Pole And Optimal Pole Placement For Isotropic Linear Systems

As a type of system with special structure,isotropic systems exist in many fields such as military,energy,aerospace,and industry.Isotropic rotor-bearing systems,gyroscopes,rotating discs,doubly-fed induction machines,self-excited induction generators,and rolling missiles are typical examples of this system,and all of them are widely used.Different from many researches on the analysis and processing of specific physical systems,it is of great theoretical significance to study the general methods of such systems.Based on the isotropic system,this paper considers the pole placement problem in the continuous and discrete cases to keep the final isotropy of the system still established.Due to the unique structure of this kind of system,the transformation of its original real system state equation into a reduced-order complex system with a halved state can decouple the system and increase the degree of design freedom.What's more,the eigenvalues,feedback control laws,transfer functions,controllability and observability of the two systems are completely equivalent.Therefore,after designing the controller for the complex system and then returning to the original system,the isotropy of the system remains unchanged.Then,the reason for designing the isotropic feedback control law for isotropic systems is given,as well as the corresponding theorems for the isotropic solutions of algebraic Riccati equation and Sylvester equation.Through the real diagonalization of the state matrix of isotropic systems with different eigenvalues,every two columns of the corresponding eigenvector matrix will become an isotropic submatrix.This feature is used to design general iterative algorithms based on algebraic Riccati equations for continuous and discrete isotropic systems.At the same time,the special processing and description of this algorithm to ensure that the feedback control law is isotropic matrix,and the design of some optimal and general pole configuration methods based on this algorithm are given.These methods enable a variety of flexible pole configurations.Finally,through numerical examples and the modeling and simulation of several typical systems,the design method is verified and analyzed.The results show that the method designed in this paper achieves the isotropic preservation of isotropic systems and has a good control effect.