-delay systems with time-varying state variables,and gives the results in the case of state feedback.The results are given in the context of status feedback.The main research works are as follow:1.For a class of continuous multi-input multi-output nonlinear differential-algebraic timedelay systems,the input-output decoupling control problem is discussed.Using nonlinear differential geometry theory and time-delay operators,a new definition of extended M-derivatives and extended M-brackets for state delays are proposed.Based on the concept of relative order of M-vectors,sufficient conditions for the existence of static state feedback controllers are given,and the stability of closed-loop systems is studied.The controller ensures that the closed-loop system is decoupled input-output.Finally,a numerical example is given to illustrate how to use the proposed decoupling algorithm to implement the input-output decoupling of the system.2.For a class of state variables with time-delay nonlinear differential-algebraic systems,the decoupling problem is solved.Using delay operators and extended M-derivatives,sufficient conditions for decoupling of system disturbances are discussed.Two kinds of nonlinear feedback control algorithms with measurable and unmeasurable interference are given.The numerical examples verify its effectiveness.3.For a class of nonlinear differential-algebraic time-delay systems,the concept of asymptotic output tracking of the system is proposed.Using the delay operator,extended M-derivatives and M-vector relative order,the asymptotic output of a nonlinear differentialalgebraic time-delay system is studied.For a given reference output,the conditions for asymptotic output tracking of this type of systems are obtained,and the feedback control law of the systems is given.The output of the systems tracks a given reference output asymptotically.The numerical example illustrates the correctness and feasibility of the proposed method.