Stability Analysis of Wireless Measurement and Control System Based on Dynamic Matrix

Transcription

1 Sensors & ransducers, Vol 6, Issue, January 4, pp - Sensors & ransducers 4 by IFSA Publshng, S L Stablty Analyss of Wreless Measurement and Control System Based on Dynamc Matrx, Yongxan SONG, Kewe LI, Yuan FENG, Zjan DONG School of Electronc Engneerng, Huaha Insttute of echnology, Lanyungang, Jangsu,, Chna School of Electronc and Informaton Engneerng, Jangsu Unversty, Zhenjang, Jangsu,, Chna E-mal: soyox@6com Receved: 4 October /Accepted: 9 January 4 /Publshed: January 4 Abstract: Focus on data packet loss and tme delay problems n wreless greenhouse measurement and control system, and temperature and humdty were taken as the research objects, the model of temperature and humdty nformaton transmsson was set up by decouplng technology accordng to the characterstcs of wreless greenhouse measurement and control system Accordng to related theory of exponental stablty n network control system, the stablty condtons judgment of temperature and humdty control model was establshed, the lnear matrx nequalty that tme delay and packet loss should satsfy was obtaned when wreless measurement and control system was stable operaton he feasblty analyss of lnear matrx nequalty (LMI) was mplemented Usng LMI toolbox n MALAB, and the crtcal values of tme delay and packet loss rate were obtaned when the system was stable operaton he wreless sensor network control system smulaton model wth tme delay and packet loss was set up usng rueme toolbox he smulaton results have shown that the system was n a stable state when tme delay and packet loss rate obtaned were less than the crtcal values n wreless greenhouse sensor network measurement and control system; Wth the ncrease of tme delay and packet loss rate, and stable performance drops; When tme delay and packet loss rate obtaned were more than the crtcal values, the measurement and control system would be n a state of flux, and when t was serous, even can lead to collapse of the whole system As a result, the crtcal values determnaton of tme delay and packet loss rate provded a theoretcal bass for establshng stable greenhouse wreless sensor network (WSN) measurement and control system n practcal applcaton Copyrght 4 IFSA Publshng, S L Keywords: Lnear matrx nequalty, Packet loss rate, Decouple, Stablty, WSN Introducton Wreless sensor networks (WSN) technology s a knd of new technology that can make people obtan nformaton of measurement and control at any tme, place and envronment, t can be wdely used n natonal securty, mltary, agrcultural automaton, envronmental montorng, health care and many other felds [] Compared wth the tradtonal wred networks, WSN has characterstcs of flexble placed, easy extenson and Ad-hoc network and so on However, compared wth the tradtonal measurement and control cable network, wreless network system have much longer tme delay and much larger packet loss, as the growth of tme delay and packet loss ncreases, the performance stablty of the measurement and control system drops [6] When tme delay exceeds a certan value or packet loss Artcle number P_755

2 Sensors & ransducers, Vol 6, Issue, January 4, pp - exceeds a certan value, the system stable performance wll fell sharply, and the whole measurement and control systems may become paralyzed, as a result, t s a key problem that greenhouse WSN measurement and control system can be stable operaton In the paper, the proposed wreless greenhouse measurement and control system was modeled and analyzed, accordng to the exponental stablty theory and Lyapunov stablty crteron, and the crtcal values for system tme delay and packet loss rate were analyzed, fnally, the tme delay threshold and the crtcal value of packet loss rate were obtaned, and a theoretcal bass was provded to establsh stable greenhouse WSN measurement and control system Structure of Greenhouse Measurement and Control System Greenhouse Measurement and Control System Structure Based on Feld-Bus Greenhouse technology wdely