Optimal Sample Rate for Wireless Sensor Actuator Network

Transcription

1 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 Optimal Sample Rate or Wireless Sensor Atuator Network Amir M Jaari and Walter Lang Abstrat In order to implement a wireless sensor network in proess automation appliations, it is needed to speiy the sample rate or the sensors. Beause o the hardware and power supply limitations, wireless sensors are applied to disrete event ontrol system. In wireless sensor network the highest sample number is restrited in omparison to the wired network. Moreover, the lowest sample number is also onstrained by the limitations imposed by the ontrol limits values. In this paper, relations between sample number and atuator s requeny drit in disrete domain is ormulated and presented. The entral and autonomous wireless sensor network strutures are introdued. In addition, ways to ompromise the sample number with the atuator s requeny and ontrol limits value are aknowledged. One approah to ind the optimal sample rate or eah network struture is proposed. It is shown when the sensor network beomes larger, autonomous network an partly ompensate ommuniation number and energy onsumption inrease by adding the sample number whereas entral network does not support this eature. Index Terms Autonomous Network, Central Network, Sample Number, Wireless Sensor Atuator Network (WSAN. I. INTRODUCTION Implementation o wireless sensor network (WSAN in automation proess appliations is one o the steps or establishing autonomous logisti systems [2]. WSAN implementation in industrial automation systems suh as Heating, Ventilation and Air Conditioning system (HVAC is a researh subjet [][3]. In order to implement WSAN in an automation proess appliation, two strutures are onsidered: Central struture and Autonomous struture. In a Central Network, the sensors measure the environmental parameters and send their data to the enter o the network. In the enter the ontrol tasks are loated. The Center proesses the data and perorms the ontrol tasks. Aterwards the instrution will be sent to atuators. None o the network nodes i.e. sensor or atuator do not have any possibility to make deision. They are just subordinate to enter or another one in hierarhial struture and ollow the instrutions [8][7]. In suh onventional struture the data ollow is rom sensor to the enter or rom the enter to the atuator. In Fig., it is shown that whih part o system model reside inside the enter. Set point + - Plaed in Center Atuator Sensor System Plaed in Sensor Output Figure : Controller o the system reside in enter One o the limitations with the entral network is salability. When the network size in terms o nodes numbers and appliations inreases, the system an be divided to the subsystems and eah subsystem has its own enter whih is responsible or loal deisions. In suh oniguration the deision whih requires the inormation rom dierent subsystems is made in system s enter (supreme enter whih loates over the subsystems. In omparison to one entral system in suh distributed struture, the enter o the system devolves sum o its tasks and authority to the subsystems [9][], but the point is that either in eah subsystem or in whole system there is a enter. Versus the entral struture, autonomous struture is onsidered as alternative. In [] and [2] two advantages o lower energy onsumption and more robustness are derived or the autonomous network. This paper oers a method or inding optimal sample number. Moreover it shows that how the autonomous network is apable to ope with salability in omparison to the entral network. Autonomous network an be deined as a network in whih every node makes deision or itsel and it does not aept the authority o other nodes [7][8][9][]. In terms o authority they are in the same level. A enter does not exist in autonomous network [7][9][8]. Eah node share its own inormation with the others without restrition, thereore eah o them has aess to the inormation o the others to make its own deision [7] [8]. Versus Hierarhy or entral network, this struture is alled Heterarhy [7] [8]. In this struture the routing algorithm should be target-oriented. In a entral network eah sensor sends its measured parameters on eah sample time periodially, but in autonomous network the sensor makes deision when it M.S Amir M Jaari is with the Institute or Mirosensors, -atuators and -systems (IMSAS at the university o Bremen, Bibliothekstrasse, - D Bremen Germany, (phone: +49 ( ; ax: +49 ( ; jerey@imsas.uni-bremen.de. Pro. Dr. Ing Walter Lang is the proessor and head o the Institute or Mirosensors, -atuators and -systems (IMSAS at the University o Bremen, Bibliothekstrasse, - D Bremen Germany ( wlang@imsas.uni-bremen.de. Set point + Atuator System Measurement Figure 2: On-o ontrol system model Output (Advane online publiation: 9 November 29

