NETWORKED CONTROL SYSTEM: THEORY AND SIMULATIONS. A Project by. Sandeep Bimali

Transcription

1 NETWORKED CONTROL SYSTEM: THEORY AND SIMULATIONS A Project by Sandeep Bimali Bacelor s Degree in Electronics Engineering, Tribvani University, Nepal December 21 Sbmitted to te Department of Electrical and Compter Engineering and te faclty of te Gradate Scool of Wicita State University in partial flfillment of te reqirements for te degree of Master of Science December 25

2 NETWORKED CONTROL SYSTEM: THEORY AND SIMULATIONS I ave examined te final copy of tis Project for form and content and recommend tat it be accepted in partial flfillment of te reqirement for te degree of Master of Science, wit a major in Electrical Engineering Dr Jon M Watkins, Committee Cair We ave read tis project And recommend its acceptance: Dr Steven R Skinner, Committee Member Dr Coskn Cetinkaya, Committee Member ii

3 ACKNOWLEDGEMENTS I wold like to express my tanks to my project advisor, Dr Jon M Watkins, for is gidance and continos spport trogot te project work He as been a continal sorce of information and fres ideas in te process of completing tis project I wold also like to tank Dr Steven R Skinner and Dr Coskn Cetinkaya for reviewing my project and serving on my project committee A big tanks to my friend, Deependra Malla, wo took is personal time to review and elped me edit te project report My family and my beloved wife Megna deserve my deepest gratitde for teir constant sorce of love and encoragement trogot my stdies iii

4 TABLE OF CONTENTS CHAPTERS 1 Introdction 1 2 Backgrond 2 21 Networks and Control 2 22 State Space Models for Systems wit Delay 3 23 Fndamental Isses in Networked Control Systems 6 24 Compensation for Network Indced Delays 7 3 Simlation Framework 1 31 TreTime A Simlation Environment 1 4 Simlation Reslts Simlation Model 17 5 Conclsion 21 List of References 22 iv

5 Capter 1 Introdction Te stdy of Networked Control Systems NCSs brings togeter te istorically separate disciplines of compter networks and control teory Feedback control systems, werein te loops sed to control te beavior of a plant are closed trog a real-time commnication network, are called networked control systems Te defining featre of an NCS is tat information is excanged sing a network among control system components sensors, controller, and actator Te insertion of te commnication network in te feedback control loops makes te analysis and design of an NCS complex Conventional control teories wit many ideal assmptions, sc as syncronized control and non-delayed sensing and actation, mst be reevalated before tey can be applied to NCSs Te isses tat needs to be addressed wile designing an NCS inclde, network-indced delays tat occrs wile excanging data among devices connected to te sared medim, and packet losses, becase of te nreliable network transmission pat, were packets not only sffer transmission delays bt, even worse, can be lost dring transmission In tis project, an attempt as been made to analyze te stability of an NCS reslting from te network-indced delay sensor-to-controller delay and controller-toactator delay A simple compensation sceme as been proposed to minimize its effect For tis prpose, I ave sed TreTime, a Matlab toolbox for simlation of distribted real-time control systems 1

6 Capter 2 Backgrond 21 Networks and Control Network control systems NCSs combine two engineering fields, control and compter networks Compter networks can be wired or wireless Becase NCSs are implemented over a network, a good nderstanding of nderlying commnication network protocols, sc as Eternet, Token Bs or Token Ring is reqired to analyze and model te system s beavior Te International Organization for Standardization ISO as created a reference model for compters in a network to commnicate wit eac oter, called Open System Interconnection OSI Te OSI model is te primary arcitectral model for networks It describes ow data and network information are transmitted from an application on one compter, trog te network media, to an application on anoter compter Te OSI reference model breaks tis approac into sever layers: te application layer, te presentation layer, te session layer, te transport layer, te network layer, te data link layer and te pysical layer from te top to te bottom respectively Media Access control MAC, wic is a sb layer of te data link layer, is responsible for te pysical transmission of data to te proper device on a local area networks LAN sing a ardware address and also andles error notification Te IEEE 82 committee as issed standards for LANs [2]: IEEE 823 Eternet, IEEE 824 token bs and IEEE 825 token bs 2

