Create a tunable (parametric) model of the second-order filter:

where the damping ζ and the natural frequency ω_n are tunable parameters.

wn = realp('wn',3);
zeta = realp('zeta',0.8);
F = tf(wn^2,[1 2*zeta*wn wn^2]);

F is a genss model with two tunable Control Design Blocks, the realp blocks wn and zeta. The blocks wn and zeta have initial values of 3 and 0.8, respectively.

Examine the number of tunable blocks in the model using nblocks.

nblocks(F)

This command returns the result:

ans =

     6

F has two tunable parameters, but the parameter wn appears five times — twice in the numerator and three times in the denominator.

Rewrite F for fewer occurrences of wn.

The second-order filter transfer function can be expressed as follows:

Use this expression to create the tunable filter:

F = tf(1,[(1/wn)^2 2*zeta*(1/wn) 1])

Examine the number of tunable blocks in the new filter model.

nblocks(F)

This command returns the result:

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 performance time of calculations involving the model. However, the number of occurrences does not affect the results of tuning the model or sampling the model for parameter studies.