Wireless Event-driven Networked Predictive Control Over Internet

Transcription

1 UKACC International Conference on Control 22 Cariff, UK, 3-5 September 22 Wireless Event-riven Networke Preictive Control Over Internet Wenshan Hu, Hong Zhou, an Qijun Deng Abstract In networke control systems, the network uncertainties can egrae the control performance an even result in instability, especially for the Internet-base control system with wireless communication in which the transmission elay coul be many times of the sampling perio of control systems. NPC (Networke Preictive Control) is an active metho to compensate for the effects of network uncertainty. However, control systems nee to make long time preiction ue to the long transmission istance. Without an accurate mathematical moel, the control performance can not be guarantee. In orer to aress this problem, a new NPC scheme esigne for wireless NPC with long time elay is introuce in this paper. It uses the information of the previous preiction errors to correct the future preictions. A correction algorithm is esigne to reuce the preictive errors. To valiate the new control schemes, both simulations an experiments have been conucte. The results show that even with not so accurate mathematical moels, the new schemes can still maintain goo control performance in Internet-base NPC with wireless communication. I. INTRODUCTION In the last ecae, network technology has been evelope rapily. More an more network technologies have been applie to control systems [-8]. With the emergence of high spee network technology, a cluster of evices can be linke together economically to form istribute networks. Due to the use of network, especially Internet, the complexity an costs of istribute control systems are reuce greatly an the maintenance of the systems becomes much easier [9-]. Control systems with evices from ifferent locations can be integrate together using the existing Internet infrastructure which provies a cheap solution for remote ata transmission an ata exchanges. Internet base control systems allow remote monitoring an ajustment of plants over the Internet aroun worl. Recently, wireless networke control systems become a popular research area in control theory an inustrial applications. Without reuiring network cables, evices can be connecte into networks using wireless communication, which is promising for remote inustrial controls an factory automations. For example, istribute power generation an microgris [-2] play more an more important roles in Manuscript receive September 5, 2. This work was supporte by the National Science Founation of China uner Grant 643. Wenshan Hu Hong Zhou an Qijun Deng are with Department of Automation, School of Mechanical an Power Engineering, Wuhan University, Wuhan, 4372, China ( wenshan.hu@whu.eu.cn) new energy research area. In these systems, unlike big power stations in conventional gris, small an meium sie power generation units are locate iversely. Wireless wie area networks (WWAN) such as WiMAX, CDMA, GPRS allow rapi evelopment, flexible installation, fully mobile operation which are ieally suitable for these istribute inustrial applications. The technologies of the Internet of Things are evelope rapily in recent years. The research of NCSs is a key part in Internet of Things. In the future Internet of Things, iversely locate objects an evices are connecte to Internet using both wire an wireless communication. Information such as control commans an measurement ata is transmitte through networks. In wireless networks, the ranom time elay an ata ropouts inuce by the ata transmission an traffic congestion are even worse than wire ones. These network uncertainties isturb the control performance an even result in instability. Therefore, a wireless networke preictive control systems are stuie in this paper. The networke preictive control consists of the control preiction generator an network elay compensator [3-8]. The control preictive generator provies a seuence of future control preictions an the network elay pick up the appropriate control signal from the seuence to eliminate the effects of network transmission elay. Because of the long time elay in wireless networks, the moel base preiction may not be accurate ue to the moel uncertainties. To tackle this problem, NPC is moifie an the preiction errors are correcte using the previous preictive errors in this paper. II. DESIGN OF WIRELESS WIDE AREA NPC A. Structure of Wireless Wie Area NPC Fig. is the structure of the propose Internet-base NPC with wireless communication. It can be separate into two sies: the controller sie an the plant sie. Both sies are connecte to the Internet using wireless connections. Most of the control calculations are implemente on the controller sie. It coul be a powerful mainframe computer which has the capability to serve many control loops. The tasks on the plant sie are simple. This part can be achieve using a low-cost solution with limite computing capability such as MCU or ARM embee control boar. The iagram of this kin of system is shown in Fig /2/$3. 22 IEEE 668

