Proceedings VCM 2012 76 thiết kế hệ thống nhận dạng khẩu lệnh tiếng việt

Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 559 Mã bài: 129 Communication delay Compensation for NCSs based on AR modeling Bù trễ truyền thông đối với các hệ thống điều khiển có nối mạng dựa trên mô hình AR Nguyen Trong Cac, Nguyen Van Khang Hanoi University of Science and Technology e-Mail: cacdhsd@gmail.com, khangnv@mail.hut.edu.vn Abstract Communication delay in Networked Control Systems (NCSs) are random in nature. A distributed real-time control system linked through a communication network is bound to be affected by the randomness of communication delay patterns. Real time feature in NCSs does not only depend on the real time of each part but also depends on the flexible links between parts. In time-sensitive NCSs, if the delay time exceeds the specified tolerable time limit, the plant or the device can either be damaged or have a degraded performance of system. In order to study the communication delay compensation for NCSs, in this paper Autoregressive (AR) modeling was proposed. The simulation results for communication delay illustrate that the AR model is able to compensate for the delay, thus guaranteeing the stability of NCSs in the presence of unpredictable delays. Keywords: Networked Control Systems; communication delay; Autoregressive modeling. Tóm tắt Trễ truyền thông trong các hệ thống điều khiển có nối mạng (NCSs) là ngẫu nhiên trong tự nhiên. Một hệ thống điều khiển thời gian thực phân tán được liên kết với nhau thông qua một mạng truyền thông bị ràng buộc bởi ảnh hưởng ngẫu nhiên của các thành phần trễ truyền thông. Tính năng thời gian thực trong NCSs không chỉ phụ thuộc vào thời gian thực của từng thành phần mà còn phụ thuộc vào sự phối hợp linh hoạt giữa các thành phần đó. Trong NCSs mà nhạy cảm với thời gian, nếu thời gian trễ vượt quá giới hạn thời gian cho phép đã được quy định thì nhà máy hoặc các thiết bị có thể bị hư hỏng, làm suy giảm hiệu suất của hệ thống. Để nghiên cứu bù trễ truyền thông đối với NCSs, trong bài báo này mô hình AR được đề xuất. Các kết quả mô phỏng minh họa đối với trễ truyền thông cho thấy rằng mô hình AR có thể sử dụng để bù trễ, đảm bảo sự ổn định của NCSs với sự có mặt của trễ mà không thể dự đoán trước. Từ khóa: Các hệ thống điều khiển có nối mạng; Trễ truyền thông; mô hình Autoregressive. 1. Introduction Feedback control systems wherein the control loops are closed through a real-time network are called NCSs, The defining feature of a Networked Control System is that information (reference input, plant output, control input, etc.) is exchanged using a network among control system components (sensors, controller, actuators, etc.) [1]. Thus a network control system requires at least one link to be carried by a real-time network [2]. The most preferred network protocols for control systems are Ethernet-based Modbus, Profibus, or Controller Area Network (CAN). The time delays are not always local to the controller tasks. They can occur as transmission delays from a sensor to a controller and from a controller to an actuator, because control equipment is connected via network [3]. The communication delay in NCSs includes three parts [3]: from sensor to controller  sc , from controller to actuator  ca , falculating time of controller  c , which is related to the calculating algorithm ( c is usually small enough to be omitted as disturbance). The  sc and  ca are caused by the data transfer over the network. The data transfer in the network has time stamps, so the  sc can be easily obtained by comparing time stamps. However the  ca can not be obtained easily and directly. For the communication delay compensation for Networked Control System, so far many methods have been proposed. Different mathematical, heuristic, and statistical-based approaches are taken for delay compensation in NCSs [4]. The optimal stochastic method approaches the problem as a Linear–Quadratic–Gaussian (LQG) problem [5]. In [6] focused on the effect of delay jitter at a fixed mean delay on the quality-of-control, two sources of delay jitter are identified in EIA-852- based systems: network traffic induced and protocol induced. Li et al. [7] derived Linear Matrix Inequality (LMI)-based sufficient conditions for stability. Xia et al. [8] proposed a new control scheme consisting of a control prediction generator and a network delay 560 Nguyen Trong Cac, Nguyen Van Khang VCM2012 compensator. In [9] proposed a time delay compensation method based on the concept of network disturbance