2 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 should send the inormation to its orrespondent atuator. For example in On-o ontrol method, the sensor ompare the measured parameter with the limits value when it goes over them it sends a message to the its orrespondent atuator. In this term the sensors are autonomous entity. Based on the sent data rom sensor and by heking other parameters, the atuators make their own deision [7]. In at the ontrol tasks are perormed by the atuators. In this sense atuators are autonomous entity as well. In Fig. 2, it is shown that whih part o the ontrol system is loated where. In this paper, WSAN onsists o nodes equipped with a wireless transeiver (CC242, a tiny event driven miroontroller rom MSP 43 amily and batteries or power supply. Tmote sky rom Moteiv [4] is taken as sample o suh nodes. The wireless transeiver is IEEE standard ompliant and its radio range is limited; thereore mesh topology is applied or establishing the network. Beause o the hardware and power supply limitations, wireless nodes are not suitable or ontinuous ontrol systems. WSAN is preerably used or On-o ontrol system. In this appliation, two arbitrary limit values around the desired set-point are onsidered. When the system output is going to beome greater than the upper limit value the atuator is turned o and when it is going to beome less than the lower limit value, the atuator is turned on. Fig. 2 shows a model or suh system. The question is what the sampling requeny should be or reading the output by sensor. The sampling theorem [5] (Nyquist requeny riteria [6] annot be applied here beause the relay is not a linear element and output is broken on the limits; thereore the output signal is not ontinuous while the sampling theorem works with ontinuous signal. On the other hand sampling theorem does not oer any limitation rom above or sample requeny while we will see that it is needed or WSAN. In a ontinuous ontrol system the system output value is ontinuously ompared with the limits and the instrution is sent to the atuator instantly. In a disrete domain, the sample is taken rom output at eah sample time. The deision or the atuator is made by omparing the sample values with the limits. In disrete domain an likely go over the limit values. Suppose that a sample is taken just beore the limits, the atuator status will not hange until the next sample time. During this time the output goes beyond the limits, whih auses inauray and we all it error. In order to stay inside the ontinuous time limits interval and avoid suh errors, the new limits are deined in a disrete domain. These limits in disrete domain are inside the ontinuous time limits interval. Sine the atuator s requeny is a untion o the limits band width, it hanges with the new limits value. This way the sampling number is related to the atuator s requeny in disrete domain. In setion II, omputation shows how the disrete limits value aused the atuator s requeny drit. In the next setion the mathematial relation o atuator s requeny drit in disrete domain, sample number and limits values is ormulated or a irst order linear time invariant (LTI system. The behavior o the atuator requenies or various sample numbers and limits interval is depited. In order to redue the atuator requeny drit, sample Figure 3: Sample system step response numbers an be inreased. On the other hand higher sample numbers in entral and autonomous network auses more omputation or node s miroontroller and partiularly in entral network higher message transmission number whih onsequently results in more omputation and transmission energy onsumption. These onsiderations imply upper limit or the sample number whereas in wired network, the sample number an be inreased high enough. Now the question is what is the optimum sampling requeny? An approah to a tradeo between the sample number and energy onsumption or message transmission number is oered in the third setion. II. SAMPLE FREQUENCY CALCULATION It is assumed that the transer untion o the system in Fig. 2 is irst order and its Laplae transorm is represented by H(s whih is expressed in (. The step response o this system with T n 36 s is depited in Fig. 3. The set point value is assumed to be Y and the limit values are Y h and Y l with equal distanes rom Y. The On-o relay is implemented in the ontrol loop (Fig. 2. Fig. 4 shows the system step response or Y h.7 and Y l.5 or ten hours. The atuator On-o requeny in a ontinuous domain is alulated by (2. Figure 4: Control system with relay (Advane online publiation: 9 November 29

