Exact Order Reduction Of Roesser Model Based On Generalized Jordan Transformation And Its Application

Different from one-dimensional system,multidimensional system is a system that contains two or more independent variables,and the complexity of its analysis,opti-mization,design,simulation,testing,and fault diagnosis is higher that of one-dimensional system.Therefore,we usually need to exactly reduce the complexity of the state-space model of multidimensional systems in order to lower the design complexity and the cost of the hardware implementation.The problem of exact order reduction of the state-space model of multidimensional system is to establish a new low order equiv-alent model from the known initial model of the system,that is,the transfer function(matrix)corresponding to the new model and the original mode should be identical.The research of this problem essentially involves the minimum realization of the state-space model of multidimensional system.So far,for a given multidimensional system,there is no(sufficient and necessary)condition to judge whether there is an absolute mini-mum realization,and there is no condition to verify whether the realization of a system is minimal.Therefore,the exact order reduction of multidimensional system is a very complicated problem,which has not been solved.This paper mainly studies the exact order reduction method of the multidimension-al Roesser state-space model and applies it to the establishment of state-space model of hypersonic vehicle control system.The results show that if the block matrix of the co-efficient matrix of the state-space model contains complex eigenvalues,it is difficult to get a real form of the multidimensional Jordan standard,and the complex form of Jor-dan standard in actual system is physically impossible.In this case,in order to ensure the multidimensional Jordan state-space standard form of real number form,this pa-per presents the multidimensional generalized Jordan matrix of the coefficient matrix,the general form of intermediate transformation matrix is proved and given.On this basis,the paper proposes the order reduction method based on the generalized Jordan transformation,that is,based on the generalized Jordan transformation,the linear rela-tion of the Roesser model coefficient matrix is used to reduce the order,which solves the difficulty that the existing algorithm can not reduce the order of the system matrix with complex eigenvalues.In particular,if the equivalent transformation of the system matrix is carried out,it is possible to further reduce the order by using the proposed method,the corresponding equivalence transformation and order reduction conditions are analyzed in detail and the mathematical proof is given in this paper.In order to ver-ify the effectiveness of the proposed algorithm,we in view of the nonlinear high order complexity of hypersonic vehicle longitudinal model,the Roesser state-space model is used to describe the system on the basis of the small disturbance moving line.Then the reduced order algorithm based on generalized Jordan transformation is used to exactly reduce order of the hypersonic vehicle longitudinal model,and the lower order model is obtained,which provides a strong support for the subsequent system optimization analysis and high precision control.