and communication disturbance observer. In this method, a delay time model is not needed. Liu [10], [11] proposed a predictive control scheme for Networked Control System with random network delay in both the feedback and forward channels and also provided an analytical stability criteria for closed-loop Networked Predictive Control (NPC) systems, which is a model-based predictive control algorithm. The plant model must be accurate and it needs the synchronization of the clocks between organs. In [12] a new control scheme termed networked predictive control is proposed. This scheme mainly consists of the control prediction generator and network-delay compensator. Hu [13] proposed a new event-driven NPC scheme. The control signal applied to the actuator is selected based on the output rather than on the time delay measured. This scheme fits in the case that the model is not accurate or has uncertainty or disturbance. But the delay compensator is based on the assumption that the delay  sc and  ca , i.e., Round Trip Time (RTT) are known. Communication delay compensation thus has been studied in depth, and many solutions, some application-based and some theoretical, are proposed in the literature. Today, NCSs are moving into distributed NCSs, which are multidisciplinary efforts whose aim is to produce a network structure and components that are capable of integrating distributed sensors, distributed actuators, and distributed control algorithms over a communication network in a manner that is suitable for real-time applications [14]. In order to study the communication delay compensation for NCSs, in this paper Autoregressive (AR) modeling was proposed. The simulation results for communication delay illustrate that the AR model is able to compensate for the delay, thus guaranteeing the stability of NCSs in the presence of unpredictable delays. 2. System Design 2.1 System structure In general, time-delay appears different characteristic at different time region or under different network load, the AR modeling method can better depict this characteristic. So the AR method is used for  ca (kT) modeling. Based on the  ca (kT) modeling and the assumption that the model of the plant is prior known, a new time- delay compensation scheme for NCSs is proposed as Fig. l. Fig. 1 Block diagram of new communication delay compensation scheme for NCSs In the forward channel, there are three parts: The first part is the controller. The second part is an identifier for the time delay from the controller to actuator  ca (kT), for which we can use the data in the buffer to build the estimated models. For the characteristic of  ca (kT), an AR modeling is adopted, which is noted as an estimated one ˆ ( ) i ca kT  for each time region. The last part is networked compensator   ˆ ( ) ( ) i sc ca u kT kT kT kT     , which compensates for the network time-delay and data dropout in the forward (from controller to actuator) and feedback (from sensor to controller) channels and achieves the desired control performance. In the feedback channel, there is a predictive generator, which generates an accessorial predictive vector   ( ) ( ) sc sc y kT kT m kT kT      based on the data   ( ) sc y kT kT   in the buffer. In this scheme, a control cycle is initiated by the plant side. The plant output side sends a packet to the controller side, where the previous control signals u(kT) and previous output y(kT) are packed together for AR modelling used. When the controller side receives the packet, based on the data   ( ) sc y kT kT   received (note that there is a time-delay  sc (kT) from the sensor to the Controller r(kT) + _  ca (kT) u(kT) Identifier u(kT-  ca (kT)) Compensator Plant Z.O.H y(t) T  sc (kT) AR modeling y(kT) y(kT-  sc (kT)) e(kT) y(kT -  sc (kT)+m  kT-  sc (kT)) Network u(t) Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 561 Mã bài: 129 controller), it calculates future control sequences   ( ) sc u kT kT   , packs them into a packet together, and sends it through the network. There is another time delay  ca (kT) from the controller to the actuator. So on the left side of the identifier,   ( ) ( ) sc ca u kT kT kT     is arriving. In the feedback channel, based on the buffered data   ( ) sc y kT kT   , them-step predictive   ( ) ( ) sc sc y kT kT m kT kT      can be obtained, which is sent to the identifier also. By using a m- deep antitheses to get the time-delay  ca (kT). Here an AR modeling is built for  ca (kT) which is noted as ˆ ( ) i ca kT  for each time region. Then it is packed to the compensator