Maria Isabel Vergara-Gallego

Olesia Mokrenko

Maxime Louvel

Franc Suzanne Lesecq

¸ois Pacull

Implementation of an Energy Management Control Strategy for WSNs using the LINC Middleware

Keywords: Energy Management, Middleware, Implementation, Model Predictive Control

Energy optimisation in Wireless Sensor Networks (WSNs) is traditionally done either at the sensor node level or at the network level. To obtain even more energy savings, the final application must be considered. Control theory offers promising solutions to tackle this challenge. This paper details an implementation of a control strategy to minimise energy consumption of a WSN, while ensuring the application Quality of Service (QoS). The application QoS is expressed with the sampling period for sensor nodes and a minimum number of samples that must be available at the application level at each sampling time. With a Model Predictive Control strategy, the lifetime of the WSN is doubled compared to the basic case. The control strategy has been implemented and evaluated on a real test-bed, formed of heterogeneous sensor nodes, thanks to the LINC coordination middleware.

Introduction

Wireless Sensor Networks (WSNs) have been a hot field of research for several decades [START_REF] Yick | Wireless sensor network survey[END_REF]. A great deal of effort has been put on optimising energy consumption of single sensor nodes and/or of the whole WSN. The grail is to implement distributed applications that will run autonomously for years, without battery changes.

To make this a reality, power consumption must be drastically reduced at the sensor node level. Several solutions, that tackle this objective already exist at the design time of the node hardware and/or software. Regarding hardware design, solutions can go from the design of novel radio technologies [START_REF] Hutu | A new wake-up radio architecture for wireless sensor networks[END_REF] to microcontroller architectures [START_REF] Hempstead | Survey of hardware systems for wireless sensor networks[END_REF], and energy management methodologies [START_REF] Akgul | Power management through dvfs and dynamic body biasing in fd-soi circuits[END_REF]. At the software level, in Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

EWSN'16, February 15-17, 2016, Graz, Austria.

Copyright c 2016 ACM 978-1-4503-1169-4 ...$10.00 the literature and industry, a large number of approaches and algorithms are proposed at different layers of the communication stack to increase the network lifetime [START_REF] Anastasi | Energy conservation in wireless sensor networks: A survey[END_REF]. These approaches try to minimise the nodes active period (using duty cycle), optimise routing protocols, reduce the quantity of transmitted data, etc. However, maximising the WSN lifetime boils down to reducing the energy consumption not only of nodes (node level) or of one part of the network (network level). Energy must be considered at the global level, i.e. including the applications running on top of the WSN.

A trade-off between performance (or application Quality of Service (QoS)) and energy consumption must be found. A promising solution to find this trade-off is to rely on Control Theory. From a model of the system (here a WSN system), possibly with constrains, Control Theory can ensure the application QoS while minimising the energy consumption of the whole WSN. This control objective can be expressed with a cost function to be minimised under constraints. The associated control law will then require a bit of information from the nodes and protocol layers (for instance, energy consumption of the nodes, remaining energy in the batteries of the nodes, the work each node has to perform) in order to manage the nodes and the whole system. To our knowledge, most of the work relying on Control Theory for the minimisation of energy consumption in WSNs are related to managing the transmission power of the sensor nodes. These mechanisms are applied at the node level, where no knowledge regarding the global state of the network is required. Moreover, the application constraints are not taken into account. Note that [START_REF] Anastasi | Energy conservation in wireless sensor networks: A survey[END_REF] reviews various energy conservation schemes but none of them seems grounded in control theory. [START_REF] Pantazis | A survey on power control issues in wireless sensor networks[END_REF] proposes a classification of power control mechanisms in WSN, based on control theory. These works are actually related to power control protocols only.

The present paper details the implementation, on a real test-bed, of a control strategy based on Model Predictive Control (MPC). The objective of this strategy is to minimise the energy consumption of the whole WSN and, at the same time, to ensure the application QoS. For the selected testbed, the MPC strategy, which is described in [START_REF] Mokrenko | Dynamic power management in a wireless sensor network using predictive control[END_REF], extends the WSN lifetime by a factor of 2, compared to the situation where no MPC control is implemented. Theoretical foundation and preliminary results on a real test-bed can be found in [START_REF] Mokrenko | Design and Implementation of a Predictive Control Strategy for Power Management of a Wireless Sensor Network[END_REF]. The main goal of the present paper is to detail how it was possible to bridge the gap between theory and imple-mentation, demonstrate and validate the theoretical results. In addition, two communication technologies are deployed, leading to a heterogeneous network. The implementation is based on LINC [START_REF] Louvel | Linc: A compact yet powerful coordination environment[END_REF], a coordination middleware. Thanks to its resource-based approach and transactional guaranties, LINC makes it possible for the global controller to take decisions according to the current state of the WSN, and to force the WSN to behave as expected.

