DESIGN AND IMPLEMENTATION OF NETWORKED PREDICTIVE CONTROL SYSTEMS. S C Chai, G P Liu and D Rees

Transcription

1 DESIGN AND IMPLEMENTATION OF NETWORKED PREDICTIVE CONTROL SYSTEMS S C Cha, G P Lu and D Rees School of Electroncs, Unversty of Glamorgan, Pontyrdd CF37 DL, UK Abstract: Ths aer dscusses the desgn and mlementaton of networked redctve control systems. A networked redctve control algorthm s roosed to comensate the network delay and acheve desred control erformance of networked control systems. Two schemes of networked control systems are resented: one s the off-lne smulaton scheme and the other s a real-tme alcaton. Based on a networked control system test rg, the networked redctve control algorthm s mlemented and aled to a ractcal servo control system. The smulaton and ractcal exerment results llustrate the effcency and feasblty of the roosed networked redctve control algorthm and smulaton schemes. Coyrght 25 IFAC Keywords: Networked control, redctve control, smulaton, mlementaton.. INTRODUCTION The tradtonal communcaton archtecture for control systems whch has been successfully mlemented n many areas for decades s a ont-toont archtecture (the controller and mlementer are at the same lace) (F. Lan, et al., 2). Wth the develoment of the nternet and the dversty of hyscal setus, tradtonal control archtecture s lmted because of ther modularty and centralsaton of control. Networked control systems (NCS) has emerged as a sgnfcant toc for research as the result of the develoment of networks and arorate control methodologes. Now, NCS can be found n manufacturng lants, arcraft, HVAC systems, automobles and many other alcatons (L. G. Bushnell, et al., 2). The man feature of NCS s the exchange, through communcaton networks, of system nformaton and control sgnals between varous hyscal comonents. So ths tye of system has the advantage of greater flexblty over tradtonal control systems, ncludng greater flexblty n dagnoss and mantenance rocedures. The studes on NCS cover very wde felds lke medum of exchange, network rotocols, network control methodologes, stablty of NCS, schedulng of networked control systems (Walsh, G.C, et al., 2). In ndustral control alcatons, there are three man buses used n NCS: the Ethernet bus, tokenassng bus (e.g., ControlNet), and controller area network (CAN) bus (e.g., DevceNet). Because of the world wde use of the Internet, the Ethernet network becomes the cheaest and wdest medum of exchangng data. Ethernet uses a smle algorthm for oeraton of the network and has almost no delay at low network loads. Very lttle communcaton bandwdth s used to gan access to the network comared wth the token bus or token rng rotocol. Ethernet used as a control network commonly works at the Mb/s standard (e.g., Modbus/TCP) and at hgh seed transmsson rates of Mb/s to GMb/s. There are two rotocols, UDP and TCP, whch are used for Ethernet networks. The UDP rotocol s a connectonless rotocol that runs on to of IP networks. Unlke TCP/IP, UDP/IP rovdes very few error recovery servces, offers a drect way to send and receve datagram over an IP network. TCP however adds suort to detect errors or lost data and to trgger retransmsson untl the data s correctly and comletely receved, whch s more tme consumng.snce UDP has two crtcal advantages over TCP, namely seed and overhead, t s the rotocol that s normally used n NCS. Although the NCS has many otental advantages over exstng technology, there exsts several control roblems. These roblems are network delay, data

