Hardware Reference

In-Depth Information

When O
−1
is used, the phase of the shaped plant is 1/z
d+u
and is near zero

phase in a wider low frequency range compared with the case without O
−1
.

Such a modification can improve the robustness and convergence rate of the

AFC scheme. Additionally, such a modification might lower the sensitivity

transfer function hump from D
to y and prevent significant amplification

of other RRO harmonics or NRRO signal when canceling the selected RRO

harmonics.

We note here that by using (3.104), C
r
with a suitable gain g
i
might be

able to generate a notch at the desired frequency and at the same time have

attenuation at frequencies other than those of C
r
's center frequency [224].

Nevertheless, such a system is still governed by the Bode Integral theorem, and

hence there will be amplification of RRO and NRRO at some other frequencies.

RRO Compensation via Periodic Signal Generator using Delay Terms

In the above designs, compensating each RRO frequency requires a second

order controller. If we want to compensate for more frequencies of RRO,

the order of the compensator increases to twice the number of frequencies

to the compensated for. Adopting the same “plug-in” structure as shown in

Figure 3.49, periodic signal generators (PSGs) with a simple delay term in a

feedback loop can be used to generate the internal model for disturbance [73]

[137].

Figure 3.49: “Plug-in” repetitive compensation using periodic signal generator-

continuous time case [145].

Hara et al has proved in [73] that exponential stabilization is not achiev-

able for such repetitive control systems with strictly proper transfer functions.

However, when a low-pass filter is used in conjuction with the delay section,

the internal model is able to generate the signal with certain cancelation of the

disturbances [73] [145]. Figure 3.50 shows an example of a scheme with PSG

based control. Discrete time version of the such a scheme can be found in [156]

and the references therein.

In the case of digital control, we can assume that the plant model shown