The paper is organised as follows. Section 2 presents a description of the WSN considered here and the application. Then, Section 3 describes how the WSN has been implemented and integrated with the global controller. Section 4 presents the implementation results. Finally, Section 5 discuses the related works and Section 6 gives some global conclusions and future work directions.

System description

The system considered in this paper is a WSN deployed to monitor an environmental parameter in a particular area, using several sensor nodes. For monitoring applications in buildings, typical monitored parameters are temperature, CO 2 level (indoor or outdoor), and humidity. The values acquired by the sensor nodes are sent to a sink node that will, for instance, interact with the air conditioning unit. Though the system may contain a control part (i.e., commands can be sent to actuators), this work focuses only on the monitoring part. To reach a nominal behaviour at the application level, a certain application Quality of Service (QoS) must be provided. In this context, the application QoS refers to the minimum information required for the correct functionality of the application, and it can be defined from the sampling frequency of the nodes, and the quantity and quality of sensed values. Note that the sensor nodes are supposed to be densely deployed in the sensor field, leading to a certain degree of redundancy. As a consequence, when the minimum number of nodes needed to ensure the application QoS is lower than the total number of nodes in the network, it is possible to switch off some nodes. In this way, the network lifetime can be extended. In addition, a node can be replaced by another when, for instance, the first one runs out of energy. Nodes sensing the same environmental variables may differ according to:

• available energy: sensor nodes are powered by a battery and/or harvesting system(s), hence at every instant they have different available energy (i.e., due to different battery sizes, harvesting periods, battery ageing);

• energy consumption: to provide the same type of measurements, different sensor nodes may require different energy budgets;

• heterogeneity: sensor nodes may be heterogeneous in terms of communication protocol, data format and/or hardware characteristics. Hence, deciding which node must be active at a given instant of time is not straightforward. In addition, nodes can disconnect from the network (become Unreachable) without notice. Disconnection may be caused by energy starvation, communication problems, or hardware failures. Nodes may also join back the network when they leave the Unreachable state if they have regained enough energy thanks to harvesting systems, or if the communication is back.

Regarding heterogeneity, as multiple hardware platforms and communication protocols must be supported, it is necessary to rely on a middleware layer. Such a layer abstracts the controller from the communication protocol, data format, or any low level matter.

Figure 1 illustrates the monitoring system, which can be divided in four levels: I) the sensor nodes, II) the communication infrastructure, III) the data collection and synchronisation level and IV) the Controller. These levels are detailed in the following subsections.

Sensor nodes

Typical sensor nodes can be split in four main units, namely, computation, communication, sensing and power supply [START_REF] Akyildiz | Wireless sensor networks: a survey[END_REF]. For each node, different power modes are defined. These power modes correspond to a combination of the state for each unit in the node. The energy consumption of the node in a given power mode is given by the node manufacturer.

In a WSN, the activity of nodes (i.e. sensing, computing, communication) is usually "duty cycled": the node periodically wakes-up (i.e. the CPU is activated), senses an environmental value (i.e. the sensing unit is turned on), processes and transmits the information (i.e. the radio is activated), and finally enters the sleep mode (i.e. all units are disabled waiting for a timer event). The wake-up period (or duty cycle) determines the energy consumed by the node.

The energy management strategy implemented in this paper assigns different functioning modes to Reachable nodes. Each functioning mode is defined by a given period for sensing and communication tasks. Hence, all nodes in the network are duty cycled, and their energy consumption depends on their duty cycle for communication and sensing (i.e. each functioning mode is associated to a known energy consumption that depends on the duty cycle). Basically, the controller combines information received from the nodes regarding their remaining energy and the application QoS requirements, to decide the most suitable functioning mode for each node. For instance, if the controller objective is to minimise the energy consumption of a node, it can increase the communication period and deactivate the sensing activity (i.e. the sensing period is equal to infinity).

The controller requires information regarding the remaining energy of the nodes. This information must be sent on a periodic basis to the controller. Thus, a minimum communication duty cycle is required for the proper functionality of the controller. Notice that the nodes must embed an estimator of their remaining energy, since a sensor that measures the remaining energy in a battery does not exist.

Communication architecture

In order to exchange data with the sink, a communication architecture is defined. It determines, through a given topology, how nodes communicate with the sink. In this paper, a star topology is considered. Nodes communicate directly with the sink through a router. Hence, the controller can choose to increase the communication period of one node, without affecting the communication with other nodes.

