Research On Minimum Phase Properties Of Discrete-Time Systems Based On Triangle Sample-and-Holds

Minimum-phase(MP)properties play a significant role in the analysis of the control system and controller design process.The non-minimum phase(NMP)property extremely restricts the achievable control performance and the direct application of many control algorithms.However,a continuous-time MP system with stable zeros or zero dynamics is discretized by a sample-and-hold,maybe the corresponding discrete-time system becomes the NMP system.The control of NMP systems is more difficult than that of MP systemsZeros or zero dynamics of discrete-time systems are multivariate function of the relative degree,sampling period and sample-and-hold device,and converge to the roots of a specific polynomial.For a deterministic continuous-time system,different sample-and-holds will affect the zeros or zero dynamics properties of discrete-time systems.Therefore,studying the MP properties of the discrete-time system under different sample-and-holds is helpful to reveal the zero or zero dynamic mapping relationship during the discretization process and ensure that the MP properties are not affected during the discretization process.Aiming at the issues of MP properties of discrete-time systems not be preserved during the sampling process,this dissertation is based on a new class of triangle sample-and-hold(TSH)and studies the MP properties of discrete-time systems and conditions of MP properties preserved for a linear system,nonlinear system,and time-delay system.Further,the results of this dissertation will push the relevant researches about the analysis and design of discrete-time systems.The main results of this dissertation are presented as follows:(1)In the case of the forward triangle sample-and-hold(FTSH)and the backward triangle sample-and-hold(BTSH),this dissertation deduces the explicit expressions of the discrete-time model based on continuous-time linear single-input single-output(SISO)system.Furthermore,the relationship between the zero dynamics of the discrete-time linear system and the relative order of the continuous-time system and TSH designable parameters is clarified.The asymptotic properties and stability conditions for the corresponding discretization zero dynamics in the limiting conditions of the sampling period are also analyzed.At the same time,the results show that TSH can let the discrete-time system is MP while ZOH fails to do.What is more,FTSH provides a wider range of adjustable parameters than BTSH to ensure the corresponding discrete-time system has MP properties.(2)Because of TSH is facing the difficulties in the engineering implementation.This dissertation explores the method of BTSH and FTSH implemented by ZOH and deduces the discrete-time linear system model in the case of approximate BTSH and approximate FTSH.What is more,the asymptotic properties of zero dynamics and their stability conditions are provided.The results of this dissertation show that ABTSH and AFTSH have the same capabilities as BTSH and FTSH in ensuring the MP properties of discrete-time systems,respectively.(3)Owing to the widespread existence of the time delay phenomenon in the control engineering,the MP properties of a discrete-time linear system with a time delay when the input signal is generated by TSH were studied.This dissertation analyzes the influence rule of the time delay system input signal with TSH as signal reconstruction and gives the precise discrete-time system of linear time-delay system in the case of BTSH and FTSH,respectively.Besides,the asymptotic properties and stability conditions of the zero dynamics of the corresponding time delay discrete-time system are derived.Results show that as the time delay increase,the preservation conditions of the MP properties of the discrete-time system will decrease.(4)Furthermore,this dissertation studies the zero dynamics properties of affine nonlinear discrete-time systems generated by the BTSH and FTSH as the signal reconstruction method.Firstly,the approximate expression of the discrete-time models of nonlinear systems under the BTSH and FTSH is given.The truncation error between the approximate model and the precise discrete-time model is analyzed.Moreover,in the process of obtaining the discrete-time system model,this dissertation gives the precise discrete-time model of a linear system and the approximate discrete-time model of the nonlinear system under ?-operator because of the ?-operator has advantages than the q-operator to reflect the connection between the continuous-time domain and the discrete-time domain.The approximate error of the model is also analyzed.Finally,the asymptotic expression and the stability criteria of the zero dynamics for nonlinear approximate discrete-time system model are given.Results show that the conclusions about the MP properties of discrete-time linear systems under TSH can be extended to the nonlinear systems.