Parameter Identification And Circuit Simulation Of Linear Multi-delay Systems

Linear multi-delay systems have been widely used in the fields of mechanical control,ecology and power electronics.When the structure of the system is known,determining the parameters in the model is the basis for further analysis,design and control.Usually the internal structure of the object being considered is complex and precise,this prevents people from destroying the system but can only rely on externally measured data to determine the corresponding parameters.The effectiveness of parameters got in this way is affected by factors such as the structure of the system,noise,and excitation signals.Parameter identification has always been the important field of control.This paper aims to study the parameter identification method of linear multi-delay system and verify the effect of the given identification method through the built electronic simulation experiment platform.The content of this article has the following aspects:In the first part,the related concepts of linear delay differential equations are introduced.Also,the principle of least squares and theories of circuit analysis are shown.In the second part,the identification problem of linear multi-delay systems is studied.Firstly,a recursive noise reduction method for processing data is given,and the observation data containing noise is filtered.Secondly,considering if delay amount is known,different parameter identification algorithms are given.For systems with known delays,a parameter identification method based on numerical integration and recursive least squares method is given.For the unknown delays,the original problem is transformed into an optimization problem only about the delay amount,and the momentum gradient and the least square method are used to estimate the coefficient and the delay amount at the same time.Finally,the numerical simulation results are given to verify the method.In the third part,the circuit simulation of the linear delay system is studied.The linear dynamic system is realized by using capacitor and resistance elements,and the delay circuit is constructed by the operational amplifier and the single-chip microcomputer.Finally,the identification method is verified by the data collected by the oscilloscope.