2 droout, samlng and transmsson method, and they are not easy to overcome usng conventonal control methods. To solve these roblems, many methods have been adoted, such as the augmented determnstc dscrete-tme model method (Tham, M.T, et al., 22) and otmal droout comensator method (W. K. Ho,, et al., 2). But, these methods have ut some strct assumtons on NCS, e.g., the network tme delay s less than a samlng erod, or they have resulted n a soluton that s not ractcal to mlement. Lu et al(g P Lu,, et al., 24) have roosed a networked redctve control method where they have consdered the stablty of the closed-loo NCS. Ths method can be readly mlemented and actvely comensates for the network tme delay. Now there are a number of research aers on network control systems (Tham, M.T, et al., 22; W. K. Ho,, et al., 2,and (G P Lu,, et al., 24) but the majorty focus on control theory and system stablty analyss. The mlementaton asects of these methods n the man are not addressed on those aers. In ths aer we wll seek to address these shortcomngs by desgnng a controller and mlementng the control methodology wthn a network structure. Ths aer s organsed as follows: secton 2 descrbes the basc dea of the networked redctve control method; Secton 3 gves the smulaton of networked control systems. Secton 4 s the alcaton examle of the networked redctve control algorthm to a networked servo control system. Fnally, some conclusons are made. 2. NETWORKED PREDICTIVE CONTROL 2. Networked redctve control scheme The networked redctve control (NPC) scheme was roosed by Lu et al(g P Lu,, et al., 24). However n ths aer the tme delay n the feedback channel s not taken nto account or was taken as a constant value. But n realty the network delay n the feedback channel s tme-varyng rather than constant. But t s reasonable to assume that the tme delays n the forward channel and feedback channel are the same and are not changng very fast. The structure of NPC s shown n Fgure. r(t) Control Predcton Generator Network Delay Comensator Networked redctve controller Network Fg. The structure of NPCS Network Delay Comensator Outut Predctor u(t) Plant The NPC scheme manly conssts of a control redcton generator, an outut redctor and forward and feedback delay comensators. The control redcton generator s desgned to generate a set of future control seuences. The y(t) forward and feedback delay comensators are used to comensate for the unknown random network delay n the forward and feedback channel. The outut redctor s to create a set of lant outut redcton seuences. In the NPC scheme, all redctve control seuences at one tme are acked and sent to the lant sde through a network. The network delay s comensated by choosng the latest control value from the control redcton seuences that are avalable on the lant sde. For examle, f the followng redctve control seuences are receved on the lant sde: ut ( k t k) ut ( k t k) + ut ( t k) ut ( k+ N t k) () where u(t t-k) s the control redcaton for tme t at tme t-k. The outut of the forward delay comensator wll be ut () = ut ( t k) (2) whch s the latest redctve control value for tme t. Smlarly, n the feedback channel, the outut redcton seuence yt ( k t k) yt ( k t k) + yt ( t k) yt ( k+ N t k) (3) s acked and transmtted to the controller sde. So, the outut of the feedback delay comensator s yt () = yt ( t k) (4) whch s the redcton of the system outut for tme t. 2.2 Imlementaton of networked redctve control Consder a sngle-nut sngle-outut dscrete-tme lant descrbed by yt () = Gz ( ) ut ( ) (5) where the transfer functon G s Gz ( ) m Bz ( ) b + bz + + bm z = = n A( z ) + az + + anz (6) y(t) and u(t) are the outut and control nut resectvely, A and B are olynomals. The networked redctve control scheme can be mlemented n the followng stes: The frst ste s to dentfy the model of the lant to be controlled. Snce the erformance of the redctor

3 hghly deends on the model accuracy. The model must ft the lant as closely as ossble. In ths aer, t s assumed that the model s the same as the lant. The second ste s to desgn a controller for the system wthout network tme delay to satsfy the desred dynamc and statc control reurements of the system. Any conventonal and advanced control method can be used, such as PID, LQG and robust control methods etc. So, t s assumed that the controller s reresented by the followng transfer functon: L z ( ) D( z ) = = C( z ) c z c z d + dz + + d z Thus, the outut of the controller s (7) u() t = L( z )( r() t y()) t (8) where uts () the outut of the controller, rt () s the reference nut, yt () s the outut redcton of the lant The controller can be exressed by () = ( ) = ( ) + ( )() ( ) = = (9) ut ut t cut Dz rt dyt The thrd ste s to desgn the control redctor to generate redctve control seuences. The Dohantne euaton method has been wdely adoted. However that method s not easy to extend and rogram, artcularly n the case of a random network delay. Here, a recursve method wll be used. If the model s the same as the lant and there s no network tme delay, the redctve outut of the lant at tme t can be obtaned by yt () = Gz ( ) ut ( ) () So, the outut redcton for tme t+ can be exressed by n m () = = yt ( + t) = ayt ( + ) + but ( ) Based on euaton (9), the redctve outut for tme t+ can also be gven by ( + ) = ( ) ( + ) + ( ) ( + ) = 2 dyt ( + t) dyt ( + ) = ut t cut t cut Dz rt (2) Then, at tme t+ j the outut redcton and control redcton on the controller sde can be obtaned as follows: mn{ nj, } n = = j mn{ mj, } m = o = j yt ( + j t) = ayt ( + j t) ayt ( + j ) + bu( t+ j t) + bu( t+ j ) (3) mn{ j, } ( + ) = ( + ) ( + ) + ( ) ( + ) = = j+ mn{ j, } dyt ( + j t) dyt ( + j ) = = j ut j t cut j t cut j Dz rt j for < j N. (4) Summarsng the above rocedure leads to the followng mlementaton algorthm for the forward channel. () Gven yt ( ) and ut ( ), for =,, 2,. Let j=; (2) Calculate u ( t + j t) usng (2); (3) Calculate yt ( + j+ t) usng (3); (4) Set j=j+; (5) If j<=n, go back to ste (2), otherwse, sto. Clearly, the above algorthm gves [ ut t ut+ t ut+ j t ut+ N t] ( ) ( ) ( ) ( ) T (5) For the feedback channel, the mlementaton algorthm s smlar to the above. Based on gven yt ( ) and ut ( ), for =,, 2,, the followng outut redctons can be obtaned. [ yt t yt+ t yt+ j t yt+ N t] ( ) ( ) ( ) ( ) T (6) The forward and feedback delay comensators are mlemented as ut () = ut ( t k) and yt () = yt ( t k) (7) Therefore, the networked redctve control scheme can be mlemented. 3. SIMULATIONS OF NETWORKED CONTROL SYSTEMS 3. Synchronsaton of Networked Control Systems In networked control systems, one mortant ssue s the synchronzaton of the whole system. For the sake of smlcty, the followng assumtons have been made for the synchronzaton of NCS: ) The network delays n the forward channel and feedback channel are the same. 2) The network delays do not change very uckly. 3) The forward delay comensator s located on the controller board. To assess the forward and feedback delay, n order to desgn a delay comensator a measurement snusodal sgnal s transmtted over the network control system. Usng the current measure sgnal value dt (), the forward ath delay comensator can calculate one-ste, two-ste. and N-ste tme delay estmate of a measured sgnal dt ( ), dt ( 2) dt ( N). Comarng these values

