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,
Copyright (c) 1996-2025, SLICOT, available under the BSD 3-Clause
(License and Disclaimer).
Source Code:
fwcfconred