[基础科学]二阶系统的可对角化.pdf

19th Mediterranean Conference on Control and Automation ThCT5.7 Aquis Corfu Holiday Palace, Corfu, Greece June 20-23, 2011 Diagonalisation of Second Order Form Model Je´rˆome GUILLET Benj amin MOURLLION Laboratoire Mode´lisation, Intelligence, Processus, Syste`mes (MIPS-EA2332) Universite´ de Haute-Alsace ENSISA, 12 rue des fr`eres Lumie`re 68093 Mulhouse Cedex, France. e-mail: jerome.guillet@uha.fr, benjamin.mourllion@uha.fr Abstract— Second Order Form Model (SOFM) study, needs formulation of the SOFM is given by a reformulation of it transfer function. This can be done by the simultaneous diagonalisation of the SOFM dynamics Mq¨ + C q˙ + Kq = F u (1) matrices. The diagonalisation is performed thanks to the y = G q + G q˙ + G q¨ 1 2 3 Quadratic Eigenvalues Problem. Based on diagonalisation, we with q ∈ Rnq ×1, M, C , K ∈ Rnq ×nq , show that the inverse Laplace transform of a SOFM can be computed. To preserve the behavior of the model, new input and F ∈ Rnq ×m , G , G , G ∈ Rp ×nq . 1 2 3 output matrices are determined to