ml_ct_soss_bfsr
Balancing-free square root method for second-order sys.
Contents
Syntax
[sys, hsv] = ml_ct_soss_bfsr(sys, R, L, tselect) [sys, hsv] = ml_ct_soss_bfsr(sys, R, L, tselect, opts)
Description
Computes the reduced-order matrices of a second-order system by the balancing-free square root method. The different second-order balancing methods can be chosen via an optional paramter.
Input
sys - structure, containing the second-order system in the form:
Parameter | Meaning |
M | matrix with dimensions n x n |
E | matrix with dimensions n x n |
K | matrix with dimensions n x n |
Bu | matrix with dimensions n x m |
Cp | matrix with dimensions p x n, might be empty |
Cv | matrix with dimensions p x n, might be empty |
R - Cholesky factor of the controllability Gramian with dimensions nr x 2*n L - Cholesky factor of the observability Gramian with dimensions nl x 2*n tselect - an integer, used to determine the computation method for the order of the reduced-order model 0 - order is directly given by user 1 - computed by a relative tolerance for the hsv 2 - computed by a relative tolerance on the sum of hsv 3 - computed by absolute error bound of BT 4 - computed by relative error bound of BST 5 - computed by absolute error bound of LQGBT 6 - computed by absolute error bound of HinfBT opts - structure, containing the following optional entries:
Parameter | Meaning |
BalanceType | character array, determining the type of second-order balancing
|
Gamma | positive scalar, scaling term from the H-infinity balanced truncation |
Order | positive integer, order of the resulting reduced-order model chosen by the user if tselect == 1 default: min(10,length(hsvp)) |
Tolerance | nonnegative scalar, tolerance used in the different error formulas default: 1.0e-02 |
Output
sys - struct, containing the transformed system matrices hsv - vector, containing the characteristic singular values
Reference
T. Reis, T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comput. Model. Dyn. Syst. 14 (5) (2008) 391--406. https://doi.org/10.1080/13873950701844170
See Also