Create Tunable Second-Order Filter
This example shows how to create a parametric model of the second-order filter:
where the damping and the natural frequency are tunable parameters.
Define the tunable parameters using
wn = realp('wn',3); zeta = realp('zeta',0.8);
realp parameter objects, with initial values
Create a model of the filter using the tunable parameters.
F = tf(wn^2,[1 2*zeta*wn wn^2]);
The inputs to
tf are the vectors of numerator and denominator coefficients expressed in terms of
F is a
genss model. The property
F.Blocks lists the two tunable parameters
ans = struct with fields: wn: [1x1 realp] zeta: [1x1 realp]
You can examine the number of tunable blocks in a generalized model using
ans = 6
F has two tunable parameters, but the parameter
wn appears five times - twice in the numerator and three times in the denominator.
To reduce the number of tunable blocks, you can rewrite
Create the alternative filter.
F = tf(1,[(1/wn)^2 2*zeta*(1/wn) 1]);
Examine the number of tunable blocks in the new model.
ans = 4
In the new formulation, there are only three occurrences of the tunable parameter
wn. Reducing the number of occurrences of a block in a model can improve the performance of calculations involving the model. However, the number of occurrences does not affect the results of tuning the model or sampling it for parameter studies.