to combine with other appropriate methods to compensate the controller and apply to the actuator. Therefore, the task of the compensator side is only to generate the correct control sequence and has no internal states, so it is not necessarily have to be synchronized with the plant side. Different from NPC implementation using the synchronization requirement and that all the predictions at the plant side are based on the RTT delay, the estimator ˆ ( ) i ca kT  is plus here to solve the puzzle [10-13]. However, in the compensator, we can use the ˆ ( ) i ca kT  combined with many control schemes, such as NPC used in Liu and Hu. 2.2 AR modeling Consider a single-input single-output discrete-time plant described by the autoregressive moving average model [13]: 1 1 ( ) ( ) ( ) ( 1) A z y kT B z u kT     (1) Where u(kT) ,y(kT) are the control input vector and output vector of the systems at time t. 1 1 ( ) [ , ] A z z n    and 1 1 ( ) [ , ] B z z m    are polynomials, i.e., 1 1 0 1 1 1 0 1 0 ( ) , ( ) , 0 n n m m A z a a z a z B z b b z b z and a                Without considering the network transmission delay, a controller is designed as: 1 1 ( ) ( ) ( ) ( ) C z u kT D z e kT    (2) Where 1 1 1 1 ( ) [ , ] ( ) [ , ] c d C z z n and D z z n       are polynomials, and c 0 =1. ( ) ( ) ( ) e kT r kT y kT   (3) Where r(kT) is the reference input. It is assumed that the feedback channel time delay is  sc (kT) which can be measured through the time stamps in the packages between the output sensor and the controller. At time t, the controller side receives a packet from the plant side, including the sequences of plant output y and the previous control sequences u, which is noted as:     ( ( )), ( ( ) 1), ( ( ) ) ( ( ) 1), ( ( ) 2), ( ( ) ) sc sc sc sc sc sc c including y kT kT y kT kT y kT kT n including u kT kT u kT kT u kT kT n                  (4) These data are buffered in a data box. The control sequence can be predicted as: 1 1 ( ) (1 ( )) ( ) ( ) ( ( )) ( ) sc sc sc sc sc sc sc u kT kT C z u kT kT D z r kT kT y kT kT                           (5) Where ( ) u kT i kT  denotes the ith step-ahead prediction of u(kT) based on the previous data up to time t. Then, the m-step system output prediction is obtained as: 1 1 ( ( ) ( )) 1 ( ) ( ( ) ( )) ( ) ( ( ) ( )) sc sc sc sc sc sc y kT kT m kT kT A z y kT kT m kT kT B z u kT kT m kT kT                          (6) Correspondingly, the control signal m-step ahead prediction is: 1 1 ( ( ) ( )) 1 ( ) ( ( ) ( )) ( )[ ( ( ) ) ( ( ) ( )) sc sc sc sc sc sc sc u kT kT m kT kT C z u kT kT m kT kT D z r kT kT m y kT kT m kT kT                              (7) Where m=0, 1, 2, …, N-1 After an N-step calculation, the future control sequence ( ( ) ( )) sc sc U kT kT kT kT     and the future system output sequence ( ( ) ( )) sc sc Y kT kT kT kT     are obtained, where ( ( ) ( )) ( ( ) 1 ( )) ( ( ) ( )) ( ( ) 1 ( )) sc sc sc sc sc sc sc sc u kT kT kT kT u kT kT kT kT U kT kT kT kT u kT kT N kT kT                                    (8) 562 Nguyen Trong Cac, Nguyen Van Khang VCM2012 ( ( ) ( )) ( ( ) 1 ( )) ( ( ) ( )) ( ( ) 1 ( )) sc sc sc sc sc sc sc sc y kT kT kT kT y kT kT kT kT Y kT kT kT kT y kT kT N kT kT                                    (9) 2.3  ca (kT) Identifier It is difficult to measure the time delay from the controller to the actuator  ca (kT). There are two problems to identify  ca (kT). The first problem is how to get the current  ca (kT). The second one is which modeling method can be used to build a model for  ca (kT). In practical, the delay  sc (kT) can be measured easily, and also for the RTT. If we omit the computing time  c (kT) (very small) , the current  ca (kT) can be calculated by the following equation: ( ) ( ) ( ) ca sc kT RTT kT kT     (10) From the probability information on the  ca (kT), now, we know the time delay RTT is like a shifted Gamma [15]. According to the data we obtained, RTT is always below 0.7s. If the sample time is 0.ls, then it is reasonable to assume that time-delay  ca (kT) is always below 7-step. Based on equation (10), the time-delay  ca (kT) can be obtained, which also appears different characteristic at different time region or under different network load. Therefore, by using the data for each time region, an AR modeling for ˆ ( ) i ca kT  can be built because it behaves an evidently subsection for different time region. Model i: 1 2 1 2 1 ˆ ( ) ( ) 1 i i ca i i i n n kT kT a z a z a z            (11) With 1 ˆ ( ) i i ca i y kT y     Where ˆ ( ) i ca kT  is the estimated value for the actual  ca (kT) The