ml_ct_soss_sr

Square root method for second-order systems.

Contents

Syntax

[sys, hsv] = ml_ct_soss_sr(sys, R, L, tselect)
[sys, hsv] = ml_ct_soss_sr(sys, R, L, tselect, opts)

Description

Computes the reduced-order matrices of a second-order system by the
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
  • 'p' - position balancing (vel. Gram.)
  • 'pv' - position-velocity balancing
  • 'vp' - velocity-position balancing
  • 'vpv' - velocity-position balancing (vel. Gram.)
  • 'v' - velocity balancing
  • 'fv' - free velocity balancing
  • 'so' - second-order balancing
default: 'so'
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

ml_ct_ss_bfsr | ml_ct_ss_sr | ml_order