Hardware Reference
In-Depth Information
PES−RRO = NRRO
−50
0.01
the NRRO peak frequency in Hz is: 197.997208
3 sigma reduces by 33.2 % when RRO taken out
NRRO
σ
−100
0.005
−150
0
0
0
200
200
400
400
600
600
800
800
1000
1000
1200
1200
1400
1400
1600
1600
1800
1800
Frequency in Hz
Figure 3.46: PES NRRO power spectrum density.
well be realized by first creating a look up table using equation 3.90 and then
injecting the appropriate signal instead of implementing equations 3.84, 3.89,
and 3.90.
It is obvious from the discussions above that an inverse of the shock transfer
function is calculated at the runout frequencies. In general, inverting a plant
model at all frequencies for canceling the output PES can not be realized as
the process is a causal system and inverting the model results in a non-causal
model. It involves pure differentiation of the output signal which is not feasible.
Moreover, even if a causal approximation of the inverse of the model is used, the
noise in PES will be significantly amplified. Additionally, the high frequency
disturbances will not be canceled due to the phase error in the approximate
inverse.
RRO Compensation using Adaptive Feedforward Cancelation
Refering to the block diagram shown in Figure 3.47 where O is the feed-
back control system, the equivalent periodic disturbance d
i
(ω
i
)isrepresented
by[206]
d
i
(ω
i
)=a
i
cosω
i
t + b
i
sinω
i
t.
(3.91)
The adaptive feedforward control (AFC) attempts to reproduce the disturbance
by estimating a
i
and b
i
in an adaptive manner. The disturbance d
i
can be
exactly canceled when the estimates of the disturbance coefficients are such
that,
a
i
(t)=a
i
(t),
(3.92)
b
i
(t)=b
i
(t).
(3.93)