3 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 H ( s ( Tn s + ( t Yh ( Yl Tn ln( Y ( Y t3 l Equation (3 shows the reursive equation in a disrete domain when H(s is mapped to the z-plane with sample time T s and a normalized output. In this equation N is the sample number during T whih is equal to inverse o omputed in (2. T s is the sampling period ( s sampling requeny and is deined in (2. y( n ( exp( Ts Tn + exp( Ts Tn y( n T N Ts (3 s N ( N n y( n ( exp( N + exp( N y( n Assuming that the last sampling ours just beore the limit values; then the system output goes beyond the limit values up to the next sample time. This inident is ounted as an error. In order to avoid suh errors the new limit values are deined or disrete time system. These new values are equal to the samples o the output value on one sample period time beore the limits Y h and Y l. These limits are alled Y hd and Y ld in (4. Considering this deinition by lower sample number (Y h - Y hd beomes greater; onsequently the limits interval (Y hd - Y ld beomes smaller. Smaller limit intervals lead to a greater atuator s requeny d. In other words, by moving to disrete domain with a low sample rate, atuator s requeny inreases and we have to deal with the atuator s requeny drit. Y Y hd ld ( Y Y l h + exp( exp( h n exp( Sine Y hd should always be greater than Y ld, a boundary limit exists or sampling number N whih is deined in (5. This is our irst riteria or hoosing sampling number. As (4 (2 an example or Y h.7 and Y l.5, N should be stritly greater than 3 ( s 4*. In Fig. 5 the digitized output or the above system with N2 is depited. The time axis is or ten hours. In omparison with Fig. 4 it an be seen that the atuator s state hanges 2 perent more than its value in a ontinuous domain o the ontrol system. N > ln( + Y l Y (5 ( h In autonomous WSAN when the system output reahes its limits, sensor sends a message to the atuators. In Fig. 5 it an be seen that the number o message transmissions is double the number o the atuator s status hanges (i.e. one message or on-o and one message or o-on transient states. It denotes that the message transmission number is proportional to the atuator s requeny. Sine redution o the sample number dereases the disrete limit intervals and it leads to ampliying the atuator requeny, onsequently the number o message transmissions inreases. By raising the sample number, the miroontroller oupany and energy onsumption inreases too. This phenomenon auses losing more messages during the routing o other sensor s messages in addition to inreasing the proess energy onsumption. Thereore the sample number should be ompromised in a way that it is neither very small that auses the inrease in the atuator s requeny and message transmission nor so large that the miroontroller beomes too oupied and the proess energy onsumption inreases highly. This proess is disusses in the next setion. In a entral WSAN, sensor sends message to the enter at eah sample time (Fig. 5. Inreasing the sample number, raises the message transmissions number diretly whih auses more transmission energy onsumption and high network trai. Moreover high requeny is not beneiial or atuator s lie time as well. Redution o the sample number leads to the rising o atuator s requeny whih means the enter should send more messages to the atuator. Inreasing the sample number in entral network auses more transmission energy while in autonomous network it leads to more proess energy onsumption. In addition proess energy onsumption is muh smaller than transmission energy onsumption. Thereore sample number in an autonomous network an be greater than its value in a entral network whih implies that with the same energy onsumption, lower atuator requeny and better ontrol quality an be ahieved with autonomous oniguration. Δ ( Y ln( h ( d + exp( (exp( Y Y ( Y l h l (6 Figure 5: Digitized system output The normalized dierene between atuator s requenies in ontinuous and disrete domain is shown in (6. By this equation the sample number and atuator s requeny an be optimized. The graph o (6 is depited or Y h.7, Y l.5 and T n 36 s in Fig. 6. It is omputed by (5 that or these values, N must be greater than 3. For N4 the atuator s requeny inreases to 6.67 times (667 perent o its requeny in ontinuous domain (Fig. 6. As it is mentioned in the previous setion it indiates that 6 times (Advane online publiation: 9 November 29