Note that a cluster-tree topology can be easily implemented and evaluated. For this topology, the cluster coordinators are responsible for forwarding information from nodes in the cluster. Thus, coordinators are duty cycled and synchronised with associated nodes for data reception and forwarding. Hence, to communicate with all the associated nodes, the wake-up (or communication) period of the coordinator must be at most the shortest communication period of all the associated nodes. Therefore, the controller can change the functioning mode of all end-nodes in the network. The functioning mode of the coordinators are then set accordingly. Besides, further parameters have to be taken into account by the controller. For example, the number of hops required to send a packet to the sink, which is proportional to the energy cost of communication, must be considered. All these factors can be easily integrated in the controller, nodes must inform their role in the network (coordinator or end node) and the number of hops to the sink. The controller integrates this information to the constraints and takes decisions as for the star topology case.

More complex topologies, such as mesh networks, require the controller to know the current topology and routing information, which is highly dynamic. Indeed, the controller cannot arbitrarily change the functioning mode of the nodes as it can break the routing and topology maintenance mechanisms. Thus, the integration with a mesh network requires further work.

Data collection and synchronisation

This layer is responsible for collecting the sensed data, synchronising the sensor nodes, and calling the controller when the information is ready. These three tasks are achieved through the coordination middleware LINC [START_REF] Louvel | Linc: A compact yet powerful coordination environment[END_REF].

LINC uses an associative memory [START_REF] Carriero | Linda in context[END_REF] implemented as a distributed set of bags. This offers a decoupling in space and time between the data producer (the sensor nodes) and the data consumer (the controller). LINC has been successfully used in several application domains and currently supports around 30 technologies. The associative memory also provides an abstraction layer to present all the measurements in the same format to the controller.

To ensure the expected application QoS, sensor nodes need to communicate with the sink at a given period (according to their functioning mode). It can be of the order of seconds, minutes, hours, or days, depending on the application domain. Between two communication instants, the external timer of the sensor node is programmed according to the desired period. Then, the node enters the sleep state, waiting for a timer interrupt. Oscillators in sensor nodes are not perfect and they will drift over time. Therefore, if the clocks are not resynchronised, sensor nodes may wake up outside of the timing-window accepted by the sink. On the one hand, if the node wakes up too early, the measurement may be outdated when it is used by the controller. On the other hand, if the node wakes up too late, the controller will not take the values in consideration and may think the node is in the Unreachable state.

To avoid synchronisation problems, LINC ensures that the clocks of the nodes are resynchronised when needed. To do so, a resynchronisation frame is periodically exchanged with the nodes. The resynchronisation period depends on the type of oscillators being used by the sensor nodes (i.e., the more precise the oscillator, the longer the resynchronisation period). This parameter can be determined empirically or according to nodes' characteristics.

The resynchronisation procedure is completely independent from the controller. Thus, the latter does not need to take care of synchronisation. It only processes the measurements currently received from the Reachable nodes.

The time/space decoupling and the abstraction offered by LINC have been particularly useful here. Indeed, it is straightforward to ensure that the latest measurements are available in the associative memory. The measurements are simply added to a dedicated bag whenever this is required (sampling/ resynchronisation periods). The controller is called when the current state of the nodes is known. The LINC application waits during a configurable time to receive information from nodes. If no information is received after this time, the node is considered as Unreachable.

Control design

The controller is based on a Model Predictive Control (MPC) approach. In order to control energy saving in the WSN, the remaining energy in each sensor node i, i = 1, ..., n, is modelled with a discrete-time linear model:

x i (k + 1) = x i (k) + B i u i (k), (1)
where x i (k) is the remaining energy in the battery of sensor node i at sampling time k. B i u i (k) represents the energy that will be consumed during the time interval The energy consumption of each node during this next period of time depends on the functioning mode assigned by the controller. The controller decisions tend to minimize the energy consumption of the whole set of nodes while the application QoS is met 1 . This decision comes from the minimi- The first subset is related to the remaining energy in the batteries that must be strictly positive to avoid battery damages (lower bound). Moreover, the remaining energy cannot be infinite and a maximum value cannot be exceeded. The second subset of constraints expresses that each node can be in a unique functioning mode. The last subset expresses the application QoS. The interested reader can refer to [START_REF] Mokrenko | Dynamic power management in a wireless sensor network using predictive control[END_REF] where theoretical details are provided. The controller has been first designed in the Matlab environment, and evaluated in simulations. The numerical values used in the simulation (e.g. maximum energy in the node batteries, energy consumption in each functioning mode) have been extracted from datasheets [16]. Then, the controller has been implemented and optimised in python, leading to an efficient implementation in terms of computational time.

