Research On Model Reduction Of Discrete Time-delay Systems Based On Finite Frequency Domai

With the increasing complexity of control systems,many physical models in engineering problems need to be abstracted into higher-order mathematical models to represent.Among them,high-order,nonlinear and other problems are widespread and inevitable phenomena.They are also the hot research directions in control theory.Moreover,it is found that the frequency of the system response and the frequency of external disturbance signals are often concentrated in a specific frequency domain,not in the full frequency domain.This phenomenon allows us to improve the control performance of the required frequency domain by sacrificing the performance of the secondary frequency domain.In addition,because of the transmission of information between sensors,controllers and actuators,there is a time difference when switching different systems.The above situations will lead to time delay.These problems not only increase the computational cost,but may also cause the system instability,too conservative,or even unable to achieve the expected control effect.The actual model must have a fault tolerance,and the model uncertainty can better reflect the phenomenon,but it is often ignored in the previous modeling process.This paper focuses on the model reduction of discrete-time linear systems with finite-frequency specifications.Based on the Generalized Kalman-Yakubovich-Popov(GKYP)lemma,and using the relaxation matrix with variable parameters.We propose algorithms based on LMIs to obtain a stable reduced order model that meets the finite-frequency performance.The main research work of this paper is as follows:Firstly,we introduce the main research content of the finite-frequency and the main research methods of model reduction,as well as the advantages and disadvantages of existing research results.Based on the above analysis,the finite-frequency H∞ performance analysis index is established with the help of Parseval theorem.Secondly,we transform matrices according to generalized KYP to find the orthogonal complement form of the parameter matrices.Next we use Finsler lemma to obtain indicators with finite-frequency performance in different frequency ranges.Then,the stability conditions of the system are obtained by constructing a suitable Lyapunov function(LKF).At the end of each chapter,we give numerical examples,these numerical examples show that the proposed method has lower conservatism and more accurate approximation performance than the existing methods.Furthermore,when we study discrete linear systems with time-delay and model uncertainties,we again introduce relaxation matrices with parameters based on generalized KYP to convert the model reduction problem into a convex optimization problem.The finite-frequency performance conditions and stability conditions are obtained by using Jensen inequality,Wirtinger inequality and similarity transformation.Numerical results show that this method is feasible and has lower error than the existing methods in the literature.Finally,the linear design model of offshore floating wind turbine with limited degrees of freedom was obtained by using the MATLAB system identification tool.Then we verified the effectiveness of this reduction method in practice by abstracting the system and constructing the model.This tentative application provides theoretical support for offshore floating wind turbine control with multi-modality.