4 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 Center r hops Sensor s hops Atuator Figure 8: Central network struture that by hanging the limit values to maximum possible numbers, the atuator s requeny diers about 5 perent. On the other hand, or small N, inreasing the interval does not neessarily lead to a lower requeny dierene. Utilizing (7 oers the trade o option between three parameters: ontrol limits, atuator s requeny and sampling number. Figure 6: A sample o atuator requeny ratio more instrution messages should be sent to the atuator to turn on or o. This osillation is not reasonable or atuator either. Thereore by inreasing the sample number to 2, the atuator s requeny drit is about 2 perent whih ould be more aeptable onsidering the proess and 667 perent with pervious sample number. By inreasing sample number rom N3 to N5, the atuator s requeny dereases just about 6.5% implying 66.66% inrease o proess energy onsumption, 66.66% inrease o the node s miroontroller oupany in autonomous network and the same perent inrease o message transmission in entral network. This inrease (rom N3 to N5 sounds not very helpul. In the next setion, Equation 6 shows that the sample number is ompromised with atuator osillation whih is proportional to message transmission number. Now, we assume that we have a ontrol task with no restrition in the limit values, so that the set point Y is given and we know that the upper and lower limits have to be in equal distane rom Y in the ontinuous domain. Rewriting (6 results (7. In these equations by hoosing two arbitrary parameters, the third parameter an be omputed. For example i 2 samples number (N2 and maximum 2 perent atuator s requeny drit (( /.2 is aeptable or the sensor and atuator, Y would be.8. Fig. 7 is derived rom (7 with Y.7. This igure shows Δ ( d (7 ( Y + Δy + exp( (exp( Y + Δy ln( ( Y Δy ( Y Δy ln((( Y + Δy ( Y + Δy (( Y + Δy ( Y Δy III. SAMPLE NUMBER SELECTION In entral and autonomous networks, message transmission number is related to the sample number and atuator requeny. The sample number an be seleted in ompromise with the transmission number in entral network and energy onsumption in autonomous network. A. Central Network For entral network, the ommuniation path like Fig. 8 is onsidered. In the network shown in Fig. 8 the sensor measures the environment parameter in eah sample time and sends it to the enter through r hops. The enter heks the sensor value; i it is greater than the upper limit value it sends a message to the atuator to turn it on. When the reeived sensor value is less than the lower limit, it sends a message to turn the atuator o. In Fig. 8 with the sample number o N, the number o Figure 7: A sample o atuator requeny ratio Figure 9: Number o message transmission orresponding to eah sample number in entral struture o Fig. 8. (Advane online publiation: 9 November 29

5 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 Sensor r hops Atuator Figure : Autonomous network struture Figure : Number o message transmissions orresponding to eah sample number with dierent hops number rom enter to atuator in entral struture o Fig. 8. message transmissions rom the sensor to the enter during time T is equal to T/T s r ((T N/T r. At the same time interval T, the number o instrution message transmissions rom the enter to the atuator is equal to (T/T d 2 s (T (p(n+/t 2 s. By adding these two values the total number o transmissions in unit time is equal to (8. g ( N, r, s ( N r + ( p( N + 2 s (8 The graph o (8 with rs is given in Fig. 9 with the system parameters o the pervious setion. The untion is minimum at N6. Considering the minimum o the transmission numbers, the best sample number is equal to 6 onerning to T n & Y h & Y l. It indiates that the sample should be taken at every T s T / N 58 s. We assume that the message rom the enter to the sensor passes through s hops. In Fig. it an be seen that the number o transmissions inreases and table shows that or s rom to, the N orresponding to the minimum transmission number inreases as well. Suppose that s and sample number orresponding to the minimum number o transmissions is 6. Now we inrease the number o hops to (s, with N6 the transmission number per unit Table : Sample number orresponding to hops number rom enter to atuator Minimum s Table 2: Sample number orresponding to hops number rom sensor to enter N r Minimum g N g time is g(6,,.884 and the ratio o g(6,, to