2014 IEEE Ninth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP)Symposium on Sensor NetworksSingapore, 21–24 April 2014

Shuanglong Xie, Kay Soon Low, Senior Member of IEEE and Erry Gunawan, Member of IEEE School of Electrical and Electronic Engineering

Nanyang Technological University Singapore

k.s.low@ieee.org

Abstract—A wireless network control system (WNCS) is a control system whose network is closed over a wireless channel. The control performance can be degraded due to the imperfection of the wireless network. This paper studies the co-design of Media Access Control (MAC) layer parameters and sampling period of a model-based network control system (MB-NCS). In particular, a stability condition of MB-NCS in terms of packet loss, packet delay and sampling period is established. An adaptive tuning algorithm is proposed to find the optimum parameter set, which can guarantee the stability of control system and minimize the energy consumption. The results show that the co-design approach outperforms traditional network control system in terms of energy reduction and is robust against time-varying network traffic.

Index Terms- model-based network control system, IEEE 802.15.4.

I. INTRODUCTION

In recent years, there has been increasing interest in implementing a wireless networked control system (WNCS), whose control feedback loop is closed via a wireless network[1]. This class of system can potentially reduce system cost and simplify the maintenance as well as installation [2]. However, its control performance can be degraded due to the non-deterministic nature of the network. Among various properties of a control system, stability is the most critical one. In addition, energy consumption is another important concern as typical wireless modules have limited battery capacity. To address these two aspects, this paper proposes an adaptive algorithm to minimize the energy consumption under stability constrains.

It is of vital importance for network control system to choose a proper sampling period as it determines both the bandwidth usage and the stability of the control system. It has been reported in [3] that the use of self-triggered controller is one way to achieve optimum sampling. By varying the sampling period based on current sensor measurements, the control system can maintain stable with minimum sampling. However, the design of self-triggered control system typically assumes a perfect network environment and thus it is not robust against packet loss and packet delay. Another important sampling strategy is the model based network control system (MB-NCS) [4, 5]. The MB-NCS uses an explicit model to estimate the

current state of the system. Despite modeling errors in actual applications, the MB-NCS could still greatly reduce bandwidth usage and maintain stable.

In addition to the sampling period, the non-deterministic nature of wireless network should also be taken into account. In many applications, the packet loss and the packet delay induced by the wireless network are often characterized by some simplistic models, which are usually insufficient to represent the stochastic nature of the network. Moreover, application layer is not always independent from other layers. To achieve better design of WNCS, it requires a co-design methodology [1, 6, 7], which takes the dynamics of controlled plant and wireless network into account to make decisions adaptively, instead of a layered one. In [8], a co-design framework between a self-triggered controller and an IEEE 802.15.4 network is proposed. It aims to ensure the schedulability and provide end-to-end packet transmission while the cost of the system (i.e. energy, control performance) is not the focus. In [9], a MB-NCS and a CSMA/CD network are combined. This work is followed by a similar wireless version in [10]. A sampling strategy is derived to ensure Lyapunov stability of the control system under packet delay and packet loss. Although this framework is effective in terms of control performance, it is not energy efficient as the sampling is conservative.

This paper incorporates a self-triggered sampler into an MB-NCS under an adaptive IEEE 802.15.4 CSMA/CA network. Its aim is to overcome some of the weaknesses of existing approaches. The original contributions of this paper are as follows: 1) A novel stability condition for MB-NCS, which takes into account the packet loss and random delay; 2) An algorithm to estimate the channel state based on local measurement; 3) An adaptive tuning algorithm for energy optimization, which tunes the sampling period and MAC layer parameters based on measurements of the traffic conditions.

The outline of the paper is as follows. The system scenario is first explained in Section II. The extended stability condition of MB-NCS is discussed in Section III. In Section IV, the analysis of MAC layer is presented. An adaptive tuning algorithm is proposed in Section V. The simulation results are then shown in Section VI, followed by conclusion in Section VII.

978-1-4799-2843-9/14/$31.00 © 2014 IEEE1

II. SYSTEM SCENARIO

The MB-NCS scenario under investigation is depicted in Fig. 1. A plant is remotely controlled by a model-based controller over an IEEE 802.15.4 CSMA/CA network. The state of the plant is sampled by the sensors attached to the plant. Several other applications with unknown varying data rate share the network channel and thus contentions and collisions may occur with the proposed system. Under different traffic condition, the proposed algorithm adjusts the MAC parameters and sampling period to minimize the energy consumption under stability constraint.