adopted feld-bus control technology n developed countres, the greenhouse measurement and control system based on feld-bus has show Fg Each greenhouse has a collectng and a regulaton ste, data acquston subsystem composed of varous acquston stes, and envronmental regulaton subsystem composed of the regulaton stes Each subsystem connected wth control computer through feld-bus, each greenhouse node has a bus controller that receved commands from the control computer, and completed the correspondng task of each subsystem Control computer can be connected wth the remote management computer, and management computer connected wth Internet, n ths way, remote system mantenance can be carred out, but ts have hgh cost, not sutable for the faclty agrculture of large area Greenhouse Control System Structure Based on WSN Now, wth the rapd development of the greenhouse technology, and tend to be large-scale, but wreless network node transmsson dstance s lmted, cant satsfy the requrement of large greenhouse, as a result, a large greenhouse can be dvded nto a number of measurement and control area, as show Fg, each measurement area set up a base staton wth much snk nodes Each gatherng node was responsble for a measurement and control area, and formed a subnet wth sensor nodes and control nodes, subnets was relatvely ndependent, sensor nodes and control node determned ther snk node by dentfer [] Clusterng nodes, the sensor nodes and control nodes formed star network, and completed the data acquston and control of greenhouse envronment In advance, Sensor nodes were arranged n the specfed locato greenhouse, and were responsble for the acqustoformaton such as temperature and humdty, and sent nformaton collected to snk node through the wreless network Gatherng node transmtted collected the greenhouse envronment factors nformaton to the base staton through multple hops lnk way Base staton was responsble for communcatng wth each part gatherng node, a sngle greenhouse network control was mplemented by managng all gatherng nodes he montorng center was the data center of greenhouse measurement and control system, and was responsble for the control and management of the whole system In ths way, the wreless sensor network measurement and control area were connected through the base staton and snk node, and the measurement and control area were extended, large scale and partton management of greenhouse were realzed Fg Greenhouse measurement and control system based on feld-bus

3 Sensors & ransducers, Vol 6, Issue, January 4, pp - Fg Greenhouse measurement and control system based on WSN Analyss of Greenhouse WSN Measurement System wth me Delay and Data Packet Loss Compared wth the tradtonal wred control network, wreless sensor network (WSN) has the advantages of an area small, less economc spendng and so on, but large tme delay and hgh packet loss rate was also unable to avod Usually, WSN not only have tme delay phenomenon, but also have some packet loss phenomenon In the paper, greenhouse WSN measurement and control system wth tme delay and data packet loss were analyzed, and buld the mathematcal model of data transmsson, combnng Lyapunov stablty theory and exponental stablty theory, the gradually stable condton of greenhouse WSN measurement and control system wth tme delay and packet loss were obtaned, and fnally found the feasble soluton by LMI toolbox of Matlab, the bggest packet loss rate was determned n order to guarantee asymptotcally stable of system Model of Greenhouse WSN Measurement System wth me Delay and Data Packet Loss me delay and packet loss phenomeno Greenhouse WSN measurement and control system occurred manly n the wreless communcaton process that the sensor nodes transmtted samplng data to montorng center and montorng center transmtted the optmzaton control commands to control nodes [7] As a result, the whole process of greenhouse WSN measurement has show Fg u ( k) x( k ) r r uk ( ) x ( k ) Fg Model of greenhouse WSN measurement system wth tme delay and data packet loss In Fg, K and K were the network swtch, r and r were the connected probablty of network swtches K and K, respectvely, represented tme delay between sensor nodes and the montorng center n the k samplng perod; represented tme delay between montorng center and control nodes n the k samplng perod; t represented no packet loss when K = (closed) and K = (off), t represented the packet loss n respectve transmsson process; x( k ) and x ( k ) represented the output of sensor nodes and the nput of montorng center n the k 4

