Mathematical Problems in Engineering
the purpose of adapting the sampling rate is to optimize
bandwidth utilization not to save power. A robust and
dynamic cross-layer communication architecture for wireless
networked control system is presented in []byIsraretal.
e protocol stack for WNCS comprises ve layers. Each
layer contributes to the overall goal of reliable, power-ecient
communication. However, the control performance is not
takenintoaccountintheirwork.
A number of studies related to power eciency in wireless
sensor networks (WSNs) and wireless networks have also
been conducted in [–]. Current power eciency research
always falls into two categories: one is reducing the power
consumption of each single node in the network and the
other is balancing the power consumption of all the nodes in
network. In [], Colandairaj et al. present a dynamic power
control strategy to minimize the communication power
consumption of nodes by varying the transmission rate. A
protocol intending to balance power consumption from the
remaining battery power of the node-based routing policy is
proposed by Liang and Yang in []. e nodes with greater
remaining power are allocated with more communication
tasks. In [], Kim et al. propose a lifetime-based routing
strategy in which the survival time is estimated according to
the residual power and current ratio of power consumption.
e path with the longest node survival time is selected for
data transmission.
Recently, limited studies in [–]areconductedon
eective power saving strategies that specically target at
WNCS. Fischione et al. [] propose a trade-o between
wireless output power related to reliability and power con-
sumption, where a physical characteristic model revealed
quantitative relations with communication outage probabil-
ity. ey also focus on the lower layer optimal protocol
design by considering the application layer requirements.
Lino []discussestheoptimalsleepmodecontrolofwireless
network nodes and proposes a trade-o method between
control performance and power consumption. An optimal
control strategy is applied to optimize the control period. In
[], event-predictive control for power saving of wireless
networked control system is discussed. e key idea is to
save power by maximizing the control interval with con-
strains of appropriate control performance. e proposed
control method is rather complicated and requires online
optimization mixed integer programming, which reduces the
practicability. us, a simpler trade-o method for WNCS is
required.
Power consumption, communication reliability, and sys-
tem stability exist simultaneously and react with one another
in wireless networked control systems. Supposed that the
three factors are interdependent, most results achieved in
wireless network power management and wired networked
control systems cannot be directly applied to WNCS. us,
the motivation of this paper is to nd a bridge which can
link the three factors and make a balance among these
factors through the bridge parameter, such that the overall
satisfactory performance can be achieved. Fortunately, the
sampling period of sensor node is found to be the bridge
parameter. From this point, a joint design method of adaptive
sampling power eciency algorithm and coordinated control
method are discussed in this paper. An updating rule of
sampling period is presented to satisfy the demands of wire-
less life span under constrains of network schedulability and
control system stability. Convergence of the power eciency
algorithm is further proved. Subsequently, the control system
is a varying-period system since the sampling periods of
sensors are time-varying. It is then modeled as a class of
switched control system with two types of behavior in each
update period. e switched control law is applied to stabilize
thecontrolsystemandstabilityconditionsarediscussed.
Also, the choosing rule of update period is given.
e remaining sections are organized as follows. Section
is the problem formulation. Section presents the adaptive
power eciency algorithm. Section discusses the coor-
dinated wireless networked control system modeling and
design method. Numerical simulation is given in Section .
Section is the conclusion of this paper.
2. Problem Formulation
2.1. Description of WNCSs. Consider the wireless networked
control systems shown in Figure . ere are three kinds
of node in the system. Power consumption varies for the
dierent kinds of node.
Besides, some necessary assumptions are made in this
paper as the follows.
Assumption 1. e power of sensor and actuator nodes is
supplied by battery while the power of controller is supplied
by base station.
Assumption 2. e sensor and the actuator are clock driven
while the controller is event driven. e sampling data is
packed in one packet for transmission with time stamp.
Assumption 3. ere exists transmission delay in the control
loop, and it is assumed to be less than one sampling period.
2.2. Analysis of Power Consumption in WNCSs. Sensor power
is consumed by three processes: data sampling, sample
data reading by the ADC, and data transfer. e power
consumption of the controller node is also consumed by three
processes: receiving data, calculating control variables, and
sending data packet. e power of the actuator is consumed
by two processes: receiving data and D/A conversion. e
power consumption of dierent tasks is shown in Table (see
in []).
From the table, we get the following two conclusions:
() when the sensor transfers the same amount of data as
the actuator receives, it will consume . times more
power than the actuator will consume.
() data transfer consumes over % of the total sensor
power consumption.
Giventhatthepowerrequiredbycontrolnodescanbe
supplied by the base station in most situations, the power
required by the sensor nodes and actuators can be provided
by batteries. us, sensors utilize the maximum amount