Estimate Transfer Function Models with Prior Knowledge of Model Structure and Constraints
This example shows how to estimate a transfer function model when the structure of the expected model is known and apply constraints to the numerator and denominator coefficients.
Load time-domain data.
load iddata1 z1; z1.y = cumsum(z1.y);
cumsum integrates the output data of
z1. The estimated transfer function should therefore contain an integrator.
Create a transfer function model with the expected structure.
init_sys = idtf([100 1500],[1 10 10 0]);
int_sys is an
idtf model with three poles and one zero. The denominator coefficient for the
s^0 term is zero which indicates that
int_sys contains an integrator.
Specify constraints on the numerator and denominator coefficients of the transfer function model. To do so, configure fields in the
init_sys.Structure.Numerator.Minimum = eps; init_sys.Structure.Denominator.Minimum = eps; init_sys.Structure.Denominator.Free(end) = false;
The constraints specify that the numerator and denominator coefficients are nonnegative. Additionally, the last element of the denominator coefficients (associated with the
s^0 term) is not an estimable parameter. This constraint forces one of the estimated poles to be at
s = 0.
Create an estimation option set that specifies using the Levenberg–Marquardt search method.
opt = tfestOptions('SearchMethod','lm');
Estimate a transfer function for
init_sys and the estimation option set.
sys = tfest(z1,init_sys,opt);
tfest uses the coefficients of
init_sys to initialize the estimation of
sys. Additionally, the estimation is constrained by the constraints you specify in the
Structure property of
init_sys. The resulting
sys contains the parameter values that result from the estimation.