4 wth the returned value of the measured sgnal whch was orgnally sent from the forward delay comensator, the total the network delay (ncludng forward and feedback channels) s calculated. The forward and feedback tme delays are then assessed to be half the total network delay. gven n Fgure 5. Clearly, the NPCS also has good control erformance for random tme delay Off-lne Smulaton An off-lne smulaton scheme s resented for the networked redctve control system, as shown n Fgure 2. Ste of tme Delay Tme(s) Fg. 4 The random tme delay seuence 6 Fg. 2 Control scheme for smulaton 4 To show the oeraton of ths scheme, an off-lne smulaton scheme was mlemented usng the followng model of a servo control system: Angle(Degree) 2-2 wthout tme delay wth changng tme delay 2.866z z Gz ( ) = 2 z.6668z (8) Two cases of the network delay are smulated: one s the constant delay and the other s the random delay. The smulaton results of the networked redctve control system for the cases of -ste, 2-ste and 3- ste constant network delay n both forward and feedback channels s shown n Fgure 3. It s clear from the results that the control erformance of the closed-loo system for those three dfferent network delays s the same. Ths means that the networked redctve control scheme can actvely comensate for the network delay wthout tme delay 2 stes tme delay 4 stes tme delay 6 stes tme delay Tme(s) Fg.3 The resonses of the closed-loo NPCS wth dfferent smulated constant network delays To smulate a random network delay, a random seuence s emloyed, whch s shown n Fgure 4. The resonses of the closed-loo NPCS wth the above random delay and wthout tme delay are Tme(s) Fg. 5 The resonses of the closed-loo NPCS wth smulated random network delay 3.3 Real-tme smulaton The real-tme smulaton s that the control rogram runs n a real-tme embedded mcrorocessor system, where the lant to be controlled s stll a mathematcal model. A real-tme smulaton scheme for the networked redctve control system s roosed, whch s shown n Fgure 6. It conssts of the controller art and the smulated lant art. network mt network Fg. 6 Block dagram of real tme smulaton For the mlementaton of the real-tme smulaton scheme, uclnux s chosen as the oeratng system of the real-tme embedded mcrorocessor system. y