7 Eternet IEEE 823 ses carries sense mltiple access wit collision detection CSMA/CD protocol to control its commnication Te transmitting nodes terminate teir transmission after detected collisions Tey wait for a random period of time defined by an exponential back off algoritm and try to send te frames again Te token bs IEEE 824 is a token ring over a virtal ring on a coaxial cable A token is passed arond te network nodes and only te node processing te token may transmit If a node doesn t ave anyting to send, te token is passed on to te next node on te virtal ring Eac node mst know te address of its neigbors in te ring, so a special protocol is needed to notify te oter nodes of connections to, and disconnections from te ring Te token ring IEEE 825 as stations logically organized in a ring topology wit data being transmitted seqentially from one ring station to te next wit a control token circlating arond te ring controlling access Wen no station is transmitting a data frame, a special token frame circles te loop Te special token frame is repeated from station to station ntil arriving at a station tat needs to transmit te data Wen a station needs to transmit a data frame, it converts te token frame into a data frame for transmission 22 State-Space Model for Systems wit Delay Te time delay penomenon in control pats or state variables is navoidable in many pysical systems Time delays are common in networked control systems and te design of controllers for sc systems depends critically on knowledge of te delays Ignorance of te delay dring analysis and design of digital controllers may lead to 3

8 npredictable system performance For te ease of implementation, te realization of a discrete-time state space model of a system wit delay sorter and longer tan one sampling period is presented in te following section Delay Less Tan One Sampling Period Consider te linear state eqation wit inpt delayed by λ [1]: x& t = Ax t + B t λ, 1 yt = Cxt 2 were x is called te state vector, y is called te otpt vector, is called te inpt or control vector, A is te state matrix, B is te inpt matrix, and C is te otpt matrix Te general soltion to te eqation is x t = e A tt t A t x t + e τ B τ λ dτ t By sampling te system wit sampling period and assming a zero-order old on te inpt, te soltion for te state is x + = e A x + + A + τ e B τ λ dτ k=, 1, 2, 3 Since te delayed inpt signal t-λ is not piecewise constant over te sampling period interval, te delayed signal will cange dring one sampling period Te modified soltion to te eqation is x + = e A x + + λ A + τ A discrete-time state space model of te system is given by e + A + τ Bdτ + e Bdτ + λ 4

9 5 I 1 Γ + Γ Φ = + x x were = e A Φ, = Γ d e λ τ τ B A, and + + = Γ λ τ τ d e 1 B A Longer time Delay If te time delay,λ, is longer tan te sampling period,, one may receive zero, one, or more tan one control samples in a single sampling period Te analysis needs a little adaptation Decomposeλ, sc tat ' 1 λ λ + = d < ' λ were d is an integer Te analysis is modified to 1 1 d d + Γ + Γ = Φ + x x Te corresponding state-space description is I d x I I I d x + Γ Γ Φ = +

10 23 Fndamental Isses in NCSs Te basic problem in NCSs incldes network-indced delays, single-packet or mltiple-packet transmission of plant inpt and otpts, and dropping of network packets [1] and [3] Te network-indced delays in NCSs occr wen sensors, actators, and controllers excange data packet across te commnication network Tis delay can degrade te performance of control systems designed witot considering it and can even destabilize te system Categorized by te MAC algoritms, te media access protocols fall into two categories, ones tat prodces constant transmission periods and tose tat create time varying transmission periods Te algoritm sed in te IEEE 823 standard prodce time-varying transmission period, wereas te IEEE 824 standard and IEEE 825 standard yield constant transmission period Bonds for te transmission period will be needed to garantee stability of NCSs Also, depending on te MAC protocol, te delay between transmissions networked indced delay is divided into two grops, deterministic and nondeterministic If te MAC sb layer of a protocol access cannel is sing random backoff CSMA/CD, in te Eternet, for example, te delay from te protocol will be random On te oter and, te scedling protocols te IEEE 824 standard and IEEE 825 standard will give deterministic delay Tese isses were stdied in [1], [3], and [4] Oter concerns for stability of NCSs are lengt of transmitted packets and packet dropping Te nderlying protocol of te MAC sb layer in te network is te key to controlling te lengt of packets to be transmitted For example, in Eternet, te data field of te protocol is 15 bytes, so te size of transmitted packets is nlikely to affect 6