Actuator PlantController

SensorIEEE 802.15.4 CSMA/CA

Other Applications

Other Applications

Fig. 1 System scenario under investigation

III. STABILITY OF MB-NCS A linear state-feedback MB-NCS[4] is considered in this study. Let and u be the state and input of the plant respectively. The dynamic of the plant shown in Fig. 2 can then be described using the state space system as where

is the state matrix and is the input matrix. A model of the plant estimates the state of the plant between sampling interval and updates the control signal to the plant with a state feedback controller , where is the state of the model and is the feedback gain. When a new set of sensor measurement reaches the actuator, the new measurement is used as the state of the model: where is the sampling instant.

The modeling error can be expressed as and . The state error between the plant and model is

. Using an augmented state-space representation, the system can now be describe as [4]

(1)

where . At every sampling instant, the state of the model is reset to the actual measured state. Thus the error e would be reset to 0. For an arbitrary time instant,

, the system response of (1) with a sampling interval is as follows [4]

(2)

where is the initial state and .

The system described by (2), with update times that are independently and identically distributed (i.i.d.) random variables with probability distribution is mean-square stable [4] around the solution if:

i) (3)

ii) (4)

where is the maximum singular value of .

Plant Sensor

IEEE 802.15.4 CSMA/CA NetworkModel

K

Fig. 2 State feedback model-based network control system

In the following discussions, the result is extended by assuming that the packet is transmitted with some successful probability p for each packet. p may change over time and can be partially manipulated by choosing different MAC layer strategies. The sensor measurement will be discarded if the transmission fails. Then the sensor will attempt to send packet again in the next sampling time. Thus, the probability that the j-th actual sampling period is is equal to , where is the number of consecutive packet loss and is the nominal sampling period.

Under the condition that each transmission is i.i.d., there exists a finite probability that it becomes infinitely large. It thus imposes a problem when calculating the term

in (4) which could not account for the infinitely long packet loss sequence. This can be resolved by diagonalizing the and determining each entry of

. We then have the following corollary:

The system described by (2), with nominal sampling period h and packet successful rate p is mean-square stable around the solution if:

i) (5)

ii) , (6)

iii) = = <1 (7)

(5) can directly be derived from (3) using the properties of geometric sequence. For (6) and (7), the basic idea is that after the diagonalization, each entry of can be transformed into a geometric sequence, whose sum can be determined even when there exist infinitely long packet loss sequences. (6) ensures that the each sum is a finite number. (7) is obtained from (4) and (6), where satisfies the ( is the diagonalized matrix) and

.

2

The stability condition, regardless of the complexity of the control system, can always be expressed as a simple relationship between sampling period and packet successful probability, as the example in Fig. 3 shows. Fig. 3 demonstrates that for each given packet successful probability, there exists a maximal nominal sampling period, below which the system is stable. Therefore, given any combination of

, the proposed stability condition can immediately determine whether the system is stable or not by checking which region it falls.

Fig. 3 Relationship between sampling period and packet successful probability

for an unstable double integrator system with plant dynamics , and model dynamics , . The state

feedback controller is a P-controller with .

It should be noted that in addition to packet loss, packet delay can also destabilize the system. Fortunately, this delay can be mitigated by time-stamping the measurement packet. Upon receiving the packet, the controller uses the delayed packet to estimate the current state of the plant as follows

(8)

where the delay d can be obtained by comparing the time difference between the moment the data is measured and the moment the packet is received. If d is small, the error will be negligible with the delay compensation (8). In the co-design scheme, the error due to delay can be used as a constraint:

h (9)

IV. CHANNEL ESTIMATION OF IEEE 802.15.4 CSMA/CA

In this co-design framework, the standard slotted CSMA/CA feature of the IEEE 802.15.4 is considered. In order to estimate the channel state, the CSMA/CA network should be properly modeled. Although [11] provides a detailed model to analyze the star topology scenario where all nodes are identical, it does not apply to the proposed scenario in which the control system shares the channel with other applications with varying unknown data flows. In [12] the number of nodes in the network is assumed to be known a priori, which is also not the case in the proposed scenario. Instead, this paper proposes an approximate method to calculate the packet successful rate, worse-case packet delay and average energy consumption based on local estimation, which simply makes use of CCA and ACK information. In particular, a node uses

counters to store and update the probability that the result of CCA is busy, namely the busy channel probability (BCP) , and the probability that the result of ACK is negative, namely the transmission failure probability (TFP) . It should be noted that the proposed method also takes into account the interference and fading in the network and they are reflected in TFP.