5 uclnux s eued wth a full TCP/IP stack and s an nternet-ready OS for embedded systems. The networked redctve control strategy s realsed n Smulnk. The controller art and smulated lant art are desgned n two ndvdual Smulnk blocks. Then, the Real-Tme Worksho n Matlab whch generates, cross-comle and lnk rogram codes from Smulnk (MathWork, Real-Tme Worksho for Use wth smulnk. 24), s adoted to create executable codes for the controller and smulated lant arts. Fnally, these executable codes are downloaded to two real-tme embedded mcrorocessor systems whch are connected by Ethernet. For the real-tme smulaton, the lant and controller are the same as those used for the off-lne smulaton. The real-tme smulaton results of the networked redctve control system are shown n Fgure 7. Fg. 8 The networked controller board Tme(s) Fg.7 The resonses of real-tme smulaton realtme smulaton smulaton Because the network delays n the forward and feedback channels are not the same n the real network, the network delay cannot be comensated for exactly. However, NPC can stll acheve a smlar control erformance to one of NPCS wthout network delay. Fg. 9 The networked mlement board and servo control system The mlementaton board has eght 2-bt A/D nut channels and two 6-bt D/A channels. The lant to be controlled s a oston servo control system. 4.2 Practcal exerments The block dagram of the network based servo control system s shown n the Fgure. The transfer functon of ths servo control system was dentfed usng the least suares method and s gven n (8). network mt 4. APPLICATION TO A NETWORKED SERVO CONTROL SYSTEM 4. Networked control system test rg To aly the networked redctve control strategy to ractcal systems, a networked control system test rg s bult. Ths rg conssts of a networked control board (as shown n Fgure 8), networked mlement board and a servo control lant (as shown n Fgure 9). The kernel ch of the networked control and mlement boards s Samsung's S3C45B. It s a cost-effectve, hgh-erformance mcrocontroller soluton for Ethernet-based systems. The ntegrated Ethernet controller S3C45B s desgned for use n managed communcaton hubs and routers. The S3C45B can oerate at ether -Mbts or - Mbts er second n half dulex or full-dulex mode. network Fg. The networked servo control system The real networked redctve servo control system uses a PI controller, where the roortonal gan s 2.6 and the ntegraton gan s.2. For the samlng rate of.4s, the resonses of the real closed-loo networked servo control system are shown n Fgures -3.

6 Where the same PI controller as that gven above was used, and the forward and feedback delay comensators are emloyed. It s clearly seen from the exerment results that the NPC for a system wth network delay has smlar control erformance to the PI control for the system wthout network delay. Ths confrms that the NPC can comensate the network delay effectvely. 5. CONCLUSIONS Tme(s) Fg. The resonse of the system wthout network Delay The resonse of the system wthout network delay (.e., no network s used n the system) s shown n Fgure. The resonse of the networked control system wth network delay s shown n Fgure 2, where no network delay comensator s used. It shows that the networked control system has oor control erformance wth network tme delay Tme(s) Fg.2 The resonse of the PI control system wth network delay The control erformance of the networked redctve control strategy s gven n Fgure 3 angle(degree) NPC control PI control wth tme delay PI control wthout tme delay Tme(s) Ths aer has studed the desgn and mlementaton of networked redctve control systems. It has roosed a networked redctve control scheme to address the roblem of controllng a system over a network, the aer has resented both off-lne and real-tme smulaton studes, as well as a real-tme NPC mlementaton of laboratory test rgs. It has been shown that the NPC s an actve network delay comensaton method. Its ablty to comensate for the network delay has been demonstrated. REFERENCE F. Lan, J. R. Moyne, and D. M. Tlbury (2), "Performance evaluaton of control networks: Ethernet, controlnet, and devcenet," IEEE Contr. Syst. Mag., vol. 2, L. G. Bushnell (2), "Guest edtoral - Networks and control," IEEE Contr. Syst. Mag., vol. 2, Walsh, G.C. and H. Ye (2), Schedulng of networked control systems.. 2(IEEE Contr. Syst. Mag): Samsung, 45B Product Overvew MathWork, Real-Tme Worksho for Use wth smulnk Tham, M.T. (22), Internal Model Control, n Introducton to Robust Control. Chemcal and Processs Engneerng W. K. Ho, T. H. Lee, H. P. Han, and Y. Hong (2), "Self-tunng IMC-PID control wth nterval gan and hase margns assgnment," IEEE Trans. Contr. Syst. Technol., vol. 9, A. T. Bahll (983), "A smle adatve Smthredctor for controllng tme-delay systems: A tutoral," IEEE Contr. Syst. Mag., vol. 3, G P Lu, J Mu and D Rees (24) Networked redctve control of systems wth random communcaton delay, Proceedngs of the UKACC Internatonal Conference on Control, Bath, UK, ID-5. Fg. 3 Comarson of dfferent control strateges for the networked servo control system