g(6,, is about 4.9 whereas with sample number orresponding to the minimum transmission number this ratio hanges to g(2,, / g(6,, These two ratios omparison shows that by hanging the sample number to 2, the message transmission number is redued about 27 perent. It means adding intermediate nodes between the enter and atuator leads to the energy onsumption inrease whih is partly ompensated by inreasing the sample number. This is an advantage o inding the sample number orresponding to the minimum o equation g(n,r,s. From another angle we hold the s and start to inrease r one unit at a time. Table 2 shows that when the number o hops inreases, N does not hange signiiantly in order to ompensate the inrease in the number o hops. N should be redued but its value is limited by (5. This laim an be veriied by inequality 9. In this inequality the right side shows the ratio o message transmission inrease when the number o hops between the sensor and the enter inreases. The let side represents the message transmission inrease when the number o hops between the atuator and the enter inreases. From this observation and omparison o Fig. &, it is onluded that in entral network it is more eiient to hoose the enter loser to the sensor than the atuator. Pratially it is more eetive to onsider that the enter should be loser to the node with higher loads to deliver. In ontinuane, i we take r (sensor instead o enter, the result is still valid. This network with r is the same as an autonomous network. It implies that when the number o hops inreases, the autonomous network has less transmission number and onsequently works better. [ ( 5,, g(6,, ] > [ g(2,, g(6,, ] 5.25 > g (9 Finally, i there are r hops rom the sensor to the enter and s hops rom the enter to the atuator, the proper sample number is where g is minimal. As an example or r3 and s7, N orresponding to the minimum g is equal to 8. B. Autonomous network For autonomous network we onsider the ommuniation path like Fig.. The sensor in this igure measures the environment parameter at eah sample time. Then the sensor ompares it with the limit values; i it is greater than the upper limit, the sensor sends a message to the atuator e.g. on and when it is less than the lower limit, the sensor sends a message to the atuator e.g. on. In this paper it is assumed that the average o the proess energy or taking a sample or inding the next node by routing algorithm is ixed and it is onsidered as the unit or energy onsumption measurement. Another assumption is that the transmission energy rom one node to another is equal to e times o proess energy (energy onsumption unit. (Advane online publiation: 9 November 29

6 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 number. Obviously with dierent e, Y h and Y l sample number will hange. Considering these onditions or N, i there are other riteria as well, its value ould also be ompromised with them. For example in table 2 when r is 2, N6 but with respet to (6 and Fig. 6 the atuator requeny inreases about 5% in omparison to the ontinuous time. I this osillation is not aeptable as a riterion, N an be inreased to 8 and atuator s requeny drit redues to about 8%. Figure2: Number o message transmissions orresponding to eah sample number with dierent number o hops rom the sensor to the enter in entral struture. h ( N, r ( p( N + 2 r ( In Fig. 2 the number o transmissions or N in time T is equal to (T/T d 2 r (T (p(n+/t 2 r and in unit time it is equal to the untion h in ( (h(n,rg(n,,r. As N inreases rom Ni to Ni+, p(n or the atuator requeny drit with respet to Fig. 6 dereases. This redution auses the redution o h, the message transmission number. Equation ormulates the redution o the transmission numbers whih is equivalent to h*e o the proess energy onsumption redution. Dereasing o transmission numbers also auses redution o the proess energy or orwarding messages in intermediate nodes. We all the summation o these two energy onsumption redutions as saved energy. From another side by inreasing the N, the proess energy onsumption inreases in order to take more samples. We look at this energy onsumption inrease as ost energy. These onepts entail that by inreasing N, the transmission number dereases but N s higher limit value is also restrited. Thereore optimal N is where the saved energy is still greater than the ost energy, whih is ormulated in (2. Optimal sample number is maximum N so that the inequality 2 beomes valid. Δh i+ i h( i, r h( i +, r ( p( i p( i + 2 r Δh e + Δh Δp i+ i Table 3: Maximum N values or whih inequality o 2 is valid