Stability Analysis And Parametric Controller Design Of Uncertain Distributed Parameter Systems

The distributed parameter system is described by functional differential equation,partial differential equation and partial differential-integral equation.The systems are widely used in modern scientific and engineering systems,such as electromagnetic fields,temperature fields,elastic systems,space vehicles,robots,nuclear reactors,etc.Internal perturbation,external noise and parameter identification can cause the uncertainties of the model.The uncertainies of the system are universal and cannot be ignored in many cases.The stability analysis and controller design of uncertain distributed parameter system are fruitful.However,some existing methods still have problems in some cases and need to be further improved.For example,the problem of infinite test exists when the traditional algebraic method is used to analyze the stability of the system.The method based on the Judy-madden criterion involves fractional calculation,and the complexity is high when analyzing the system with uncertain parameters.The linear matrix inequality(LMI)method can only give some sufficient results when solving the uncertain parameters of system stability.The controller design method based on LMI can only provide certain control gain.Based on Hurwitz criterion,the discrimination system for polynomials and cylindrical algebraic decomposition algorithm,the stability and controller design problems of several typical 2D uncertain distributed parameter systems(2D systems)are studied.In this dissertation,the existing stability analysis method of 2D system is simplified,and the traditional stability judgment issue which is not easy to calculate is transformed into the issue that determines whether the polynomial is positive or not.The method can also obtain the complete stability region of the uncertain parameters of the system to ensure the stability of the 2D system with uncertain paremeters.Then the stability and robust stability analysis methods are extended to the stabilization problem and a general parametric controller is designed.Specifically,according to the model classification of 2D system,the main contributions of this dissertation including the following aspects:For 2D linear discrete system described by transfer function,a method of stability test and robust stability determination based on Hurwitz criterion is proposed,and therobust stability parameter region of the system is obtained.Different from other traditional algebraic methods,this method is explicit without polynomial recursion and fraction calculation,and the computation is small.This method is especially suitable for dealing with the problem of system stability with uncertain parameters.For continuous and continuous-discrete 2D linear systems described in the state space,the stability criterion is presented.For uncertain 2D linear systems,the method of solving the parametric stable region is given.Different from the traditional method of testing infinite frequency points and LMI method which can only provide some sufficient results,this dissertation presents a finite test method and the results are necessary and sufficient.For the 2D linear discrete systems described by the second type of Fornasini-Marchesini model,a simple and efficient stability analysis method and a general parametric controller design method are proposed.Based on the algorithm of cylindrical algebraic decomposition and Hurwitz criterion,the method simplifies some existing methods for analyzing the stability of 2D systems.Then it is applied to design parameter controller.The parameter controller designed by this method is simple in form,it can solve the control gain range to make the system stable,can select the gain parameters according to different conditions,and optimize the performance of the system.For the stability and stabilization of fractional-order 2D linear discrete systems,the stability analysis method and the control gain parameter region method are presented.The controller designed by this method can meet the requirements of different application environments.In addition,the method can also analyze the stability of fractional order 2D systems with uncertain parameters.At the same time,the LMI method,which can only analyze fractional order 2D positive system,has been extended to a wider range of applications.In this dissertation,a 2D Roesser model with data loss and time-varying delay is established,and an iterative learning control design method is presented.The problem of batch iterative learning control is transformed into a problem of stability analysis for2 D stochastic systems with time-varying delays.The mean square asymptotic stability criterion based on LMI is given.The method of obtaining the control gain of ILC is introduced to make the system stable in iteration and time direction.The simulations of different data loss cases show the effectiveness of the method.Compared with othermethods,this method has better control effect.