Observer Design For Descriptor Systems Based On Parametric Methods

In recent years,with the rapid development of science and technology,the descriptor system design method was widely used in power systems,mechanical multi-body systems,robot and so on.A series of differential and algebraic equations are used to describe the descriptor system.Through the analysis and research of the equations,the dynamic and static characteristics are revealed.Based on the descriptor system theory,this paper studies the design problem of the descriptor system observer,the main results are as follows.Firstly,based on the left eigenvector matrix,two fully parametric analytical solutions of the generalized Sylvester equation are given.Secondly,consider the design problem PI observer of the generalized time-invariant linear system,including first-order and second-order generalized time-invariant linear systems.Based on the requirement of systematic estimation error and its integral term tending to zero,regular and impulse-free conditions are given.The Jordan decomposition of the matrix pair of the error augmentation system is transformed into the generalized Sylvester equation,and the parametric form of the observer gain is given by the solution of the equation.Thirdly,study the observer design problem of descriptor fractional order system.Design PI and PD observers for descriptor fractional linear systems.According to the stability of the fractional order system,design suitable PI and PD observers.Based on the requirements of the error augmentation system,the estimation error tends to zero(the generalized PI observer also needs to ensure that its integral term tends to zero).No pulse condition.The Jordan decomposition of the matrix pair of the error augmentation system is transformed into the generalized Sylvester equation,and the parameterized form of the observer gain is given by the solution of the equation.Fourthly,design observers for descriptor time-varying systems.We design PI and PD observers for descriptor time-varying systems.Based on the requirement that the system estimation error tends to zero,the conditions of regularity and no pulse are given.The Jordan standard form of the matrix pair of the error augmentation system is transformed into the generalized Sylvester equation,and the parameterized form of the observer gain is given by the solution of the equation.Lastly,designed PI observer for the three-link manipulator.Using the related linearization knowledge,the nonlinear model is transformed into a linear model.Based on the singular value decomposition in matrix analysis,the gain matrix is obtained.The simulation diagram verifies that the observer has well estimated the state of the original system.