Design of Full-order PD Observers for Second-order Dynamic Systems

The design of full-order proportional plus derivative (PD) observers in second-order dynamic systems is investigated in this paper. Based on the solutions to a so-called generalized Sylvester equation, a parametric method to solve this design problem is proposed. This method presents the parametric expressions for the gain matrices and the left eigenvector matrix of the full-order PD observers. These parameters included in this method offer all the design degrees of freedom, which can be further utilized to satisfy certain specified performances, such as disturbance decoupling, LTR and robustness. In addition, this method utilizes directly the original system data and involves manipulations only on n-dimensional matrices. An illustrative example shows the effect and simpleness of the proposed method.