Function File: [Kr, info] = fwcfconred (G, F, L, …)

Function File: [Kr, info] = fwcfconred (G, F, L, ncr, …)

Function File: [Kr, info] = fwcfconred (G, F, L, opt, …)

Function File: [Kr, info] = fwcfconred (G, F, L, ncr, opt, …)

Reduction of state-feedback-observer based controller by frequency-weighted coprime factorization (FW CF). Given a plant G, state feedback gain F and full observer gain L, determine a reduced order controller Kr by using stability enforcing frequency weights.

Inputs

G

LTI model of the open-loop plant (A,B,C,D). It has m inputs, p outputs and n states.

F

Stabilizing state feedback matrix (m-by-n).

L

Stabilizing observer gain matrix (n-by-p).

ncr

The desired order of the resulting reduced order controller Kr. If not specified, ncr is chosen automatically according to the description of key ’order’.

…

Optional pairs of keys and values. "key1", value1, "key2", value2.

opt

Optional struct with keys as field names. Struct opt can be created directly or by function options. opt.key1 = value1, opt.key2 = value2.

Outputs

Kr

State-space model of reduced order controller.

info

Struct containing additional information.

info.hsv

The Hankel singular values of the extended system?!?. The n Hankel singular values are ordered decreasingly.

info.ncr

The order of the obtained reduced order controller Kr.

Option Keys and Values

’order’, ’ncr’

The desired order of the resulting reduced order controller Kr. If not specified, ncr is chosen automatically such that states with Hankel singular values info.hsv > tol1 are retained.

’method’

Order reduction approach to be used as follows:

’sr’, ’b’

Use the square-root Balance & Truncate method.

’bfsr’, ’f’

Use the balancing-free square-root Balance & Truncate method. Default method.

’cf’

Specifies whether left or right coprime factorization is to be used as follows:

’left’, ’l’

Use left coprime factorization.

’right’, ’r’

Use right coprime factorization. Default method.

’feedback’

Specifies whether F and L are fed back positively or negatively:

’+’

A+BK and A+LC are both Hurwitz matrices.

’-’

A-BK and A-LC are both Hurwitz matrices. Default value.

’tol1’

If ’order’ is not specified, tol1 contains the tolerance for determining the order of the reduced system. For model reduction, the recommended value of tol1 is c*info.hsv(1), where c lies in the interval [0.00001, 0.001]. Default value is n*eps*info.hsv(1). If ’order’ is specified, the value of tol1 is ignored.

Algorithm
Uses SLICOT SB16CD by courtesy of NICONET e.V.

Package: control