@TechReport{ it:2014-009,
author = {Torbj{\"o}rn Wigren},
title = {On a Limitation in Networked Flow Control},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2014},
number = {2014-009},
month = mar,
abstract = {The paper analyzes a continuous time flow control system,
with flow of a general quantity from a source node to a
sink node. The flow is one-directional, meaning that there
is a saturation between the nodes that limits the flow to
be positive and below a maximum. The controlled plant is
located in the sink node and the controller is located in
the source node. The plant and the controller are modeled
by linear filters parameterized with poles and zeros. Feed
forward control from measured disturbances is included.
Delays affect both the downlink control signal and the
uplink measurement signals. The paper proves that for large
delays, $L_2$-stability does not follow from the Popov
criterion unless the quotient of the products of all zeros
and the product of all poles is less than $1/kG_p$, where
$k$ is the slope of the saturation and $G_p$ is the gain
constant of the loop gain. In case the plant models a leaky
reservoir, the conclusion is that the amount of low
frequency gain of the controller cannot be arbitrarily high
at the same time as the amount of leakage of the reservoir
is arbitrarily low. In communications this means that an
increased requirement to regulate static errors of the
reservoir needs to be accompanied by a reduced flow
capacity.}
}