To simplify the notations, for the subsequent discussions, let the channel indicators and the MAC layer decision set , where m is the maximum backoff limit and n is the maximum retry limit.

A. Packet Successful Rate

Similar to the result in [11], the packet successful rate (i.e. reliability) is given by:

(10)

where denotes packet dropout due to retransmission limit and denotes packet dropout due to backoff limit.

B. Energy Consumption Per Packet

The average energy consumption is dependent on the average number of transmission and average number of backoff for a single packet. The average number of transmission for a single packet can be determined using simple probability theory:

(11)

Similarly, the average number of backoff within one transmission can be determined as

(12)

The average energy consumption per packet comprises of three parts, namely the power consumption due to transmission and retransmission , the power consumption due to backoff stage and the power consumption due to CCA channel sensing . From (16), can be determined as

(13)

where the power consumption per data collision and the power consumption per

successful transmission is . In (13), and

are the number of time slots on one data packet, ACK timeout, waiting for ACK, inter frame spacing (IFS) and ACK respectively. and are the energy consumption on transmitting data, idle listening and receiving data per slot respectively. Using the similar approach as in [13], the power

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consumption due to backoff stage using (11) and (12) can be derived as follows:

(14)

where is the minimum integer which is larger than or equal to . and are the minimum and maximum binary exponent respectively. Assume the worst case scenarios where the node senses busy channel in the second CCA, then using (11) and (12), can be readily determined as

(15)

Neglecting the power consumption in sleep state, the total power consumption per packet is the sum of (13)-(15) given as follows:

(16)

C. Worst-case Delay The worst-case delay is characterized in this section to estimate the largest deviation on the sampling period. Given a set of ( ), the worst-case transmission would be those that experience times of collisions and m times of backoff in each attempt. Assume that in k-th backoff, the backoff delay is slots.

The delay is thus comprised of 4 components: the delay due to backoff, the delay due to CCA, the delay due to transmission failure and the delay due to successful transmission.

(17)

where is the time taken for transmitting one slot of data, which depends on the data rate.

V. ADAPTIVE TUNING ALGORITHM

In Section III, a stability condition in terms of is developed. In Section IV, the packet successful rate, average energy consumption and packet delay are estimated based on channel traffic and MAC layer parameters. By tuning the MAC layer parameters, these performance metrics will change and thus the selection of sampling period will also be affected. The objective of the tuning scheme is to minimize the energy consumption. In general, energy consumption can be reduced by limiting the number of transmission attempts (e.g. reduce

, ). However, reducing and will also reduce packet successful rate and thus require smaller in order to stabilize the system, which will in turn consume more energy. Therefore there is a trade-off between transmission attempts and sampling interval.

The problem can be formulated as an optimization problem to minimize the energy consumption of a sensor device per packet as follows:

subject to

(18)

where refers to the maximum nominal sampling period, which can be expressed as a function of

, as shown by (5), (6) and (7). and are the lower and upper bounds of respectively. is the lower bound of packet successful rate. is a factor far less than 1 to guarantee that (9) holds. In this paper, we let .

, and can be obtained from (10), (16) and (17) respectively.

Upon receiving the latest measurements, the node would first update the channel indicators and compare it with the last-invoked values to check whether the difference exceeds a pre-defined threshold. Channel indicators can be updated as

and [14]. The parameters and are the transmission failure probability and busy channel probability of the current sliding windows respectively while is a pre-defined smoothing factor. Only when the channel indicators change significantly, the adaptive tuning algorithm will be activated. It will then calculate the optimal with respect to the new traffic condition and send the updated parameters along with the sensor measurement to the controller. The optimization problem is combinatorial. As the searching space is quite small ( takes integer value from 3 to 6 and can choose integer value from 0 to 7), it can be readily solved by exhaustive search.

VI. PERFORMANCE EVALUATION

In this study, the algorithm in (18) has been implemented using the TrueTime simulator [15], which has been modified in this study to allow the parameters of the network to be tuned dynamically. In the simulations, a sensor node is transmitting data to the controller in order to control a time-invariant linear system. The controller uses a model to approximate the state of the plant. The feedback loop is closed via IEEE 802.15.4 CSMA/CA protocol. To evaluate the power consumption, the CC2420 [16] node is used. When CC2420 is transmitting data, it consumes 11 mA at 3.0 V. For receiving data, it uses 18.8 mA at 3.0 V. In idle mode, it is 0.426 mA at 3.0 V while in sleep mode it is 0.020 mA. Furthermore, there are five other nodes acting as interference sources, four of which randomly send packets to the rest at every 10 ms.