2 t + t + t + 2 t + 2, M M t + N t + N Fig.. Structure of Internet-base NPC Central Controller Internet t ) t ) ey (,, M M ey ( t ) t nb ) t nb ) Plant Plant 2... Plant N Fig. 2. Diagram of wireless wie area networke control systems B. Plant Moel an It is consiere that the ynamic process can be escribe by the autoregressive moving average moel as A( ) = B( ) () where an are the open loop input an output of the n a plant. A( ) R[, ] with a B( n b = an ) R[, ] with b are the system = polynomials. For the local control without network transmission elay an ata ropout, a controller is esigne as C( ) = D( ) e( (2) n c where polynomial C( ) R[, ] an c an D( n ) R[, ] an = e( = r( (3) where r ( is the reference input an y ( is the system output. C. Start of a Control Cycle In this metho, a control cycle is initiate by the plant sie rather than controller sie, which is similar to the metho in [4-5]. At each sampling perio, the previous plant output seuence, previous control seuence, previous preiction error seuence e y ( an a timestamp t which inicates the current plant sie time are packe together an sent out in a single packet to the controller sie, which initiates a control cycle. The three seuences in the packet are t ) t ) e y (,, M M e y ( t ) t nl ) t nl ) where n l =max(n a, n b, n c, n ). D. Design of Controller The controller is event riven rather than time riven. It is only when the plant sie receives the ata from the feeback channel oes the controller generates control preictions. Without receiving new ata from the plant sie, it is in an ile state. It is assume that at a time instance, the controller receives a packet from the plant sie. Insie the packet, the seuence of plant outputs y (incluing y, t ), L, t n ) ), ( a previous control seuence u (incluing u, t ), L, t n ) ) an a time stamp which inicates ( a the time at which the packet is packe an sent out. Because the controller is event-riven an the time elay compensation is base on the roun trip time elay measurement, it is note that variable t inicates the plant sie time instance at which the packet is packe an sent out. It has nothing to o with the time instance at which the controller receives the packet. Using the roun trip elay preiction, the future control seuence can be generate using the algorithm escribe below without knowing any information about the controller time at all. For the sake of simplicity of analysis, it is assume that the maximum time elay is boune within N steps. The following efines the operation on the preictions: x ( t + i = x( t + i + for (4) i =,, L (5) x( t ) = x( t (6) x( t i ) = x( t i) for i =,2, L (7) where represents x(.),.) or.), an x(t + i enotes the i-th step-ahea preiction of x( base on the previous ata up to time t. Base on the ata up to plant sie time t, an the mathematical moel of the plant, the one-step plant output preiction with moel uncertainty correction can be calculate as y ( t + = ( A( )) t + + B( ) t + ) + (8) where c m is the correction factor, an m is a counter on the controller sie. c m is calculate using the information of previous preiction errors. The initial value of m is an c m 669

3 each time the controller process a packet from the plant sie, m is increase by. The etails of the calculation of c m are introuce in Section 2.E. The corresponing one-step preiction for control signal is t + = ( C( + D( )) t + )( r( t + ) t + ) Using the same metho recursively, the future plant output preictions can be obtaine base on the ata calculate at the previous step. y ( t + k = ( A( )) t + k + B( ) t + k) + c m () where k=,2,,n. The future control preictions are t + k = ( C( + D( )) t + k )( r( t + k) t + k ) (9) () where k=,2,,n. After N-step calculations, the future control seuence U(t an future plant output Y(t are obtaine, where U ( t = [ t +, t + 2, L, t + N ] (2) Y ( t = [ t +, t + 2, L, t + N ] (3) They are packe together with the timestamp t an sent back to the