error between them is: ˆ ( ) , 1,2, i i i ca ca ca kT i n         (12) This can be omitted by the controller signal optimal selection scheme designed by control researcher. From the actual plot  ca (kT), it is considered that n=35 is an appropriate one. Other model building methods may be used here too, such as Prediction-Error Identification Method (PEM) (including Least Squares (LS) method, Maximum Likelihood Estimate (MLE) method and Bayesian Maximum method) and time series models (e.g. Hidden Markov Model, Auto- Regressive Moving Average (ARMA) model, Auto-Regressive Integrated Moving Average (ARIMA)). However, for the characteristic of the time delay  ca (kT) AR modeling is the best method. 2.4 Online Parameter Identification In practical application, the accuracy of the model is important to the performance of NCSs even with the new selection algorithm. If the model is not accurate, the control quality is greatly degraded and can even make the control system unstable. Since plant systems are invariably slightly nonlinear and have parameters that are variable, dependent on operating conditions, then the model representing the plant should track these changes. Therefore, a recursive least-squares parameter estimator is adopted in the control scheme. The plant is described as: 1 1 1 0 1 (1 ) ( ) ( ) ( ) n n m m a z a z y kT d b b z b z u kT                (13) The algorithm can be written as: ˆ ˆ ˆ ( ) ( 1) ( ) ( ) ( ) ( 1) ( 1) ( ) ( ) ( ) ( 1) ( ) T T kT kT L kT y kT kT kT P kT kT K kT kT P kT kT                      ( 1) ( ) ( ) ( 1) ( 1) ( ) ( ) ( 1) ( ) T T P kT kT kT P kT P kT kT kT P kT P kT                    (14) Where the initial value of the estimated vector   1 2 0 1 ˆ ( ) , , , , , , , T n n t a a a b b b       , the regression vector is: ( ) [ ( 1), ( 2), , ( ), ( ), ( 1), , ( )] T kT y kT y kT y kT n u kT d u kT d u kT d m             (15) And  is the forgetting factor. The regression vector (kT) and y(kT) are obtained from the packet sent from the plant side. They are stored in the actuator buffer. (kT) is the difference between the actual output and the one- step prediction ˆ ( ) ( 1) T kT kT    . When (kT) is large, it indicates that the present model is not accurate. In this case, the parameter vector Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 563 Mã bài: 129 ˆ ( ) kT  will make the corresponding changes to adjust the model parameters. 2.5 Compensation Scheme The main subject of the network delay compensation scheme is how to use the proper estimated time delay ˆ ( ) i ca kT  in the future predictive control sequence. Based on above section 2.3, we can get the current model of ˆ ( ) i ca kT  for different time region. By using the proper predictive controller design scheme,   ˆ ( ) ( ) i sc ca u kT kT kT kT     can be easily obtained directly. Many methods could be used to compensate u(kT), here three representative methods are illustrated as below:  A time delay compensation method based on time interval division Divide the time interval into five parts, [0,15], (15,40], (40,100], (100,200], (200,700]. For every part, the average (AV) value is used to substitute the current time-delay ˆ ( ) i ca kT  , i.e., AV 1 = 14.5987, AV 2 = 23.9177, AV 3 =65.9032, AV 4 =133.4828, AV 5 = 418.1923 [10]. It is a simple method to get the compensation controller   ( ) ( ) ( ) sc i sc ca u kT kT AV kT kT kT        , but the error exists apparently, especially when there are uncertainty or disturbance in the system.  Use the new model ˆ ( ) i ca kT  Use the new model ˆ ( ) i ca kT  to compensate the controller by substituting i;a into the controller directly, i.e. ˆ ( ( )) i ca u kT kT   . It is the correct input putting into the plant, and the correct output is obtained, which means a precise compensation. Compared with the NPC method, we don't need to predict the input again [16], [17], and using the control signal selection scheme to choose the correct input, which has much calculating work [15].  Use NPC scheme Use the NPC scheme when there are some others uncertainty or external disturbance in the system, because at this time the precise ˆ ( ) i ca kT  is adequate to compensate the time-delay.   