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A. Adaptive Tuning Algorithm

This section presents how the proposed algorithm would choose the optimum decision set and adapt to changes in

traffic condition. Consider a control model

while the plant being

. Assume that the plant has an initial state .

Fig. 4 and behavior

Fig. 5 Parameter behavior

Fig. 6 Euclidean norm of the state of control system

The simulations are conducted for 50 times with random traffic conditions stated below and the mean value of each parameter is used. For each simulation, the simulation time is 100s, which is long enough to observe the variation of plant state. The traffic condition in each simulation is as follows:

every interference node sends packets at every 10 ms whose sizes are uniformly distributed between 8 to 12 bytes in the first 50 seconds. To study the impact of traffic conditions on the tuning parameters, the packet sizes increases sharply by 300% on average at 50th second, following uniform distribution between 36 to 44 bytes. The packet size is set to be uniformly distributed in order to simulate the complex traffic conditions in such networks. Figs. 4-6 show the behavior of the channel state, tuning parameters and control system trajectories under a sharp traffic change. In Fig. 4, it can be observed that is stable after 30s but increases rapidly after a sudden traffic change at time 50s. Meanwhile, keeps fluctuating regardless of traffic change. In Fig. 5, the backoff limit increases from 4 to 5 soon after a traffic change to ensure a high packet successful rate while retry limit decreases from 1 to 0 to avoid a possible long delay. This is a typical tradeoff between packet successful rate and delay. The sampling period drops from 590 ms to 260 ms. Fig. 6 presents the Euclidean norm of state as a function of time. The Euclidean norm is used to measure the control performance. It is observed that while the parameters are tuned to minimize the energy consumption, the control performance is not compromised.

B. Energy Consumption

In this section, the performance of the proposed adaptive algorithm is benchmarked with another model based approach named MBPNCS [9]. The MBPNCS is jointly designed between a model-based control system and a network. Instead of adopting an adaptive tuning approach, the controller in a MBPNCS takes into account all possible network scenarios and choose the smallest sampling period in order to ensure the stability of the control system. The same IEEE 802.15.4 CSMA/CA network is assumed for the MBPNCS. The simulations are conducted for 50 times. The number of nodes that send interference packets is increased to 20. The performance is evaluated under 5 different levels of traffics in which the average data rate of each interference node is 2, 4, 6, 8, 10kbps respectively. The performance metrics under evaluations are the energy consumption and relative root mean square error, similar to [9, 10] to determine the control performance.

Fig. 7 Energy consumption of adaptive tuning algorithm over MBPNCS under

different traffics (mean value and standard deviation)

5

Fig. 8 Control performance of adaptive tuning algorithm over MBPNCS under

different traffics(mean value and standard deviation)

In Fig. 7, the average energy consumption with its standard deviation is presented. The results show that the proposed approach outperforms the MBPNCS in that it consumes far less energy in each data rate setting. Fig. 8 shows the control performance (relative RMS error) with its standard deviation. The results from these two figures demonstrate that the proposed algorithm consumes 59.1% less energy than MBPNCS on average while guarantees slightly better control performance. The main reason is that the proposed algorithm can adapt to the changes in the network traffic and tune the parameters accordingly while MBPNCS considers the worst-case scenario and use the most conservative parameters.

VII. CONCLUSIONS This paper proposes a co-design framework for jointly tuning the parameters of MAC layer and the sampling period of the control system. The interaction between different layers allows designers to take into account all the parameters and formulate the energy optimization problem properly. The approach to estimate the traffic condition without any prior knowledge of the network has been presented. The proposed algorithm has been compared with existing algorithms. The result shows that this dynamic co-design algorithm can quickly adapt to the changes in channel state and outperform the MBPNCS with energy reduction of 59.1%.

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APPENDIX Notaions of MAC layer

Symbols (values)

Definitions

m maximum backoff limit

n maximum retry limit

(0) minimum binary exponent

(3) maximum binary exponent

busy channel probability

transmission failure probability

(10.56 J) energy consumption for transmitting data per slot

(0.409 J) energy consumption for idle listening per slot

(18.05 J) energy consumption for receiving data per slot

(240bits) length of data packet

(48bits) length of inter frame spacing

(180bits) length of waiting for ACK

(0.32ms) time duration for one slot of data

6