The Development And Improvement Of(PIDCDTDS) Toolbox For The PID Controller Design Of Time-delay Systems

In this thesis,we will study the design of PID controller for time-delay systems and develop the PIDCDTDS toolbox.It is a very classic and important problem to illustrate the design of PID controllers for time-delay systems,since the widespread use of PID control in modern industry and the prevalence of time delay.This thesis is based on the frequency sweeping framework.By this method,we can obtain the detailed stability interval of the parameter τ However,we also need artificial analysis after drawing the frequency sweeping curve.In particular,the gain(kP、kI,kD)and time-delay parameter τ in the time-delay PID control system are all free parameters.To the best of the authors’ knowledge,although the four-parameter problem is deeply studied in many literatures,the research on four free parameters is not yet sufficient.By introducing the auxiliary characteristic equation and the algebraic criterion,we can link the critical imaginary root with the index ΔNU of describing the number of unstable roots of the system.Hence,we can study the variation of the system in the parameter space and analyze the asymptotic behavior of the critical imaginary root.Eventually,this controller design problem with four-free-parameter is solved analytically.This study can not only solve the problem that the system has multiple roots and degenerate critical imaginary roots,but also obtain the multiple time-delay stability intervals or time-delay stability intervals that do not start from zero.At the same time,by comparing with the examples in the existing literature,we can find that our method is able to obtain similar or even better results by using the simplest controller.Therefore,on the basis of theoretical completeness,we have developed the PIDDDTDS toolbox,which is very simple to operate.It only needs to input the transfer function,the range of the controller gains(kP,kI,kD),and the maximum search value of the time-delay parameter τ.We can obtain the stable domain(kP,kI,kD,τ)without any work experience and design knowledge of the PID controller.In practical applications,it can provide guidance for engineers of selecting the appropriate controller gain in the stability domain of the time-delay system.At present,we have applied it to the design analysis of the time-delay PID controller for DC motors,and can obtain multiple timestabilization intervals for stabilizing the DC motor.This applies our research from theory to practice and lays the foundation for the application of our research in practice.