Implementation Description

The main objective of this work was to validate theoretical and simulation results. Thus, the proposed energy management approach is implemented on a real test-bed composed of heterogeneous wireless sensor nodes. The test-bed is now described, along with the data collection approach.

Test-bed description

The hardware test-bed considered here consists of one sink, one router, and 6 sensor nodes spread over a given area. The sensor nodes chosen for experimentation are the Openpicus Flyport Wi-Fi 802.11g [16] with Wi-Fi transceiver and with EnOCean transceiver TCM-310 [START_REF] Enocean | [END_REF], leading to a heterogeneous deployment. Table 1 gives the power consumption of the Flyport platform. The Openpicus Flyport Wi-Fi 802.11g platforms embed a Microchip PIC 16-bits processor with a Wi-Fi radio module and ready-to-use protocol stacks. Openpicus provides a FreeRTOS-based framework implementing the CSMA-CA MAC protocol and the TCP transport protocol. Applications are written as FreeRTOS tasks.

When using Wi-Fi, Openpicus nodes form an infrastructure topology: they connect to one access point or router. The latter forwards all the received packets from/towards the sink. For the EnOcean protocol, an EnOcean transceiver is energy between nodes for fault tolerance connected to the GPIOs of the Openpicus platform. This transceiver exhibits very low-power serial communication, that permits the exchange of very short frames. The EnOcean node communicates directly with the sink, this latter making use of an EnOcean USB dongle module.

Definition of the functioning modes

For the energy management strategy, two functioning modes and an Unreachable state are defined for each node, for both the Wi-Fi and the EnOcean transceiver:

• in Mode 1 (or Active mode): both the communication and sensing tasks are activated periodically. The sensing period is equal to the communication duty cycle T s = 1 min;

• in Mode 2 (or Standby mode): the node sensing unit is disabled. The node wakes-up periodically, as requested by the controller, to report to the sink its battery state and to receive commands (i.e. its functioning mode for the next period of time) from the controller. The communication period of a node in this mode is equal to the controller period T c = 1 hour;

• nodes enter the Unreachable state when they are unable to communicate with the sink due to network issues, hardware damage, or lack of energy. When a node transmits a frame to the sink (to send a sensed value or available energy) it waits for an answer. The answer can be an acknowledgement, a resynchronisation frame, or a command frame asking the node to change its functioning mode.

Definition of the application QoS

The application QoS is expressed as the minimum number of measurements that must be provided by the WSN to the application over a defined time period. Hereafter, this application QoS is called mission, which must be guaranteed by the controller. This latter assigns a functioning mode to the nodes, taking into account the nodes that are unreachable.

In the scenario, d 1 nodes must be assigned to the Active mode, in order to meet the mission, while minimising the overall energy consumption. Moreover, the mission can change dynamically, i.e. depending on a time schedule or on external events. This dynamic mission permits following the needs of the application during the system evolution. Here, we consider that during the working hours, when people are present in the office, the mission is defined with d 1 = 3 nodes in Mode 1, while during the night period, when there is nobody in the office, d 1 is equal to 1.

The lifetime of the WSN is defined as the period of time during which the mission can be fulfilled. This time should be the time before the number of reachable nodes is smaller than the minimum number of required active nodes (d 1 ).

Data Collection

To collect data from the sensor nodes, the first step is to encapsulate the nodes in LINC. This is made easy by the PUTUTU framework [START_REF] Pacull | Self-organisation for building automation systems: Middleware linc as an integration tool[END_REF] that provides generic LINC objects to speed up integration of sensor and actuator technologies. For instance, the EnOcean protocol was already integrated in the framework. Figure 2 illustrates the LINC application put in place. The application is composed of three LINC objects all running in the sink:

• The openpicus wifi object acts as a TCP server that listens for connections from Wi-Fi nodes. It stores measurements and battery information sent by these nodes.

• The openpicus enocean object opens a serial connection with the EnOcean dongle to communicate with the EnOcean nodes. It stores the sensed values and battery information sent by these nodes.

• The controller object collects information about the battery status of all reachable nodes (from the two other objects). It periodically calls the controller to get the new functioning mode for each node in the network.

