This paper presents a joint design method for wireless networked control system (WNCS) to balance both the demands of network service and the control performance. Since the problems of power consumption, communication reliability, and system stability exist simultaneously and interdependently in WNCS, most of the achieved results in the wireless network and wired networked control system cannot be used directly. To coordinate the three problems, sampling period is found to be the linking bridge. An adaptive sampling power efficiency algorithm is proposed to manage the power consumption such that it can meet the demands of network life span. The sampling period is designed to update periodically on the constraints of network schedulability and system stability. The convergence of the power efficiency algorithm is further proved. The sampling period is no longer a fixed value, however; thus, increasing the difficulty in modeling and controlling such a complicated timevarying system remains. In this work, a switched control system scheme is applied to model such a WNCS, and the effect of networkinduced delay is considered. Switched feedback controllers are introduced to stabilize the WNCS, and some considerations on stability condition and the bounds of the update circle for renewing sampling period are discussed. A numerical example shows the effectiveness of the proposed method.
Wireless networked control systems are composed of distributed fields and plant devices (sensors, actuators, and controllers) interconnected via a wireless network [
Most studies on WNCS analyze the effects of the wireless medium on overall closedloop control systems in [
A number of studies related to power efficiency in wireless sensor networks (WSNs) and wireless networks have also been conducted in [
Recently, limited studies in [
Power consumption, communication reliability, and system 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. Thus, the motivation of this paper is to find 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 efficiency algorithm and coordinated control method are discussed in this paper. An updating rule of sampling period is presented to satisfy the demands of wireless life span under constrains of network schedulability and control system stability. Convergence of the power efficiency algorithm is further proved. Subsequently, the control system is a varyingperiod system since the sampling periods of sensors are timevarying. It is then modeled as a class of switched control system with two types of behavior in each update period. The switched control law is applied to stabilize the control system and stability conditions are discussed. Also, the choosing rule of update period is given.
The remaining sections are organized as follows. Section
Consider the wireless networked control systems shown in Figure
Structure of wireless networked control systems.
Besides, some necessary assumptions are made in this paper as the follows.
The power of sensor and actuator nodes is supplied by battery while the power of controller is supplied by base station.
The sensor and the actuator are clock driven while the controller is event driven. The sampling data is packed in one packet for transmission with time stamp.
There exists transmission delay in the control loop, and it is assumed to be less than one sampling period.
Sensor power is consumed by three processes: data sampling, sample data reading by the ADC, and data transfer. The power consumption of the controller node is also consumed by three processes: receiving data, calculating control variables, and sending data packet. The power of the actuator is consumed by two processes: receiving data and D/A conversion. The power consumption of different tasks is shown in Table
Power consumption of different tasks.
Task  Energy consumption (nAh) 

Receive data  8 
Transfer data  20 
Read data  0.011 
Sample data  1.08 
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 2.5 times more power than the actuator will consume.
data transfer consumes over 90% of the total sensor power consumption.
Given that the power required by control nodes can be supplied by the base station in most situations, the power required by the sensor nodes and actuators can be provided by batteries. Thus, sensors utilize the maximum amount of power consumption in WNCS. Managing the power consumption of sensors is the key to prolonging the survival time of the wireless network. A direct and effective method is to reduce as much of the transmission consumption as possible by properly adjusting the amount of sample data. This principle is the basis of our power control algorithm.
In wireless networks, the average power consumption of sending a packet can be described as [
Survival time is dependent on transfer intervals. It can be prolonged by increasing the transfer intervals. Based on this premise as well as on the knowledge of the relationship between sampling period and control performance, we can cooperatively design the control and the network performances by adaptively adjusting the sampling period with a proper rule.
For the consideration of simplicity and generality, we choose one of the control loops in the WNCS to describe the power control algorithm. Let
For the WNCS described in Figure
According to Formula (
The remaining power relationship at the two adjacent updating instants is given by
We assume that the sensor node has sampled the plant with the sampling period
Power control error is defined as
The following Lyapunov function is introduced to prove convergence of the adaptive sampling power efficiency algorithm:
From inequalities (
The actual survival time is unavailable at the current instant because the power consumption is time varying. However, it can be predicted by the known information of the remaining power and sampling period at the current instant. Formula (
Taking IEEE 802.11b as an example, the lower bound of the sampling period of sensor
Wireless network parameters under 802.11b direct sequence spread spectrum.
Parameter  Value 


