A method of multiscale eigensystem assignment is presented for vibration suppression of flexible structures.The method can alter the original modes by appropriate feedback forces

so that the sensitive parts of the flexible structure reach their steady states at faster rates than other parts

while vibration in sensitive parts is reduced to allowable level.The new control scheme can quickly remove the vibration energy from the sensitive parts of the flexible structure to meet the requirements of high performance.By selecting a model transformation matrix T in Eq(1)

the vibration energy of the controlled system is redistributed over the sensitive and insensitive parts.The resulting active damping conrol gain is K2=(T-1 )TG2T-1

where the elements of G2 are solved from the ideal characteristic equations (5)

in which ( n2-3n+2)/2 elements of G2 are determined artificially.Finally

a simple example demonstrates the effectiveness of this new control scheme.