plant sie. E. Calculation of Moel Uncertainty Correction Factor In conventional NPC, if the mathematical moel of the plant is not accurate enough, the control performance woul be egrae greatly. It normally results in big static errors in some practical applications. Because the preiction is not accurate ue to the moel uncertainty, the controller thought the plant ha reache the target position, so it stops the ajustment of the control signals. However, the plant oesn t follow the controller s preiction. Therefore, the static errors can not be correcte. In orer to cope with this problem, a moel uncertainty correction algorithm is introuce in this paper. Base on the history preiction error seuence obtaine from the plant sie, the controller estimates the correction values for the future preiction. The estimation metho is similar to the iea of PI control. Different from the PI control algorithm, the target of the metho is to minimie the preiction errors rather than the control resiuals. Therefore, the input is the preiction error rather than resiual. The transfer function between preiction error e y ( an the correction factor c( is T k p ( k p kit ) c( = ( k p + ki ) e( = e ( y (4) where the proportional gain k p an integral gain k i are the two parameters of the algorithm. Written in the incremental form, (4) is escribe as T T c( = ( ) c( = ( k ( k k T ) ) e ( (5) where c( is the increase of c(. p With c( calculate by using (5), the correction factor can be obtaine, c( = c( t ) + c( (6) However, ue to the stochastic nature of the Internet, the time elay is ranom. Therefore, the previous correction value c(t-) may not be available on the controller sie. In orer to simplify the analysis, the correction factor on the controller sie c m is use to replace c(. Euation (6) can be rewritten as c = c + c( ) (7) m m t Combine with (6), the moel uncertainty correction factor is obtaine as cm = cm + k pe y ( ( k p kit ) e y ( t ) (8) With the previous correction factor c m- an previous preiction errors e y ( an e y (t-) available, it is straightforwar to calculate the current correction factor c m. If the transmission elay between the plant sie an the controller is constant an there is no ata ropout, c m is eual to the corresponing c(. However, in real network environment, the packet with plant sie timestamp t may arrive earlier than the packet with timestamp t-. In that case, c m is not c( but it is close to c(. F. Design of Plant Sie The plant sie receives the packet from the controller, in which the timestamp t the control seuence U(t an plant output seuence Y(t are packe. To calculate the RTT elay, the timestamp t is picke up an compare with the current plant sie time t c t = t t (9) c where t is the RTT elay. Accoring to the time elay measurement t, the t -th value in the seuence U(t is picke up an applie to the plant actuator. t + t ) = t t (2) + Similarly, the t -th value in seuence Y(t is also picke up as the preicte plant output. yˆ ( t + t ) = t t (2) + The preicte plant output ŷ(t+t ) is then compare the real plant output t+t ). The preiction error e y (t+t ) is obtaine as e t + t ) = t + t ) yˆ( t + t ) (22) y ( The history ata of the plant output y, control signal u an preiction error e y are buffere as below p i y 67

4 ) ) 2) 2) e y ( ),, (23) M M e y ( ) nb ) nb ) These ata are packe with the current time stamp t c an sent out the controller sie, which initiates another control cycle. III. SIMULATION RESULTS In orer to valiate the propose metho, a spee control system for a cooling fan is consiere. The control system is esigne to rive a fan to the target spee. The mathematical moel is ientifie as B( ) G ( ) = = (24) A( ) where the input is the PWM uty cycle (range from to ) applie to the fan motor an the output is the voltage reaing from the spee sensor (range is from v to 3v). The power supply voltage is 2v an the sampling time is.s. The following Proportional-integral Controller is esigne when the network transmission elay an ata ropout is not consiere. D( ) G c ( ) = = (25) C( ) Spee Networke Control without Compensation Fig. 3. Simulation of networke control without compensation The unit step response of local control without communication elay an the networke control without any network uncertainty compensation are shown in Fig. 3. It inicates that the performance of local control is uite goo. However, in the networke environment, the roun trip time elay varies from 4 to 6 steps (.4s to.6s), the control performance egraes greatly with huge