= N(2π/ω), where N is the integer value of the Number of estimation periods
parameter. These operations are shown in the following diagram.
As the averaging time T increases, the contribution of components in y(t) at frequencies
other than ω go to zero. R(T) and I(T) become constant and can be used to calculate the
frequency response of the plant at ω. For further details, see [1].
Superposition Mode
When Experiment mode is Superposition, the block uses a recursive least squares
(RLS) algorithm to compute the estimated frequency response. Assume that the plant
frequency response is G(jω) = γ∠jθ. When a signal u(t) = Asin(ωt) excites the plant, the
steady-state plant output is y(t) = Aγsin(ωt + θ), which is equivalent to:
yt =γcosθAsinωt+ γsinθAcosωt.At any given time, Asin(ωt) and Acos(ωt) are known. Therefore, they can be used as
regressors in an RLS algorithm to estimate γcos(θ) and γsin(θ) from the measured plant
output y(t) at run time.
When the excitation signal contains a superposition of multiple signals, then:
ut =A 1 sinω 1 t+A 2 sinω 2 t+....In this case, the plant output becomes:
Frequency Response Estimator