Stable And Non-collocated Output Tracking Control For One-dimensional Wave Equation With Uncertainties

In modern engineering control problems,the partial differential equation system can describe many physical models of actual engineering.The control problem described by distributed parameter control system is more accurate than ordinary differential equation.The representation object of partial differential equation control system is the same as that of distributed parameter control system.Driven by the development of technology,the related theory of the modeling process of the actual physical model has been greatly improved.The distributed parameter system(DPS)has also made great progress.One of the research focuses has been stability theory in distributed parameter control theory.In recent years,the problem of non-collocated output tracking and consistency tracking of distributed parameter systems with uncertain factors has aroused the research interest of many scholars.The non-collocated performance output tracking of a type of one-dimensional wave equation model system with uncertain factors and the consistent synchronization control between multiple system models of one-dimensional wave equation network are studied.The research problem is described by the coupling of each system of the one-dimensional wave equation model.After careful analysis and research,the research on the output tracking of the distributed parameter control system has been further developed.This paper is mainly divided into the following parts.The following is a detailed description of the research content.In the second chapter,the method of active disturbance rejection control(ADRC)is introduced.The control process is to obtain nonlinear error feedback by combining the output signal of the tracking differentiator and some of the output variables of the extended state observer to obtain the non-linear error feedback,calculate the main control output law,and then use the calculation to compensate for the disturbance and suppress the influence of the disturbance.And finally get the control feedback law of the system controller.In addition,by improving the acceleration function of the existing tracking differentiator.In this chapter,a fast exponential integrative nonlinear tracking differentiator is proposed.The fast exponential integral type tracking differentiator is briefly explained.Finally,the simulation effect of the second-order controlled object of the ADRC is shown,which better explains the effective treatment of the system uncertainty by the active disturbance rejection controller,and demonstrates the superiority of the control performance of the ADRC.The contents of the third chapter are as follows.The control of one-dimensional wave equation model tracking non-differentiable trajectory signals with uncertain factors-output non-collocated control problems are mainly studied.Among them,control input and disturbance signal,control input and output information exist under two boundary conditions respectively.The disturbance rejection strategy is derived from the use of the ADRC in this chapter,The output feedback controller is designed to deal with the uncertain disturbance factors in the control system,and the servo system is designed to solve the output tracking problem.First,In order to obtain the differential information of the signal,a tracking differentiator is designed.Then,the output feedback controller is designed to overcome the influence of disturbance on the controlled object,and the output tracking auxiliary system and servo system are constructed to prove the uniqueness of the system solution.Finally,the stability and fitness of the closed loop system are considered.The purpose of tracking the trajectory signal u _ref(t)by the one-dimensional wave equation w(0,t)is completed.The numerical simulation process of the one-dimensional wave equation control model was completed in the Matlab simulation environment,and the simulation results verified the feasibility of the controller design process.In the last section,the synchronous tracking control problem of a multi-Agent system with N network one-dimensional wave equation model with general disturbance and time-varying structure disturbance is considered.First,the output feedback control is established based on the estimation/cancellation strategy of the ADRC.The idea of active disturbance rejection control is to find a consistent strategy by establishing an infinite dimensional disturbance observer.This chapter only uses the input and output measurement information of the one-dimensional wave equation network to follow the system to design an infinite-dimensional extended state observer that estimates the interference information of the network system.So as to provide any degree of attenuation and suppression to matching interference.Secondly,the synchronization controller is designed according to the network communication protocol and topology matrix to realize the information exchange between each network system to achieve system status and output synchronization.Finally,the Lyapunov function is designed and its derivative is obtained,and then the stability of the synchronization controller is proved,and the stability and well-posedness of the closed-loop system of the network one-dimensional wave equation are proved.When there is general time-varying structural disturbance signals in the synchronization process,the ADRC method is used to effectively shorten the disturbance signals estimation time and reduce the estimation error.Three numerical examples of one-dimensional wave equation network systems show the effectiveness and feasibility of the designed controller.The article concludes with a summary of the research content and process of this article,The future research issues facing the distributed parameter control system output tracking and active disturbance rejection control technology are proposed.The research direction of distributed parameter system in the future is illustrated.