overshoot an very long settling time, which is unacceptable in practical applications. In orer to compensate for the effects of the network uncertainty, the NPC methos propose in this paper has been aopte. Fig. 4. shows the simulation results. For comparison, two simulations have been conucte. One is the conventional NPC, the other is the NPC with moel uncertainty correction esigne for NCS on WWANs. Because the mathematical moel in simulation is perfectly accurate, the NPC methos can fully compensate for the effects of the network uncertainty. Therefore, there is no moel preiction error at all. The results of local control an NPC with an without moel uncertainty are exactly the same. Spee NPC (Ol) NPC with moel uncertainty correction(new) Fig. 4. Simulation of long istance WNPC without moel uncertainties The mathematical moel can not always reflect the ynamical behaviors of the real plant in practical applications. If the power supply voltage of the cooling fan changes from 2v to v, corresponingly, the mathematical moel (24) will be change to B( ) G ( ) = = (26) A( ) If the NPC algorithm still uses the ol mathematical moel to calculate the preictive control seuence, the preiction errors will be inevitable, which results in big static error shown in Fig. 5. The target output shoul be for the unit step response, but the real output finally settles own at.84. The control performance has been egrae greatly. It shows the preiction errors can result in big static error if the moel is not accurate. Spee NPC (Ol) NPC with moel uncertainty correction(new) Fig. 5. Simulation of long-istance WNPC with moel uncertainties To cope with this problem, the moel uncertainty compensation metho propose in this paper is applie. The previous preiction errors are use to correct the future preictions, an the PI correction algorithm tries ecreasing the preiction errors as the control process going on. In this case, the both parameters k p an k i are.. With the preiction becoming more accuracy, the plant output is uickly approaching the target, as shown in Fig. 5. The control performance has been improve significantly 67

5 comparing with the conventional NPC. A. Test Rig IV. EXPERIMENTAL RESULTS A networke cooling fan spee control test rig has been setup to valiate the effectiveness of the propose control algorithm. The whole system consists of three parts: a PC base remote controller on the controller sie an a networke moule mae by Chinese Acaemy of Sciences (CAS) an a cooling fan on the plant sie. The PC an the networke moule are connecte via Internet an long-istance wireless network. The picture of the test rig is shown in Fig. 6. It can be seen that the cooling fan is place on the left han sie an the networke moule is on the right han sie. The PC controller with the IP aress is locate in the campus of Wuhan University. The networke moule is connecte to the GPRS wireless network provie by China Mobile. The PC controller works as the server sie an the networke moule works as the client sie, so the communication channel between them can be establishe. The communication protocol aopte in the experiments is UDP. The iagram of the whole wireless networke control system is shown in Fig. 7. without network an networke control without time elay compensation. The target spee jumps from RPM to 22 RPM at s. It can be seen that in local control, the control performance is goo, but network uncertainty egraes the control performance greatly. Delay Fig. 8. Roun trip time elay measurement In orer to compensate for the network uncertainty, NPC algorithm is aopte. The experiments of both the conventional NPC an NPC with moel uncertainty correction propose in this paper have been conucte. Because the mathematical moel ientifie is uite accurate, both the ol an new methos are able to maintain goo control performance in the networke environment, which is shown in Fig Spee (RPM) Networke Control without Compensation 4 2 Fig. 9. Results of local control an networke control without elay compensation Fig. 6. Cooling fan control test rig Spee (RPM) NPC(Ol) NPC with Moel Uncertainty Correction(New) 4 2 Fig. 7. Experimental iagram B. Experimental Results The roun trip time elays are measure uring the experiments, which are shown in Fig. 8. It can be seen the roun trip time elay varies from 4 to 7 steps (.4 to.7s). Fig 9. shows the experimental results of local control Fig.. Results of networke preictive control When the working conition of the cooling fan is change, the ol metho no longer works properly. For example, if the power supply voltage ecreases from 2V to V, the ol metho results in a big static error, which is similar to the 672

