baggepinnen
commented
3 years ago @mapi1 do you think this is related to https://github.com/baggepinnen/ControlSystemIdentification.jl/commit/890a3ee9e022055a136c1128146846eb402b6e14 or https://github.com/baggepinnen/ControlSystemIdentification.jl/commit/2d212e3106670708092bd4bf50c09cdc6314db8d ?
Here's some code to roughly reproduce what's seen above since no code was posted
using ControlSystemIdentification, ControlSystems, Plots
using Random, LinearAlgebra
default(size=(500,280))
N = 500 # Number of time steps
t = 1:N
Δt = 1 # Sample time
u = randn(N) # A random control input
G = tf(0.8, [1,0,0.25], 1) # An interesting system
sim(sys,u) = lsim(sys, u, t)[1][:]
y = sim(G,u)
yn = y + randn(size(y));
# Validation data
uv = randn(N)
yv = sim(G,uv)
ynv = yv + randn(size(yv));
na,nb = 2,1 # Number of polynomial coefficients to estimate
d = iddata(yn,u,Δt)
Gls = arx(d,na,nb)Chaning the inputdelay parameter does recover a better transfer function (but does not change the numerator order as would be expected)
julia> Gls = arx(d,2,1)
TransferFunction{Discrete{Int64}, SisoRational{Float64}}
-0.053195176045275815
----------------------------------------------------
1.0z^2 + 0.020944097150896568z + 0.13061559216712304
Sample Time: 1 (seconds)
Discrete-time transfer function model
julia> Gls = arx(d,2,1, inputdelay=2)
TransferFunction{Discrete{Int64}, SisoRational{Float64}}
0.8711130327440996
---------------------------------------------------
1.0z^2 - 0.008279348253820712z + 0.1078308656207146
Sample Time: 1 (seconds)
Discrete-time transfer function model@peroveh note that arx is expected to perform poorly since what you are simulating is an output-error process but you're estimating an input-error model. They should not perform this poorly though, and I believe it's related to an internal index shift that has gone wrong.
peroveh
mapi1
Apparent issues with several of the arx() estimators used in your identification_arx.ipynb example with slightly modified AR and ARMA transfer functions with the following solvers: (I assume they all should handle the MA part also given nb is specified? I did not find an armax version)
1) Tested pure AR with two imaginary poles on
A small error is added to simulated data
Testing various specifications of system order (denominator and numerator). I am a bit uncertain if n is the number of coefficients here or the order?
With na=2,nb=2,nc=1 (?) they all gave reasonably similar and ok results..
With na=2, nb=1 (should suffice for the numerator) the arx versions start failing bad, while n4sid still does well
With na=nb=4 (too high?) , the arx and plr also goes bad (large errs in both numerator and denom) Again n4sid good.
As can be seen the n4sid has typical coefficient errors in the e-8 range, while the others are up to e-1 Per Ove Husøy