Study On Controller Design For Second-order Discrete Time Delay Systems

In the actual process of industrial production,the phenomenon of time-delay is ubiquity.Many controlled plants with time-delay can be approximated as a second-order system with purely time-delay.Due to the existence of time-delay,the controlled volume of the system often can not reflect the current state of the control system in time and it may affects the dynamic performance of the control system.It sometimes even affects the stability of the system.Therefore,it increases the difficulty of analysis and design of controller.On the other hand,with the rapid development of computer technology in recent years,discrete systems have been widely used in the industrial control fields,the analysis and control of discrete time-delay systems has become the difficulties and hot spots of present research.Therefore,the controller design of the second-order discrete-time delay system has significant theoretical and practical meaning.The distribution of the eigenvalues determine the stability and dynamic performance of the system and it can provide an important theoretical basis for the design of the system controller.In this thesis,the distribution of eigenvalues of discrete time-delay systems is analyzed and the controller based on pole placement is used to design and study the controller of discrete time-delay systems to achieve the desired system performance.The prime task and research results of this thesis are as follows:(1)The distribution of the eigenvalues of discrete time-delay systems:Based on the Tchebyshev polynomials,the characteristic polynomials of discrete time-delay systems are described.Stability criterion of characteristic polynomial and the theorems of the number of eigenvalues in discrete circles based on Tchebyshev expressions are obtained.(2)Design method of discrete-time system controller based on pole placement:Combining with the conclusions of the distribution of the eigenvalues,a controller design method based on generalized Nyquist curve for pole placement is first studied.Afterwards,a controller design method based on Hermite-Biehler theorem is studied by means of calculation.Finally,the simulation and validity verification of the method are carried out for the second-order discrete time delay system.(3)The further improvement of the design method of discrete time-delay system controller:the aboved methods mainly focus on the configuration of the dominant pole,and only limit the non-dominant poles in a region.As the position of non-dominant pole also affects the performance of the system,in order to improve the performance of the system furtherly,the design method of PID controller based on generalized Nyquist curve is improved and the quadrant configuration of non-dominant pole is completed.Second-order discrete time-delay systems are simulated and validated.(4)Sensitivity analysis of discrete time-delay controller design method:When the parameters of the second-order discrete-time delay system are fluctuating,the eigenvalues of the discrete-time delay control system designed based on the pole placement method are studied and analyzed.We analyze the fluctuation of the model parameters a,b and c respectively and the pure time-delay ? compare them with the Smith predictor.Finally,the corresponding conclusions are obtained.