4 Sensors & ransducers, Vol 6, Issue, January 4, pp - samplng perod respectvely; uk ( ) and u ( k ) represented the output of montorng center and the nput of control nodes n the k samplng perod respectvely he whole greenhouse WSN measurement and control system wth packets lost has four knds of data transmsson state, e, K and K were n a connected state, x ( k ) x( k ) and u ( k) u( k), and the probablty of ths state was ˆr r r; K was close and K was open, x ( k ) x [( k ) ] and u ( k) u [( k ) ], the probablty of ths state was rˆ r ( r ) ; K was open and K was close, x ( k ) x [( k ) ] and u ( k) u( k), the probablty of ths state was rˆ ( r) r ; K and K were open, the probablty of ths state was rˆ 4 ( r ) ( r ) In order to analyze convenently, supposed that the sensor nodes were the clock drver, samplng perod was ; he montorng center and control nodes were event drven, namely, the relevant operaton was mmedately carred out when the nformaton has been receved; he packet loss rate of wreless sensor network was certan, and data transmsson was a sngle drecton; Closed loop delay of wreless sensor network (WSN) was certan, and, So, the controlled object of greenhouse WSN measurement and control system wth tme delay and packet loss was show the followng xt () Axt () Bu( t ), () where x() t R was state varables, n m u() t R was system control nput, A and B were the correspondng dmenson constant respectvely, and [, ) We put the formula () dscrete, and as show the followng x[( k ) ] x( k ) ( ) u ( k ) ( ) u [( k ) ], () where A At e, ( ) e Bdt, ( ) At e Bdt State feedback controller model was show the followng uk ( ) Kx( k), () n m where uk ( ) R was controller output, K was the controller gan, and has a correspondng dmenson When the data transmsso the greenhouse WSN measurement and control system wth tme delay and packet loss was n state (e K and K were n a connected) x ( k ) x( k ) (4) u ( k) u( k) (5) Usng (), (), (4) and (5), (6) was gve the followng x[( k) ] ( ) K ( ) x( k) x[( k ) ] ( ) K ( ) x( k) u ( k) K u[( k) ] (6) When the data transmsso the greenhouse WSN measurement and control system wth tme delay and packet loss was n state (e K was close, and K was open) u k u k ( ) [( ) ] (7) Usng (), (), (4) and (7), (8) was gve the followng x[( k) ] ( ) ( ) x( k) x[( k ) ] ( ) ( ) x( k), (8) u ( k) I u[( k) ] When the data transmsso the greenhouse WSN measurement and control system wth tme delay and packet loss was n state (e K s open, and K was close) x k x k ( ) [( ) ] (9) Usng (), (), (5) and (9), () was gve the followng x[( k) ] ( ) K ( ) x( k), x[( k ) ] I x( k) u ( k) K u[( k) ] () When the data transmsso the greenhouse WSN measurement and control system wth tme delay and packet loss was n state 4 (e K and K are open) u k u k ( ) [( ) ], () Usng (), (), (9) and (), () was gve the followng x[( k) ] ( ) ( ) x( k) x[( k ) ] I x( k) u ( k) I u[( k ) ] () 5

5 Sensors & ransducers, Vol 6, Issue, January 4, pp - herefore, the probablty of four knds of states connected wth the connectvty rate of network swtch K and K, the system stable performance changed wth the changes of r and r Analyss of Exponental Stablty Condtons n Greenhouse WSN Measurement and Control System Supposed that zk ( ) { x( k), x ( k), u [( k ) ]}, and the 4 knds of data transfer states n the greenhouse WSN measurement and control system of can be gve the followng where z[( k ) ] z( k),,,4, () ( ) K ( ) ( ) ( ) ( ) K ( ) ( ) ( ) K I ( ) ( ) I K ( ) ( ) 4 I I In order to facltate the wrtng, the x( k ) expressed wth x( k ), ( ) expressed wth, ( ) expressed wth Accordng to references [8], when V( x( k)) a V( x( k)), system exponental was stablty, and ensured that the system was asymptotcally stable L R, M R and N the symmetrc postve defnte matrces, and Lyapunov functon was r r R were chosen V( x( k)) x ( k) Lx( k) x ( k) Mx( k) u ( k ) Nu ( k ) So, when (4) was met, the ndex of the system was stablty V( x( k)) a V( x( k)) x ( k) Lx( k) x ( k) Mx( k) u ( k) Nu ( k) a x ( k) Lx( k) a x ( k) Mx( k) a u k Nu k ( ) ( ) (4) When the data transfer n greenhouse WSN measurement and control system was n state, namely, =, substtutng () and (6) nto (4), (5) was gve the followng La L L K L K MK K L K ( L N) K a M K M L LK La N (5) Accordng to the complement nature of Schur, (5) was reduced, and (6) was gve the followng a L K NK a M K K a N (6) K M K L In the same way, when the data transmsso greenhouse WSN measurement and control system was n state, namely, =, substtutng () and (8) nto (4), and after t was reduced, (7) was gve the followng a L a M ( a ) N ( ) ( ) (7) M L When the data transmsso greenhouse WSN measurement and control system was n state, namely, =, substtutng () and () nto (4), and after t was reduced, (8) was gve the followng a L M a M K K K N a N K L (8) When the data transmsso greenhouse WSN measurement and control system was n state 4, namely, = 4, substtutng () and () nto (4), and after t was reduced, (9) was gve the followng a4 L M a4 M N a N ( ) 4 L (9) herefore, accordng to the four data transmsson state n Greenhouse WSN measurement and control system and the exponental stablty theory, the matrx nequalty that can guarantee the ndex stablty of four state was obtaned, n the case of the state feedback system wth tme delay and data transfer connectvty rate r, r, (t has show Fgure ), f there was a scalar a, a,,,4 6

6 Sensors & ransducers, Vol 6, Issue, January 4, pp - and symmetrc postve defnte matrces L R, M R r r, and N R, and met (6), (7), (8), (9) and (), the system guaranteed the exponental stablty UA x CV x() t K p u( t ) x() t K u( t ) x V () a a a a a () rr r( r) ( r) r ( r)( r) 4 Bggest Network ransmsson Packet Loss Rate Analyss of System emperature and humdty were two mportant parameters n greenhouse envronment, and they were a par of strong mutual couplng factor, that s, when the temperature was adjusted, humdty easly changed, when the humdty was controlled, and wll affect the temperature too [-5] herefore, when the nformaton transfer mathematc model was bult, the couplng process must be carred out Supposed that the temperature was x () t n greenhouse, the humdty was x () t n the greenhouse, the temperature control nput n the greenhouse was u () t, the humdty control nput n greenhouse was u () t, accordng to the lterature [], temperature control structure block dagram and humdty control structure block dagram have show Fg 4 and Fg 5 In Fg 4 and Fg 5, was ar densty, C p was the constant pressure heat capacty, V was the effectve volume of greenhouse, was the lumped parameters consderng the thermodynamcs constants and ar moble and so on factors n greenhouse u () t C V p x () t s x () t Fg 4 emperature control structure block dagram u () t x () t V s x () t Fg 5 Humdty control structure block dagram So, the temperature and humdty control equaton wth tme delay and packet loss can be obtaned, as show the followng In general, UA J / mk sec, Kg/ m, Cp 6 J / ( Kg K), [,] Set, each montorng the effectve volume of gatherng node was 4 m, the samplng perod of sensor nodes was s, network nduced total delay was s, the gan of control process was, to smplfy the analyss, the wreless connectvty rate between sensor nodes and the montorng center was equal to that of montorng center and the control node, supposed that r r r 9, () s gve the followng 69 xt () xt () u( t ) 5 () We put () dscrete, and () was gve the followng x[( k ) ] x( k) ( ) u ( k) ( ) u[( k ) ], () where A e, A ( ) e Bdt, ( ) A e Bdt, and substtutng data nto t, as follows 764, ( ), 754 ( ) 5 6 Supposed that a 57, a 87, a 49, a4 595, and substtutng r r r 9,, ( ) and ( ) nto (6), (7), (8), (9) and (), the feasble solutons can be found Usng LMI toolbox n Matlab, as follows L 44 8 M 6 N K Due to L, M, N and K exsted, so the greenhouse WSN measurement and control system was exponental stablty Accordng to (6) and (), for WSN control systems wth tme delay and packet loss, when the system was stable ndex, the upper bound of maxmum allowable data r meet (4) 7