The updates are propagated to the openpicus wifi object and the openpicus enocean object. These latter send the new functioning mode to each node if it has changed. The first time the nodes communicate with the sink, their clock is synchronised with the sink clock and keep synchronised according to the synchronisation period. The synchronisation period can be adjusted dynamically. Empirical experiments have shown that a synchronisation period of around 6 hours is appropriate for this implementation. This synchronisation period leads to a maximum clock drift of a couple of seconds, which is acceptable given the dynamics of the application.

Experimental Results

To evaluate the energy management strategy, an experiment of a duration of 30 hours was run. The experiment started at T 0 = 8 a.m. Figure 3 shows the functioning modes of the sensor nodes during the experiment. The EnOCean node is S6. We can see that the mission defined above is fulfilled during all the experiment: during the working hours, 3 sensors are Active, and during the night period, 1 sensor is Active.

In Figure 3 it can be observed that the node number 6 became Unreachable after 6 hours, when its battery reached the minimum energy level. Node 4 was disconnected twice from the network after 10 hours, during 1 hour, and after 14 hours, during 2 hours. The disconnection is due to radio channel perturbations. The same phenomenon happens with nodes 2 and 5. When a node falls in the Unreachable state, it is no longer taken into account by the controller when solving the control problem. When the controller receives again information related to the remaining energy of this sensor node, it adds the node again in the set of nodes to be controlled. Note that the nodes do not possess "wake-up on event" capability. Therefore, if an active node (mode 1) becomes unreachable, due to the duty cycle T c = T w = 1 hour for the nodes in mode 2 (stand by), the controller will assign a node in mode 2 to mode 1 when the control period T c is elapsed. This means that we can observe periods of time no longer than T c when the mission is not fulfilled. If nodes could be woken up at any time by an external mechanism, before the end of the duty cycle, this issue would be solved. Note that, in the present scenario, nodes do not embed harvesting systems. In this latter case, when the battery of a node is drained, it can re-enter the "game" when it has regained enough energy to communicate and be placed by the controller in the Active or Standby mode.

Using the MPC approach, the fulfilling of the application QoS is increased up to 36, 7% compared to the "basic" control. The basic control presents the management of the node activity when only mission is ensured without any other parameter to control.

This scenario is also evaluated to demonstrate the scalability of the MPC approach. Table 2 shows the simulation results of one step computation time in Matlab environment for 6, 18 and 54 sensor nodes. We estimated the one step computation time with 54 nodes to 10.81 sec, this step needs to be computed every hour (T c = 1 hour) in our example.

Related Work

To the authors' knowledge, most of the research works regarding power management in WSN focus on the protocol stack [START_REF] Anastasi | Energy conservation in wireless sensor networks: A survey[END_REF][START_REF] Pantazis | A survey on power control issues in wireless sensor networks[END_REF], or on the optimisation of the node units. The application needs are seldom taken into account in the energy/power management strategies [START_REF] Passos | Dynamic power management in wireless sensor networks: An application-driven approach[END_REF]. This latter proposes a Dynamic Power Management (DPM) strategy at node level, that takes into account application constraints to keep the sensor node, as much as possible, in a sleep or idle state without losing the real time responsiveness of the network application. The DPM strategy is based on a hybrid automaton. It is implemented within the node. The main advantage, compared to our approach, is that the control strategy is fully distributed. However, the DPM strategy does not have a global knowledge of the WSN state and the changes in the application needs. Moreover, having the DPM strategy embedded within the node implies an overhead in the energy consumption of the node. Note that there is no real implementation of the proposed DPM strategy.

This paper relies on a middleware layer to apply the Control approach on a real WSN. The controller can then collects information from the nodes and sets some parameters of the network (i.e. the functioning mode of each node). Middlewares and frameworks have been proposed with similar purposes. For instance, PyFUNS [START_REF] Bocchino | Pyfuns: A python framework for ubiquitous networked sensors[END_REF] is a framework that modifies network parameters according to the application. In PyFUNS applications are written as python scripts, then, the framework calibrates the network for energy efficiency. However, it is suitable only for nodes running the ContikiOS. Whereas the architecture described here, may support, thanks to LINC, any operating system and communication stack. MILAN [START_REF] Heinzelman | Middleware to support sensor network applications[END_REF] is a middleware that continuously controls the network's functionality according to the application demands. The implementation of such mechanism is very complex given the huge number of parameters that must be taken into account. It seems difficult to integrate Control Theory with MILAN where several assumptions are made on the WSN behaviour.

