JuliaControl
gain is not working
From @baggepinnen on February 23, 2016 20:2
Should be renamed to static gain, or dcgain as in matlab. Should also be * working properly*
Copied from original issue: mfalt/Control.jl#24
We can still not handle if the tf has both a pole and a zero in 0, this returns NaN, and we get a finite gain for unstable systems. It is also incorrect for SisoZpk, we should probably implement a dcgain for each of the siso types.
The implementation for ss works better now, but can not handle when A is not invertible (for example with uncontrollable states). I think this could be solved using the psuedo-inverse. However, we still return a finite gain for unstable systems (same as matlab). The function is also wrong for discrete systems (which should be easy to fix when the other issues are taken care of).
The previous implementation (where nz=length(tzero(sys)))
sys.C*(sys.A^(nx - nz - 1))*sys.B
still seems completely wrong.
Great! @baggepinnen is currently implementing minreal for statespace (in lqg branch) which might be of use, but feel free to use some other way if it is more robust/efficient.
I have already forked the repository, and I will create a branch 15-dcgain-fix. In the functions I will not assume pole-zero cancellations (as anyways it is not encouraged to do cancellations in the right half plane or outside the unit disk), so I will pay attention to the poles directly. And I will calculate G(s=0) and G(z=1) in the limit. As a result, the user needs to call the minreal or some other function to explicitly demand pole-zero cancellations. The output of minreal will be of transfer function and/or state-space form, and hence, the dcgain function should work fine.
We can talk more about it when I create the pull request.