11 real-time feedback signals, wic are only few bytes eac Te information can even be lmped and transmitted in one packet Packet dropping is often an inevitable event in network data transmission despite te provision network protocols Network packet drops occasionally appen on an NCS wen tere are node failres or message collisions In real-time feedback control, data sc as sensor measrements and calclated control signals, it migt be advantageos to discard te old ntransmitted message and transmit a new packet if it becomes available In tis way, te controller always receives fres data for control calclation 24 Compensation for Network-Indced Delays Te compensation for NCSs in considered for sensor-to-controller delay, τ sc only Sensor-to-controller delay can be known wen te controller ses te sensor s data to generate te control signal, provided te sensor and controller clocks are syncronized and te message is time stamped Ts an estimator can be sed to reconstrct an approximation to te ndelayed plant state and make it available for te control calclation On te oter and, controller-to-actator delay is different, in tat te controller does not ave te information on ow long will it take te control signal to reac te actator, terefore, no exact correction can be made at te time of control calclation Feedback systems [1] are categorized as fll-state feedback or otpt feedback systems Wit fll-state feedback, te estimator compensates τ sc In te otpt feedback system, te estimator as to do bot compensation for τ sc and estimate te states of te system Tese metods are possible if te delays are measrable 7

12 Fll-state Feedback Wit fll-state feedback, te only task of te estimator is to compensate for te delay, τ sc, to acieve a more accrate plant state at te time te control signal is calclated Let a system be described as in 1 and 2 For every plant otpt, te data is time-stamped by te sensor in order to acqire te information abot crrent time delay, τ sc, k Sensor information reaces te estimator at time + τ sc,k By assming tere is no measrement noise and all states are measred, te plant information [3] at tat time is x + τ sc, k = x + τ sc, k = e A τ + sc k sc, k τ, A τ sc, k s x + e B s ds were, x + τ sc,k is te estimated state at time + τ sc,k Applying te state feedback control law to te system were δ k τ = τ sc, k + 1 sc, k Φ ~ δ = Φ δ + Γ δ K, k Aδ k Φ δ = e k Γ δ = k δ k e k, and A s + τ sc k = K x + τ sc,, k ~ x k τ sc k + 1 = Φ δ k x + τ sc, Bds k,,, k 8

13 Otpt Feedback In practice, all states of some systems are not measred Here we assme tat te otpts from te plant are te only information we know An estimator is needed to estimate te state A conventional crrent-state estimator is sed in tis stdy Witot te delay, a crrent estimator [4] is given by x k + 1 = xˆ k L c y k + 1 C xˆ k + 1, were, x ˆ k + 1 = Φ x + Γ, k + 1 = K x k + 1 and L c is te estimator gain Te estimator is calclated in two steps Te estimator state x is projected forward to te next sample, x ˆ k + 1 Ten te calclation is corrected wit te received plant otpt to give x k + 1 Wen τ sc is taken accont, te crrent estimator sceme is described by 1 Correction based on y : x = xˆ + L c y C xˆ, 2 Forward to x + τ : sc x + τ = e sc τ A sc + + τ sc A + τ sc s e B s ds, 3 Calclate te control law: + τ sc = K x + τ sc, 4 Forward to k+1 : + Aτ sc F + s xˆ k + 1 = e x + sc + e + τ sc τ B s ds 9

14 Capter 3 Simlation Frameworks Tere are many different ways to simlate te dynamics of a network control system Likewise, many packages exist to simlate te discrete events of a network system Traditional control design sing Matlab/Simlink, often disregards te temporal effects arising from te actal implementation of te controllers Presently, controllers are often implemented as tasks in a real-time kernel and commnicate wit oter nodes over a network Conseqently, te constraints of te target system, eg, limited central processing nit speed and network bandwidt mst be taken into accont at a design time For tis prpose, I ave sed TreTime, a toolbox for simlation of distribted realtime control systems TreTime makes it possible to simlate te timely beavior of realtime kernels execting controller tasks TreTime also makes it possible to simlate simple models of network protocols and teir inflence on networked control loops 31 TreTime- A simlation environment TreTime is a Matlab/Simlink-based package written by Henriksson et al, [5] wic was designed to simlate te temporal beavior of mlti-tasking real-time kernels containing controller tasks Te TreTime simlation environment offers two simlation blocks a compter block and a network block as sown in te Figre 1 1