7 Sensors & ransducers, Vol 6, Issue, January 4, pp - aa aa lg lg lg, (4) r 4 r r a aa a So the bggest packet loss rate of wreless network loop crcut was 59, due to each snk node was n the parallel, so as long as wreless packet loss rate between the sensor node and the montorng center and that of between the montorng center and the control nodes were not more than 59 % n the greenhouse, and the greenhouse WSN measurement and control system was exponental stablty 4 Smulaton Analyss In vew of the above analyss of greenhouse wreless sensor network measurement and control system wth tme delay and packet loss, t was smulated usng rueme toolbox, and analyzed that the sze of tme delay and hgh and low packet loss mpacted on the stablty of the whole greenhouse wreless sensor network 4 Smulaton Platform and Archtecture Matlab smulaton platform was manly mplemented by rueme toolbox, rueme toolbox was smulaton software based on Matlab/Smulnk, the functon of the correspondng module can be realzed by Matlab language or C++ language, the smulaton model has show Fg 6 Wreless Network of the whole greenhouse measurement and control system was smulated by rueme Wreless Network module, usng rueme Kernel module to smulate the sensor nodes and control nodes n Wreless networks, usng rueme Kernel module to smulate the montorng center of the whole Wreless measurement and control system he SND port of rueme Wreless Network receved samplng nformaton packet of sensor nodes, accordng to the nternal settngs of rueme Wreless Network, the tme delay and packet loss of Wreless Network were smulated, and the processed packets were sent to the montorng center through the rev port, the packets receved n the montorng center were correspondng processed, then sent packets to the rueme Wreless Network SND port by snd port Wreless Network transmsson qualty was smulated, and sent to the control nodes through the rev port In Fg 6, DC Servo module was wreless network data transfer functon, and descrbed control of the control varables n the measurement and control system wo output dsplay module dsplayed the system data u and control output sgnal y, respectvely 4 Smulaton System and Results DC servo module was set to s 69, t was the transfer functon of controlled object, and the system equaton was gve the followng x ( t) 69 x( t) u( t) y( t) x( t) In order to ensure the rapd and stablty of the wreless network control system, PD control algorthm was adopted n montorng center, the control dscrete model was as follows uk () Pk () Dk () krk (() yk ()) adk d ( ) bd(( yk) yk ()), where d ad, NKd bd, N was the Nh d Nh d dfferental gan, h was the samplng perod, K was the proportonal gan, was dfferental constant d Fg 6 Greenhouse WSN measurement and control system smulaton model 8

8 Sensors & ransducers, Vol 6, Issue, January 4, pp - IEEE854 communcaton protocol was adopted n wreless network module, the data transmsson rate was set to 5 bts/s, mnmum data frame was set to 4 bts, the samplng perod was set to s, dfferental gan N was set to, the proportonal gan was set to, dfferental constant d was set to 5, and tme delay that sensors send data to the montorng center was set to 5 s, tme delay of montorng center processng data and make optmzaton scheme was set to 5 s, tme delay that the montorng center wll eventually sent control commands to the control node was set to s, the random packet loss of the entre wreless network was %, the nput sgnal n the montorng center was sne wave, smulaton was started n the absence of nterference, under the condton of s, the smulaton control output and samplng graphcs were show Fg 7 and Fg 