Digital Signal Processing Reference
In-Depth Information
Output
Output
Input
Input
Fig. 4
A saturation nonlinearity is shown at the
left
and a dead zone nonlinearity at the
right
Thirdly, the fact that the DSP is actually inside a feedback loop imposes the
constraints discussed at the end of the previous section, too much gain causes
closed-loop instability and too precise tracking can cause amplified sensitivity to
disturbances.
The main impact of the real time constraint on the DSP is that it must be designed
to guarantee that it produces a control signal at every sampling instant. The main
impact of the nonlinearities is from the saturation. A control signal that is too
large will be truncated. This can actually cause the closed-loop system to become
unstable. More commonly, it will cause the performance of the closed-loop system
to degrade. The most famous example of this is known as integrator windup as
discussed in the following subsection. The dead zone limits the accuracy of the
control. The impact of the sensitivity and stability constraints is straightforward.
The design of DSPs for control must account for these effects as well as the obvious
direct effect of the controller on the plant.
There is one more general issue associated with the digital implementation
of controllers. It is well known that the Nyquist rate upper bounds the interval
between samples when a continuous-time signal is discretized in time without
loss of information. For purposes of control it is also possible to sample too fast.
The intuitive explanation for this is that if the samples are too close together the
plant output changes very little from sample to sample. A feedback controller bases
its actions on these changes. If the changes are small enough, noise dominates the
signal and the controller performs poorly.
3.1
Simple Cases
controller in the figure is a signal processor, taking the signals
d
c
and
y
as inputs
and producing the signal
u
as output. The objective of the controller is to make
y
(
t
)=
d
c
(
t
)
∀
t
≥
0. This is actually impossible because all physical systems have