or dierent r. r N Δp i+ i r ( r ( i + ( i (( e + r 2 2 r > ( (2 For Y h.7, Y l.5 and T n 36 s table 3 shows N as in previous setion orresponding to eah r. For example when r2 then N5 and T s T /N 9 s is the optimum sample IV. CONCLUSIONS In this paper the entral and autonomous struture or wireless sensor atuator network is deined. The meaning and deinition o autonomous regarding to text book in politi siene, logisti and networking is briely oered. Regarding to eedbak loop model, it is shown how these two strutures an be realized and by onsidering typial sensor node it is explained that or whih kind o ontroller they an be applied. Following it is presented that the sensor s sample number seletion in WSAN or proess automation appliation is not as straightorward as ommon methods used in wired network. Sample number has impats on the atuator s requeny, number o message transmissions and sensor node s miroontroller oupany. It has been shown that atuator s requeny gets loser to its value in ontinuous domain by a higher sample number. Low sample number auses the atuator s requeny inrease and onsequently redution o atuator s lie time. Moreover, this phenomenon inreases the requirement or sending instrutions to the atuator. In a wired ontrol systems this problem an be solved by inreasing the sample number to a high enough value. But in WSAN inreasing sample number auses side problems. In autonomous WSAN, higher sample number inreases miroontroller oupany and proess energy onsumption. In entral WSAN, higher sample number leads to more message transmission energy onsumption in the nodes whih are supplied by batteries. In this paper the above onstrains are taken into aount and an approah or inding the sample number orresponding to the atuator s requeny drit is oered. In addition a tradeo tehnique between the atuator s requeny, sample number and limits value interval is introdued. For inding the optimum sample number in entral WSAN a untion is given and the optimum N is the orresponding variable to the minimum value o this untion. With the same untion it is shown that when the number o hops between nodes inreases, the autonomous network an oer less message transmission number by higher sample number and onsequently better untionality. This property o autonomous network is known as an advantage o autonomous oniguration versus salability o the network. An inequality is given or autonomous network whih states dierene between the saved and ost energy. The optimal sample number is where this dierene beomes minimal. (Advane online publiation: 9 November 29

7 IAENG International Journal o Computer Siene, 36:4, IJCS_36_4_5 REFERENCES [] Masato Yamaji, Yosuke Ishii, Tomomi Shimamura, and Shuji Yamamoto, Wireless Sensor Network or Industrial Automation, 5th International Conerene on Networked Sensing Systems, 28. Date: 7-9 June 28, pp: [2] R. Jedermann, C.Behrens, R.Laur,W. Lang, Intelligent ontainers and sensor networks, Approahes to apply autonomous ooperation on systems with limited resoures. In: Hülsmann, M.; Windt, K. (eds.: Understanding Autonomous Cooperation & Control in Logistis The Impat on Management, Inormation and Communiation and Material Flow. Springer, Berlin, 27, pp [3] Fredrik O, Erik Pramsten, Daniel Roberthson, Joakim Eriksson, Nilas Finne, Thiemo Voigt, Integrating Building Automation Systems and Wireless Sensor Networks. SICS Tehnial Report T27:4 May 27. [4] MoteivCorporation.tmote-sky-datasheet [5] Katsuhiko Ogata, Disrete-Time Control Systems, Seond edition, Prentie-Hall In, 995.pp [6] Alan V.Oppenheim, Ronald W.Shaer, John R.Buk, Disrete-Time Signal Proessing, Seond edition, Prentie-Hall In, 999. pp [7] Falko Dressler, Sel-organization in Sensor and Ator Networks, John Wiley & Sons, 27. [8] Neil A. Duie, Challenges in Design o Heterarhial Controls or Dynamis Logisti Systems, First International Conerene on Dynamis Logisti, LDIC 27, August 27, pp: [9] Preston King, Federalism and Federation, Taylor & Franis, 982. [] Daniel J.Elazar, Exploring Federalism, University o Alabama Press, 987. [] Amir M Jaari, Adam Sklorz, Walter Lang, "Energy Consumption Comparison between Autonomous and Central Wireless Sensor Network, In: "Communiations o SIWN", ISSN: (Print ISSN: (CD-ROM Vol. 6, April 29, Page(s: [2] Amir M Jaari, Dirk Hentshel, Walter Lang, Robustness in Autonomous and Central Wireless Sensor Network: The Orhard Example, In: The Fourth International Conerene on Systems and Networks Communiations (ICSNC 29, September 2-25, 29 - Porto, Portugal, (in press. (Advane online publiation: 9 November 29