Identification For Linear Continuous-Time Systems With Time Delays Based On Sine Responses

Due to the influence of transmission medium,surrounding environment and human factors,the control signals will inevitably have time delays in the transmission process.The occurrence of time delays seriously affects the control quality and even stability of the systems,Therefore,it is of great theoretical significance and application prospect to study the parameter identification methods of time-delay systems.In this thesis,based on the observation data of sinusoidal responses,the parameter identification methods of linear continuous time-delay systems are studied,and the main contents are as follows:1.For the linear systems,their sinusoidal responses are sinusoidal signals with phase delays and the same frequency as the input signals,that is,a linear combination of sinusoidal signals and cosine signals with different amplitudes.Therefore,for the firstorder linear continuous time-delay systems,sinusoidal signals with different frequencies are given respectively.Based on the measured data of the sinusoidal responses of the systems,a stochastic gradient(SG)algorithm for estimating the amplitudes of the sinusoidal signals and the cosine signals in the sinusoidal responses is derived.Then,according to the obtained amplitudes,a gradient-based iterative(GI)algorithm is derived to identify the parameters of the original systems.By combining the two algorithms,the stochastic gradient and gradient-based iterative(SG-GI)algorithm for the first-order systems is derived.By introducing the theory of multi-innovation identification,the multi-innovation stochastic gradient and gradient-based iterative(MISG-GI)algorithm for the first-order systems is proposed.2.For the second-order linear continuous time-delay systems,different frequency combined sinusoidal signals are applied,and the output response is a linear combination of multiple sinusoidal responses with different frequencies,that is,a linear combination of sinusoidal signals and cosine signals with different frequencies and amplitudes.Based on the measured data of the sinusoidal responses of the systems,a stochastic gradient(SG)algorithm for estimating the amplitudes of the sinusoidal signals and the cosine signals in the sinusoidal responses is derived.Then,according to the obtained amplitudes,a gradient-based iterative(GI)algorithm is derived to identify the parameters of the original systems.By combining the two algorithms,the stochastic gradient and gradient-based iterative(SG-GI)algorithm for the second-order systems is derived.By introducing the theory of multi-innovation identification,the multi-innovation stochastic gradient and gradient-based iterative(MISG-GI)algorithm for the second-order systems is proposed.3.The identification methods of the first-order and second-order systems are extended to the high-order systems.For the high-order linear continuous time-delay systems,different frequency combined sinusoidal signals are applied.By measuring the observation data of the sinusoidal responses of the systems,the amplitudes of the sinusoidal signals and cosine signals in the sinusoidal responses of the systems are identified,and the system parameters are solved according to the relationship between the amplitude parameters and the system parameters.Then a stochastic gradient and gradient-based iterative(SG-GI)algorithms for the high-order systems are proposed.By introducing the theory of multi-innovation identification,the multiinnovation stochastic gradient and gradient-based iterative(MISG-GI)algorithm for the high-order systems is proposed.In conclusion,based on the observation data of sinusoidal responses,this thesis adopts the idea of step-by-step identification,and discusses the identification problems of the linear continuous time-delay systems from the shallower to the deeper.Each algorithm includes identification steps,flow charts and corresponding simulation examples.According to the simulation results,the effectiveness of the algorithms is illustrated.Finally,the thesis draws conclusions and prospects,and the problems to be solved and other aspects worthy of further study are briefly introduced.