8 Smulaton results shown that the wreless network packet loss rate was %, and t was unchanged, tme delay that sensors sent data to montorng center was changed and tme delay that montorng center sent control commands to control nodes was changed too, and ths wll affect control output and control nput sgnal, as the extenson of tme delay, the system shock enhanced obvously, even can lead to nstablty Stablty of the system related to samplng perod, the smaller the samplng perod was, the greater the stablty of the system was At the same tme, the data transfer rate was changed, mnmum data frame and control algorthm parameters wll affect the stablty of the system When the wreless network packet loss was 5 %, the rest parameters remaned the same, wthout nterference, the control nput and output sgnals smulaton was show Fg 9 and n Fg Fg 9 he control nput when the Packet loss rate was 5 % Fg he control output when the Packet loss rate was 5 % (dotted lne s the reference nput sgnal) he smulaton waveform had a proportonal control, and the results were show Fg and Fg Fg he control nput when the Packet loss rate was 5 % Fg 7 he control nput when the Packet loss rate was % Fg he control output when the packet loss rate was 5 % (dotted lne s the reference nput sgnal) Fg 8 he control output when the Packet loss rate was % (dotted lne s the reference nput sgnal) It can be seen from the smulaton graph, wth the ncrease of packet loss, the system oscllaton frequency wll be ncreased, and the ampltude wll be also ncreased When packet loss was more than 9

9 Sensors & ransducers, Vol 6, Issue, January 4, pp - the crtcal value, wth the passage of tme, the system overshoot volume wll be bgger and bgger, eventually, the whole system was a state of out of control 5 Conclusons In ths paper, we dscussed the stablty problem of wreless greenhouse measurement and control system Frst, the strong couplng factors of temperature and humdty were decouple, a correspondng control mathematcal model of WSN measurement and control system was establshed Secondly, the exponental stablty condtons of the temperature and humdty dscrete control system was analyzed usng the control system stablty ndex determnaton methods, Fnally, usng the LMI toolbox n Matlab, the feasblty soluton was obtaned to meet the exponental stablty n the greenhouse WSN measurement and control system, and determnes packet loss threshold when the system was not out of control Acknowledgment hs work was supported by the Prorty Academc Program Development of Jangsu Hgher Educaton Insttutons (PAPD) and Project BK98 of the Jangsu Provnce Natural Scence Foundaton References [] L Ke-We, Zhang Rong-Bao, Xe Zh-Chao, Stablty analyss of tme-delay of WSNs measurement and control system, ransducer and Mcrosystem echnologes, Vol 8, Issue 6, 9, pp 6-8 [] Wu Junhu, Research and applcaton of low-cost greenhouse envronment control system, Dssertaton, School of Electroncs and Informaton Engneerng, ongj Unversty, Shangha, [] Ge Yang, Wang Jngcheng, Networked control system wth random delay and packet loss based on dynamc matrx, Informaton and Control, Vol 4, Issue 6,, pp [4] Yang Chunx, Guan Zhhong et al, Stablzaton of networked control systems wth wreless sensors based on tme-delay weghted fuson, Control heory & Applcaton, Vol 8, Issue,, pp [5] Zhang Rongbao, L Kewe et al, Effect of packet loss probablty of transmsson on greenhouse WSN measurement and control system, Journal of Jangsu Unversty, Vol, No 5, 9, pp 8-86 [6] J Huang, Y J Wang, S H ang, et al, Robust stablty condtons for remote SISO DMC controller etworked control systems, Journal of Process Control, Vol 9, Issue 5, 9, pp [7] Ruo Hu, Stablty Analyss of wreless sensor network servce va data stream methods, Appled Mathematcs & Informaton Scences, Vol 6, Issue,, pp [8] A Rabello, A Bhaya, Stablty of asynchronous dynamcal systems wth rate constrants and applcatons, IEEE Proceedngs on Control heory Applcaton, Vol 5, Issue 5,, pp Copyrght, Internatonal Frequency Sensor Assocaton (IFSA) Publshng S L All rghts reserved (