Research On Partial Eigenstructure Assignment For Vibration Systems

Vibration systems are a class of dynamic models describing vibration process,which are widely used in structural engineering,circuit systems,aerospace,and other fields.Similar to the descriptor systems,the eigenstructure of the vibration systems has a decisive effect on the stability of the systems.Specially,in singular vibration systems,the infinite eigenvalue may lead to impulsive behavior which is bad for the stability.This study presents research on partial eigenstructure assignment for vibration systems.The specific contents of this thesis are as follows.A new method is presented for partial eigenstructure assignment problems in vibration systems using velocity-displacement active control.The parametric expressions are given for velocity-displacement active controller using no spill-over property.The partial eigenstructure assignment problems are transformed into solving Sylvester matrix equation using the closedloop characteristic equation.The reduced order is done for the derived Sylvester matrix equation,and several lower order matrices equations are obtained.A new iterative method is constructed for solving the matrices equations,and the convergence analysis is provided.The numerical solutions of controller gains are computed using the proposed iterative algorithm.The partial eigenstructure assignment problems are investigated using acceleration–velocity–displacement active control in singular vibration systems.The problems are transformed into solving matrix equations using the receptance matrix method.Iterative sequences are constructed,and the iterative feasibility is presented for solving the matrix equations.The partial eigenvectors of the closed-loop systems are reassigned by imposing modal constraints.An algorithm is proposed to get numerical solutions of the derived matrix equations.The initial value condition is discussed to obtain the minimum norm solution of the problems.The designed acceleration–velocity–displacement active control can solve the partial eigenstructure assignment problems depending only on original vibration systems information.The proposed numerical algorithm can obtain the minimum norms of controller gain,which implies minimum control energy consumption.The robust minimum norm partial eigenstructure assignment problems are studied in singular vibration systems using acceleration-velocity-displacement active control.A new parametric method is proposed for solving the partial eigenstructure assignment problems using the imposed modal constraints technique.A conditional number method is used to detect the robustness of eigenvalues.A robust minimum norm optimization function is constructed.The robust minimum norm partial eigenstructure assignment problems are discussed in singular vibration systems by setting appropriate weight factors.Algorithms are presented for solving the corresponding problems.