15 Figre 1: Te TreTime block library Te blocks are variable-step, discrete, Matlab S-fnctions written in C++ Te TreTime kernel block also called Compter block exectes ser-defined tasks and interrpts andlers Te TreTime network block distribtes messages between compter nodes according to a cosen network model Bot blocks are event driven wit te exection determined bot by external and internal events Te blocks inpts are assmed to be discrete-time signals, except te signals connected to te A/D converters of te compter block, wic can be continos time Te scedle and monitors signals indicate te allocation of common resorces dring te simlation Te TreTime Kernel Block Te TreTime kernel block S-fnction simlates a compter wit a simple bt flexible real-time kernel, A/D and D/A converters, a network interface, and external 11

16 interrpt cannels Te exection of te tasks and interrpt andlers is defined by te ser-written code fnctions Te task is te main constrct in te TreTime simlation environment Tasks are sed to simlate bot periodic activities, sc as controller and I/O tasks, and aperiodic activities sc as commnication tasks and event-driven controllers An arbitrary nmber of tasks can be created to rn in te TreTime kernel Eac task is defined by a set of attribtes and a code fnction Te attribtes inclde a name, a release time, a worst-case exection time, an exection time, a priority, and a period Interrpts may be generated in two ways: externally or internally An external interrpt is associated wit one of te external interrpt cannels of te compter block Te interrpt is triggered wen te signal of te corresponding cannel canges vales Internal interrpts are associated wit timers Te corresponding interrpt is triggered wen te timer expires Wen an external or internal interrpt occrs, a ser-defined interrpt andler is scedled to serve te interrpt An interrpt andler is defined by a name, a priority and a code fnction Te code associated wit tasks and interrpt andlers is scedled and exected by te kernel as simlation progresses Te simlated exection time of eac segment is retrned by te code fnction Te TreTime Network Block Te network block is event driven and exectes wen messages enter or leave te network A message contains information abot te sending and te receiving compter 12

17 node, arbitrary ser data typically control signals, te lengt of te message and optional real-time attribtes sc as priority or a deadline In te network block it is possible to specify te transmission rate and te medim access control protocols A long message can be split into frames tat are transmitted in seqence, eac wit an additional overead Wen te simlated transmission of a message is completed, it is pt in a bffer at te receiving compter node, wic is notified by a ardware interrpt Simlation Scenario Te scenario sed for te simlation is sown in Figre 2 Continos Plant Sensor Node Actator Node Network Controller Node Distrbance Node Figre 2: Continos plant to be controlled over a network 13

18 Te sensor, actator, controller and distrbance nodes are modeled sing te TreTime kernel block and te network block is modeled sing te TreTime network block Te TreTime blocks are connected wit ordinary Simlink blocks to form a realtime control system Te time-driven sensor node contains a periodic task, wic at eac invocation samples te process and transmits te sample package to te controller node Te controller node contains an event-driven task tat is triggered eac time a sample arrives over te network from te sensor node Upon receiving te sample, te controller comptes a control signal, wic is ten sent to te event-driven actator node, were it is actated Te model also contains a distrbance node wit a periodic task generating random interfering traffic over te network Figres 3 and 4 sow te implementation of te TreTime network and te TreTime kernel block Figre 3: TreTime network block 14

19 Figre 4: TreTime kernel block A Proportional-Integral-Derivative controller or PID controller is implemented for te controller A PID controller compares a measred vale from a process wit a reference set point vale Te difference or error signal is ten processed to calclate a new vale for a maniplated process inpt Te maniplated process inpt brings te process-measred vale back to its desired set point Te PID-controller is implemented according to te following eqations If t is te control signal sent to te system, yt it s measred otpt, a PID controller as te generical form t = K 1 [ e t + T i t e t dt + T d de t ] dt were, K= Gain of te controller et = difference between set point rt set point and measred otpt yt, ie et =r t-yt T i = integration time, and T d =derivative time Te PID controller is tned by adjsting te derivative control parameters to improve te oversoot and settling time 15

20 Te derivative part is given by D t = KT d de t d t Using te backward difference rle, a discrete version of te derivative part is given as Td KTd N D = D y y, k=, 1, 2, 3 T + N T + N d were, N = gain at iger freqencies = sampling period Te controller parameters are given by d A d Td = T + N d B d KTd N = T + N d 16

