The Study Of Optimal Control Of Discrete Systems With The Exponential Decay Performance

With the development of society and the rapid development of science and technology,computers performance and the level of control technology have been improved continuously.More and more scholars pay attention to the control theory of discrete systems.In practical engineering,the field involved time delay phenomenon is more extensive,and the phenomenon of time delay usually exists in almost all of the actual control systems.The existence of time delay often degrades the performance of the systems.In addition,the control systems are more or less disturbed by the outside world,and the dynamic performance and steady state performance of the systems will be worse.Therefore,it is significant to study the problem of time delay and disturbance.Firstly,this paper gives a brief overview of the discrete systems.In this paper,the time delay systems are introduced retrospectively,and the research methods and research trends of delay phenomenon in this field are presented.The optimal control theory and its development are summarized,and the research statuses of the optimal control theory of the time delay systems are elaborated.Finally,the vibration control problems are summarized,and active vibration control technology are mainly introduced,and the research and development and the optimal control problems of active vibration control are sketched.Secondly,for the discrete system,the optimal control problem of state variables with time delay is studied.A new discrete system is obtained by adding exponential decay,and the optimal control problem aimed at this discrete system is studied.The optimal control problem of the original system is transformed into a two point boundary value problem(TPBV)with neither a leading term nor a delay term by introducing a sensitivity parameter,and the optimal control law is obtained by summation of series.Finally,the feasibility of the method is verified by experimental simulation.Then,the discrete system with random disturbance is studied.Firstly,the Calman filter is used to estimate the random noise disturbance,and then the original system is analyzed by the separation principle to obtain the optimal control law.Finally,the feasibility of the method is verified by experimental simulation.Finally,the vibration model of the cantilever beam on elastic base is chosen as the research object,and the optimal control problem of the discrete system with external disturbance based on the exponential attenuation performance is studied.According to the knowledge of vibration mechanics,the vibration differential equation of cantilever beam with flexible foundation is derived,and then the state space expression of cantilever beam system with flexible foundation is obtained by combining the piezoelectric equation.The discrete system is obtained by discretizing the continuous system,and it is a discrete system with continuous disturbances that we want to study for a discrete system with continuous disturbances.The optimal control of discrete system with disturbance is studied,and the feasibility of the method is verified by experimental simulation.