11 Mbps 

1 Mbps 

10, 50, 20 us 

34, 24 bytes 

80 bytes 

14 bytes + PHY header 
CW_{min}, CW_{max}  32, 1024 
For a SISO system, the maximum sampling period can be obtained using Shannon sampling theorem. For a MIMO system, the following method can be used to obtain the upper bound. If the system feedback control law is given ahead, then
However, the above optimal problem is difficult to solve directly. The following iteration method can be used to obtain the approximate optimal value of
Let
Let
Let
Considering the generality, one of the control loops in the WNCS is chosen as an example to illustrate the modeling approach. For the WNCS power consumption managed by algorithm in Section
We consider a plant of control loop
Discretizing system (
For the discrete switched system (
Consequently, the closedloop WNCS can be written as
The control gains
Evolution over one period of switched WNCS with two types of behavior.
Denoting
The next thing we should do is to guarantee the closedloop system remaining stable with the designed state feedback control gains when the switching signal is temporarily uncertain. Consider the scalars
Moreover, consider the following two scalars,
Then, the stability of the closedloop WNCS (
Let
We consider the following Lyapunov functions:
Since the controller gains
Combining inequalities (
With the definitions of
Let
Without loss of generality, we assume that the system starts with a mixedmode behavior,
Given that
Consider the WNCS with adaptive sampling period rule (
According to Theorem
Condition (
Simulation studies are performed on a WNCS closed by an IEEE 802.11b wireless network with two control loops sharing the network resources. The two control loops are assumed to have the same dynamics but with different initial conditions:
The wireless network parameters are set as in Table
In Table
Simulation parameters.
Parameter  Value 

Initial energy of both sensors 
0.15 J 
Sensor 1 expected survival time 
75 s 
Sensor 2 expected survival time 
70 s 
Unit transmission energy 
25 dbm 
Number of sampling period candidates 
10 
The minimum sampling period of loop1 
1 ms 
The maximum sampling period of loop1 
256 ms 
The minimum sampling period of loop2 
1 ms 
The maximum sampling period of loop2 
256 ms 
Solving matrix inequalities (
Controller gains of ten sampling modes.
Sampling period (/ms)  Controller gain 





















With the above simulation parameters and controller gains, the curves of survival time prediction, power consumption, and control output of both control loops are shown in Figures
Sensor 1 survival time prediction.
Analyzing the simulation curves, we have the following results.
Figures
The power consumption in three cases of minimum sampling, maximum sampling, and the proposed adaptive sampling is compared in Figures
Figures
Combining Figures
Sensor 1 power consumption comparison in three cases.
Control loop1 output comparison in three cases.
Sensor 2 survival time prediction.
Sensor 2 power consumption comparison in three cases.
Control loop2 output comparison in three cases.
This paper presents a joint design method for wireless networked control systems with limited power constraint. A power efficiency algorithm based on the adaptive sampling period is put forward to satisfy the demands of sensor survival time and system stability. Then, the timevarying control system with transmission delay is modeled as a switched system with uncertain switching signals. A dwelltimedependent control method is discussed to guarantee the stability of WNCS. Simulation results show the effectiveness of the proposed method and indicate that it can achieve good tradeoff performance. Methods by which to reduce power consumption from the aspect of a single node as well as balancing power consumption from the global network perspective are worthy of further exploration.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The working is sponsored by The NSFC (no. 61202473) and The Natural Science Foundation of Jiangsu Province (no. BK2012551).