21 Capter 4 Simlation Reslts 41 Simlation Model Te simlation setp is sown in Figre 5 Te TreTime blocks are connected wit ordinary continos Simlink blocks to form a real-time control system Figre 5: Simlation model Reslts In te following simlations, an Eternet-type network is assmed A 1-ms sampling interval is sed in te sensor node Te exection time of te controller is 5 17

22 ms and te ideal transmission time from one node to anoter sensor-to-controller and controller-to-actator is 15ms, giving an ideal rond-trip delay of 35ms We frter assme tat an interfering, ig-priority task is execting in te controller node wit a 7- ms period and a 3-ms exection time In te first simlation, te network bandwidt occpied by te messages generated by te interfering node is set eqal to zero Te control performance reslting from tis sitation is sown in Figre 6 Figre 6: Control Performance witot interfering network messages Next we consider a more realistic simlation were messages generated by te interfering node occpy 5% of te network bandwidt Colliding transmissions in te network will case te rond-trip delay to be even longer wit te reslting degraded control performance sown in te simlated response in Figre 7 18

23 Figre 7: Control Performance wit interfering network messages and interfering task in te controller node Te transmission of messages over te network can be seen in detail in Figre 8 Controller Node Sensor Node Network Scedle Interf Node Time [ms] Figre 8: Network Scedles sowing te allocation of common resorces A ig means sending or execting, a medim signal means waiting, and a low means idle Finally, for an attempt to cope wit te delays a simple compensation is introdced By time-stamping te messages sent from te sensor node, it is possible for te controller to determine te actal delay from sensor to controller Te total delay is estimated by adding te expected vale of te delay from controller to actator assmed to be same as from te sensor to controller Te new control signal is ten calclated 19

24 taking a mean of te set of te controller parameters calclated for different delays Figre 9 and 1 sows te control performance and network scedle sing tis compensation Figre 9: Control Performance wit delay-compensation and interfering node occpying 5% of te network bandwidt Controller Node Network Scedle Sensor Node Interf Node Time [ms] Figre 1: Network Scedles sowing te allocation of common resorces A ig means sending or execting, a medim signal means waiting, and a low means idle To compare te reslts between te two scemes, it wold be necessary to rn many simlations nder different network conditions Tis as not been done for tis stdy 2

25 Capter 5 Conclsion Tis project analyzed some of te teoretical aspects and fndamental isses in networked control system Design of controllers in networked control system critically depends on te knowledge of delays Te discrete-time state space model of a system wit delay sorter and longer tan one sampling was presented Te fndamental isse in networked control system incldes network-indced delay, ie te delay tat occrs between sensor, controller and actator wen excanging data packet across te commnication network Sensor-to-controller delay and controller-to-actator delay ave different measres Sensor-to-controller delay can be known wen te controller ses te sensor s data to generate te control signal, provided te message is time stamped Controller-to-actator delay is different; owever, in tat te controller does not know ow long it will take te control signal to reac te actator, terefore, no exact correction can be made at te time of control calclation A simlation scenario was developed sing TreTime software, wic is a Matlab/Simlink toolbox to simlate distribted real-time control systems In te simlation, te data sent from sensor to controller were time stamped tere by giving an estimate of te sensor-to-controller delay Since time stamping does not compensate controller-to-actator delay, sing different delay estimation tecniqe and algoritm to compensate tis delay will obviosly prodce even better reslts 21

26 LIST OF REFERENCES 22

27 [1] W Zang, MS Branicky, SM Pilips, Stability of Networked Control Systems, IEEE Control System Magazine, Febrary 21 [2] AS Tanenbam, Compter Networks, 3 rd ed Upper Englewood Cliffs, NJ: Prentice-Hall, 1996 [3] GC Wals, H Ye, LG Bsnell, Stability Analysis of Networked Control Systems, IEEE Transactions on Control Systems tecnology, Vol 1, No 3, May 22 [4] GC Wals, H Ye, Scedling of Networked Control Systems, IEEE Transactions on Control Systems tecnology, Vol 21, No 1, Febrary 21 [5] M Anderson, D Henriksson, A Cervin, TreTime 13-Reference Manal, Department of Atomatic Control, Lnd Institte of Tecnology, Jne 25 23