Reduction of state-feedback-observer based controller by coprime factorization (CF). Given a plant G, state feedback gain F and full observer gain L, determine a reduced order controller Kr.
Inputs
LTI model of the open-loop plant (A,B,C,D). It has m inputs, p outputs and n states.
Stabilizing state feedback matrix (m-by-n).
Stabilizing observer gain matrix (n-by-p).
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.
Optional struct with keys as field names.
Struct opt can be created directly or
by function options. opt.key1 = value1, opt.key2 = value2.
Outputs
State-space model of reduced order controller.
Struct containing additional information.
The Hankel singular values of the extended system?!?. The n Hankel singular values are ordered decreasingly.
The order of the obtained reduced order controller Kr.
Option Keys and Values
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.
Order reduction approach to be used as follows:
Use the square-root Balance & Truncate method.
Use the balancing-free square-root Balance & Truncate method. Default method.
Use the square-root Singular Perturbation Approximation method.
Use the balancing-free square-root Singular Perturbation Approximation method.
Specifies whether left or right coprime factorization is to be used as follows:
Use left coprime factorization. Default method.
Use right coprime factorization.
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.
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.
The tolerance for determining the order of a minimal realization of the coprime factorization controller. TOL2 <= TOL1. If not specified, n*eps*info.hsv(1) is chosen.
Boolean indicating whether equilibration (scaling) should be
performed on system G prior to order reduction.
Default value is true if G.scaled == false and
false if G.scaled == true.
Note that for MIMO models, proper scaling of both inputs and outputs
is of utmost importance. The input and output scaling can not
be done by the equilibration option or the prescale function
because these functions perform state transformations only.
Furthermore, signals should not be scaled simply to a certain range.
For all inputs (or outputs), a certain change should be of the same
importance for the model.
Algorithm
Uses SLICOT SB16BD by courtesy of
NICONET e.V.
Package: control