6 simulation results. As shown in Fig., the static error is aroun 2RPM which is not acceptable in practical applications. However, if the new metho propose in this paper has been aopte, the result is very close to the local control even with a not so accurate mathematical moel. Same with the simulations, both parameters k p an k i for the moel correction algorithm are.. The results prove that the propose methos can compensate for the effects of both network uncertainties an moel uncertainties in the NPC system effectively. Spee (RPM) NPC(Ol) NPC with Moel Uncertainty Correction(New) Fig.. Results of networke preictive control with v power supply V. CONCLUSIONS In this paper, a new wireless Internet-base NPC with moel uncertainty compensation has been introuce. It is esigne for the networke control systems on with wireless communication. In these systems, because of the long transmission elay, the control systems have to cope with the cases that the time elay is many times of the sampling perio. The NPC metho is able to cope with that situation very well, but it reuires very accurate mathematical moels. With imperfect moels, the control performances woul be affecte. In this paper, base on the NPC, a moel uncertainty correction algorithm is esigne to tackle this problem. In orer to valiate the propose metho, both simulations an experiments have been conucts. The results show that even not so accurate moels, the new NPC scheme can still maintain goo control performance in WWAN base networke control systems. [6] W. Xu, Z. Zhou, Q. Liu, Hybri one-way elay estimation for networke control system, Avances in Engineering Software, Vol. 4, 2, pp [7] Y. Tipsuwan, an M. Chow, Gain scheuler mileware: a methoology to enable existing controllers for networke control an teleoperation-part II: teleoperation., IEEE Transactions on Inustrial Electronics, Vol. 5, Dec. 24, pp [8] W. A. Zhang an L. Yu. A robust control approach to stabiliation of networke control systems with time-varying elays, Automatica, Vol. 45, 29, pp [9] Y. Xia, M. Fu, P. Shi, Analysis an Synthesis of Dynamic Systems with Time-elays, Springer, 29. [] Y. Xia, M. Fu, G.-P. Liu, Analysis an Synthesis of Networke Control Systems, Springer, 2. [] M. Proanovic an T. C. Green. High-uality Power Generation through Distribute Control of a Power Park Micro Gri. IEEE Transactions on Inustrial Electronics, vol. 53, pp , 26. [2] F. Katiraei an M. R. Iravani. Power Management Strategies for a Microgri with Multiple Distribute Generation Units. IEEE Transactions on Power Systems, 26, 2(4): [3] J. X. Mu, D. Rees an G. P. Liu, "Design an stability analysis of networke preictive control systems," UKACC International Conference on Control, Bath, 24 [4] G. P. Liu, S. C. Chai an D. Rees, "Networke Preictive Control of Internet/Intranet Base Systems," Chinese Control Conference, pp , 26 [5] G. P. Liu, Y. Xia, D. Rees an W. S. Hu. Design an stability criteria of networke preictive control systems with ranom network elay in the feeback channel., IEEE Transactions on Systems, Man, an Cybernetics- Part C, Vol. 37, pp [6] G. P. Liu, Y. Xia, D. Rees J. Chen an W. S. Hu. Networke preictive control of systems with ranom network elays in both forwar an feeback channels, IEEE Transactions on Inustrial Electronics, Vol. 54, 27, pp [7] W. S. Hu, G. P. Liu an D. Rees. Event-riven networke preictive control systems, IEEE Transactions on Inustrial Electronics, Vol. 54, 27, pp [8] W. S. Hu, G. P. Liu an D. Rees. Networke preictive control over the Internet using roun-trip elay measurement, IEEE Transactions on Instrumentation an Measurement, Vol. 57, 28, pp REFERENCES [] H. B. Song, L. Yu, W.A. Zhang, Networke H filtering for linear iscrete-time systems, Information Sciences, vol. 8, pp , 2 [2] F. W. Yang, Z. D. Wang, Y. S. Hung, M. Gani, H control for networke systems with ranom communication elays, IEEE Transactions on Automatic Control, vol. 5, pp.5 58, 26. [3] L.Q. Zhang, Y. Shi, T.W. Chen, B. Huang, A new metho for stabiliation of networke control systems with ranom elays, IEEE Transactions on Automatic Control, vol. 5, pp. 77 8, 25. [4] W. A. Zhang, L. Yu, H. B. Song, H filtering of networke iscrete-time systems with ranom packet losses, Information Sciences, vol. 79, pp , 29 [5] D. Yue, Q. L. Han, J. Lam, Network-base robust H control of systems with uncertainty, Automatica vol. 4, pp ,