Other coordination middlewares, also using associative memory, have been used for WSN, such as Agimone [START_REF] Hackmann | Agimone: Middleware support for seamless integration of sensor and ip networks[END_REF], TeenyLIME [START_REF] Costa | Teenylime: transiently shared tuple space middleware for wireless sensor networks[END_REF] or Agilla [START_REF] Fok | Agilla: A mobile agent middleware for self-adaptive wireless sensor networks[END_REF]. However they do not offer the same properties as LINC (e.g. distributed transactions, support of many protocols and integration frameworks). Moreover, these works focus on developing applications for WSN where this paper integrates Control Theory. Hence, the guarantees offered by LINC are vital.

Conclusions

This paper has presented an implementation of a control strategy for global energy management of a WSN. The implementation is based on the LINC coordination middleware. This papers detailed the different aspects taken into account for the proper implementation, such as data collection and synchronisation.

Experimental results, on a star topology, show that the WSN is correctly integrated with the controller. Functioning modes of nodes are set according to decisions taken by the global controller, which minimises the energy consumption of the whole WSN while ensuring the application Quality of Service. The simulation results show that the control strategy is scalable. The control approach is based on Model Predictive Control. This permits to add new constraints or control objectives if needed. For instance one may way to spread the measurements for redundancy purpose. LINC has been used in several domains such as smart buildings, smart cities or smart parking. Hence the proposed approach may be extended to other applications or domains.

Future work directions include the implementation of the control strategy on a WSN with a more complex topology, such as mesh networks. Such implementation will require a deeper knowledge about the network status such as routing information and current topology. Another interesting direction is to have a distributed controller and study the impact of distribution on the existing software architecture.

Figure 1 .

 1 Figure 1. WSN System levels

  [kT c , (k + 1)T c ]. T c is the control period. u i = [u i1 ... u ih ... u im ] T is the control input. It is related to the functioning mode h, h = 1, ..., m, of node i, where u ih ∈ {0, 1}. The control matrix is B i = [b i1 ... b ih ... b im ]. b ih represents the amount of energy consumed by node i working in mode h.

Figure 2 .

 2 Figure 2. LINC Application for integration

Figure 3 .

 3 Figure 3. Functioning mode of each sensor node vs. time

Table 1 .

 1 Power consumption of Flyport platform and EnOCean transceiver (Supply Voltage 3.3 V)[START_REF] Enocean | [END_REF] 16]

	Mode	Power	Remarks
	Wi-Fi con-nected	162,70 mA	MCU on / Wi-Fi on, con-nected to access point
	Wi-Fi not connected	39,75 mA	MCU on / Wi-Fi on but not connected
	EnOcean Rx 61.21 mA No Wi-Fi
	EnOcean Tx 52.21 mA No Wi-Fi
	Hibernate	28,21 mA MCU on and Wi-Fi off
	Sleep	1,44 mA	MCU off and Wi-Fi off
	sation of a cost function under constraints. Note that the opti-
	misation problem is a Mixed Integer Quadratic Programming
	(MIQP) one, the optimisation variables being both boolean
	values (u i ) and positive real values (x i ) with bounds. More-
	over, a set of constraints must be taken into account.

Table 2 .

 2 Scalability of the MPC approach

	Number of nodes	6	18	54
	Time [sec]	0.36 5.13 10.81

Note that different control objectives can be added thanks to the flexibility of the MPC approach. For instance, the controller could balance the

Acknowledge

This work has funded by the Artemis ARROWHEAD (grant 332987) and the H2020 TOPas project (grant 676760).

7 References


S Pattofatto

H Zhao

A Poitou

A new Hopkinson bar method to investigate the compacting behaviour of fresh concrete

A new experimental test, based on the Hopkinson bar measurement technique is used in order to analyze the compaction process of a fresh concrete under successive impacts. The use of this modified Hopkinson bar technique allows for the measurement of the compacting stresses during one impact. In fact, the measurement device allows to measure the stress/time response of the material during each shock independently. In particular, the study is focused on the analysis of the stress/time curve during the first shock on the freshly-mixed concrete specimen. It happens that the stress response exhibits the occurrence of the equivalent of a phase change for the granular material. It is therefore possible to measure at what moment this phenomenon happens. Then, we show that, considering a model of shock front for the propagation of the compacting wave, the phase change occurs at a density that depends on the impact velocity. The results shows that the increase of the impact velocity leads to an increase of the phase change density.

