PID eigenstructure assignment in second-order dynamic systems: A parametric method

The design of eigenstructure assignment in second-order dynamic systems via proportional-integral-derivative (PID) feedback is considered. Based on a group of parametric solutions to a type of generalized Sylvester matrix equations, a complete parametric method for the proposed eigenstructure assignment problem is presented. This method gives simple complete parametric expressions for the PID feedback gain matrices and the closed-loop eigenvector matrices. In addition, the proposed method offers all the design degrees of freedom, which can be utilized to satisfy certain performance specifications in real applications. An illustrative example shows the effect of the proposed approach.