INTRODUCTION

Prefabricated concrete products are widely used in the world and have an important economic interest. They are generally processed by moulding from semi-liquid soft fresh concrete. During the moulding process, the fresh concrete undergoes a compaction up to 60% in order to obtain a good strength of the final products. This compaction is generally performed by a combined action of a compression and an assisting vibration [START_REF] Cusens | The influence of amplitude and frequency in the compaction of concrete by table vibration[END_REF]. But in fact, the vibrating system in the industrial manufacturing process in Europe generates successive strikes on the mould containing the products [START_REF] Pattofatto | Comportement dynamique du béton frais. Application au procédé de fabrication des parpaings[END_REF][START_REF] Decroix | Comportement rhéologique des mortiers et bétons frais vibrés : construction d'un modèle et optimization des compositions[END_REF]. As a consequence, one point of view is to consider the forming process as a series of independent impulsive low velocity impacts, which is complementary to a smooth sinusoidal vibration assumption. For this purpose, a shock test based on the Hopkinson bar technology has been developed.

Former results of application of this tests showed the global efficiency of successive impacts compared to a quasi-static compacting process [START_REF] Pattofatto | Experimental analysis of fresh concrete under dynamic loading[END_REF]. The study presented here is focused on what happens during one impact, and in particular during the first impact. In a first section, the studied material and the experimental device are presented. In a second section, the experimental measurements performed during each successive shock are given. The results show that the material undergoes somehow a phase change. Thus, a modeling of the compacting process is given, based on a shock theory and finally the dependency of the densification density versus impact velocity is stated and discussed.

DESCRIPTION OF THE TEST

Material

The studied material is a particular fresh concrete for industrial use, which formulation is the following (in wt% of dry material): granulates 35%, sand 57.3%, cement 7.7% and water 7.3%. The granular phase (aggregates and sand) is polydisperse: grain sizes range from 0 to 6 mm. All the grains are dried at the ambient atmosphere before mixing during 2 min. The material is introduced into the mould in a "rain" way. During the test, the specimen of fresh concrete is cylindrical, of constant diameter 62 mm, and initial height 200 mm. The initial density of the specimen is about 1450 kg/m 3 .

Experimental device

Hopkinson bar measurement technology was introduced by Hopkinson [START_REF] Hopkinson | A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets[END_REF] and applied to material testing by Kolsky [START_REF] Kolsky | An investigation of the mechanical properties of materials at very high rates of loading[END_REF]. Generally used in order to test solid materials, it also serves for soils studies [START_REF] Semblat | 3D-Hopkinson bar: new experiments for dynamic testing on soils[END_REF].

The device is a vertical nylon Hopkinson bar apparatus that was described and validated in a former paper by the authors [START_REF] Pattofatto | Experimental analysis of fresh concrete under dynamic loading[END_REF]. The configuration of the test is depicted in figure 1. The test consists in dropping several times the impact bar onto the specimen in order to compact it (see figure 2). Fresh concrete is introduced in a vessel fixed to the structure so that it is directly crushed between the impact bar and the transmitter bar during one test. The measurements given by the bars allow to determine, during the whole shock length, stress and velocity at the interfaces specimen/bars. The fact that the measurement is performed on both sides of the specimen allows to measure the time for the compression wave to travel across the specimen. Regarding the processing of the measured signals, a shift is applied in order to determine the values at the interface. In fact, the duration of the compaction is longer than the measuring capacity of the bars when a classical processing is performed [START_REF] Davies | The dynamic compression testing of solids by the method of the split Hopkinson pressure bar[END_REF]. Then a special shift algorithm is applied to extend the measuring time of the bars [START_REF] Zhao | A new method for the separation of waves. Application to the SHPB technique for an unlimited duration of measurement[END_REF].

The configuration of this experiment can be viewed as a reproduction of the "Proctor" compaction tests used classically in soils mechanics [START_REF] Proctor | First of four articles on the design and construction of rolled-earth dams. Fundamental principles of soil compaction[END_REF]. In this test, the only measurements are the energy of the falling mass performing the compaction and the resulting apparent density of the specimen. In our experiment, the Hopkinson bar give additional stress measurements.

RESULTS AND DISCUSSION

Experimental results

The basic measurement is the variation of the apparent density following an impact. It is the measurement of the apparatus considered as a pseudo-Proctor test. The main noticeable result is that 55% of the total compaction is achieved during the first impact. For every following impact, the increase in apparent density is less than 6%. The additional results given by the Hopkinson bars are the following. Figure 3 shows the stress response measured on both sides of the specimen for the first impact. The stress is calculated as the nominal stress, the cross-section of the specimen remaining constant. Figure 4 shows the measurements but during the fifth impact of the series applied on the same specimen. It is mentioned that the analysis given about figure 4 is also applicable to every result measured from impacts 2 and next.

The comparison of the figures 3 and 4 shows that the first impact is qualitatively different from the others:

the stress level is at least 3 times lower, the impact duration is at least 3 times higher, the impact chronology is different: a large plateau of almost zero stress, then a sharp increase and thenafter the unloading. For the others, there are two successive sharp loadings before the unloading, the sharp increase of the stress occurs first on the transmitter bar and then on the impact bar, whereas for the other impacts is it the contrary.

Discussion

The observations are explained by assuming that the material undergoes, during the first impact, somehow a phase change. In fact, it is considered that before the sharp increase of the stress, shown in figure 1, the material behaves like a highly compressible fluid-like material. It is relevant because the freshly-mixed material is very loose and has almost no cohesion. After the sharp increase, the material behaves like a weakly compressible solid-like material. The transition between the two states is considered to be a phase change. This assumption is linked to a phase transition classically observed in model granular materials [START_REF] Metcalfe | Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials[END_REF].

Experimentally, we observe that this phase change occurs during the first impact. This justifies the fact that the stress response is different between the first impact and all the others. Supposed explanations can therefore explain all the observations made in section 3.1, and in particular the fact that the sharp increase of the stress happens on one hand on the impact bar first and on the other on the transmitter bar first:

the plateau at almost zero stress must correspond to the propagation of the phase change in the height of the specimen. The stress is almost zero because the initial cohesion of the material is very low and when the first layer of the specimen has turned to solid, it is locked and the following layer is being compacted (figure 5). This phenomenon can be modelled by a shock front theory that is given in next section, when the shock front arrives at the interface with the transmitter bar, there is the sharp increase of the stress at this interface. The reflected wave travels across the speicmen and induces the sharp increase on the impact bar some time later, for other impacts, the material has a solid-like behaviour and the expected stress response is: the creation of a compression wave by the impact bar, shown by the increase of the stress at this interface. Then this wave propagates into the specimen and arrives at the transmitter bar with an increase of the stress some time later. The second loading phase is due to the reflected wave.

Shock modelling

Contrary to a classical device, the measurement of the stress history during the first impact allows to observe somehow a phase change and to propose a compaction process. We supposed, in former section, that the phase change of the material propagates into the specimen as a plane shock front in the sense that there is a moving discontinuity of the state of the material. The mean celerity of this discontinuity can be calculated from the duration for the shock front to travel across the specimen, depicted by the plateau length in figure 3.

It is supposed in this modelling that the material has a RPPL (rigid perfectly plastic locking) behaviour [START_REF] Reid | Dynamic uniaxial crushing of wood[END_REF]. It is consistant with the strenghtening behaviour of the material measured during a quasi- static compression test (strain rate of 1 mm/s), depicted in figure 6. The locking density D , corresponds to the phase change mentionned in section 3.1.

The mass conservation at the shock front is written :

D (V i -C s ) = -0 C s (1)
where V i is the impact velocity, C s the celerity of the shock front and 0 the initial apparent density.

In this case we can calculate the expression of the celerity of the shock front :

C s = D D -0 V i (2)
It is supposed that D is actually the unknown and that it is calculated from the measuremement of the shock front celerity C s . The value of the celerity is a mean calculated by dividing the height before the impact by the time when occurs the sharp increase of the stress on the transmitter bar (e.g. it is about 16 ms in figure 1). The locking densities are calculated for different first impacts performed at different impact velocities. The results are shown in figure 7. It is noted that the order of magnitude of the density is relevant with the compression test shown in figure 6. The results show that the increase of the impact velocity tends to increase the density of the phase change of the material.

CONCLUSIONS

A new Hopkinson bar method is presented. It is applied to the study of the compacting behaviour of a fresh concrete. In addition to a classical compaction test such as Proctor test, this apparatus allows to measure the stress response of the material submitted to an impact. In particular, it allows to detect the occurence of a somehow phase change. An explanation of the observations is given and leads to a shock front model for the compaction process during the first impact. This model allows to calculate the effect of the impact velocity on the phase change density of the material.

Figure 1 .

 1 Figure 1. Experimental device.

Figure 2 .

 2 Figure 2. Procedure for one test.

Figure 3 .

 3 Figure 3. Stress measurements for the first impact.Figure 4. Stress measurements for the fifth impact on the same specimen.

Figure 4 .

 4 Figure 3. Stress measurements for the first impact.Figure 4. Stress measurements for the fifth impact on the same specimen.

Figure 5 .

 5 Figure 5. Supposed compaction process during the first impact.

Figure 6 .

 6 Figure 6. The RPPL model and a quasi-static compression test result.

Figure 7 .

 7 Figure 7. Effect of the impact velocity on the calculated density of phase change.