ˆ ( ) ( ) ( ) ( ) i i sc ca i sc ca u kT kT kT kT kT kT         can be predicted also based on the ˆ ( ) i ca kT  1 1 ˆ ( ( ) ( ) ( ) ( )) ˆ 1 ( ) ( ( ) ( ) ( ) ( )) ˆ ˆ ( ) ( ( ) ( )) ( ( ) ( ) ( ) ( )) i sc ca sc ca i sc ca sc ca i i sc ca sc ca sc ca u kT kT kT kT kT kT C z u kT kT kT kT kT kT D z r kT kT kT y kT kT kT kT kT kT                                             (16) Two cases should be considered: while the control packet is received during the control cycle and control packet is not received during the control cycle, which is similar as Hu [13]. Here we don't repeat the details here. For the random communication delay, packet data dropout, and some disturbance in the network, there must be some prediction error in a real network system. In this case, the stability problem of the closed-loop system is solved using the theory of switched systems. For the NCSs with random communication delay, the closed-loop system is stable if there exist positive definite matrixes N N P   such that: , , T k f k f T PT P  (17) Where: , , , k f k f k f A B T P Q          (18) 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 n a a A                                         0 0 0 0 0 0 0 0 0 0 0 m b b B                          ,0 , , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f k k T k f p p P                                                    564 Nguyen Trong Cac, Nguyen Van Khang VCM2012 ,0 , , 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 f k k T k f q q Q                                                                     And  , , ( , , , ) N N k f k f A B P Q    , , ; 1,2, , 1 f k k k N          3. Simulation and evaluation of results The AR modeling based communication delay compensation scheme proposed in this paper is applied to a servo motor control system with distribution structure using CAN bus which is described in [13], the model of the plant was identified as: 1 1 1 2 3 4 1 2 3 ( ) ( ) ( ) ( )( ) 0.05409 0.115 0.0001 1 1.12 0.213 0.335 B z y t G z u tA z z z z z z z                  Where the input u(t) is the voltage applied to the motor, and the output y(t) is the voltage sampled from an angle sensor. The sampling time is 0.02 s. When the communication delay is not considered, a controller is designed as [13]: 1 1 1 1 ( ) 0.502 0.5 ( ) ( ) 7 ( ) ( ) 1 D z z u t e t y t C z z            Software for simulation is called as TrueTime to be run in a background of Matlab/Simulink [18]. In the library of TrueTime, there is a network block, to be used for simulation of network systems. In this block, values can be set such as, transmission speed, communications frame, bus access protocol and some other parameters such as: delay of pre-processing and post-processing, communications frame and data loss probability. Simulation results are shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 Time(s) Output(v) Fig. 2 Simulation of NCSs without communication delay 0 1 2 3 4 5 6 7 8 9 10 -1000 -500 0 500 1000 Time(s) Output(v) Fig. 3 Simulation of NCSs without delay compensator while communication delay is constant 0 1 2 3 4 5 6 7 8 9 10 -800 -600 -400 -200 0 200 400 600 800 Time(s) Output(v) Fig. 4 Simulation of NCSs without delay compensator while communication delay is random 0 1 2 3 4 5 6 7 8 9 10 -8 -6 -4 -2 0 2 4 6 8 10 Time(s) Output(v) Fig. 5 Simulation of NCSs with communication delay using AR modeling based compensation scheme Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 565 Mã bài: 129 From Fig. 5, we can be seen that, AR modeling is better than some other modeling, as studied in [19]. Comparison results are specified in Table 1. Table 1 Comparison of communication delay between AR modeling and some other modeling Non - Delayed Continuous System (ms) Smith Predictor modeling (ms) D ahlin Algorithm (ms) AR modeling (ms) 20 40 40 30 4. Conclusion Compared with the current communication delay compensation methods, there are some advantages to this new scheme in this paper. Firstly, this scheme uses the AR method for  ca (kT) modeling, which has been a puzzle for the measurement of  ca (kT) for many years. Other methods such as real-time recursive least-square parameter identification method can be used furthermore; Secondly, the synchronization between the plant and controller sides is no longer needed in this new scheme; Thirdly, in this scheme, many other controller design methods can be flexibly used according to the actual need of the plant, such as NPC or LQR. They can compensate for the time- delay accurately through using  ca (kT) identifier. References [1] Z. Wei, M.S. Branicky, and S.M. Phillips: Stability of Networked Control Systems. IEEE Control System Magazine, Vol. 21, No. 1, 2001, pp. 84-99. [2] Ray, Y and Halevi: Integrated Communication and Control Systems: Part II Design Considerations. ASME Journal of Dynamic Systems, Measurement and Control, Vol. 110, 1988, pp. 374-381. [3] J. Nilsson: Real-Time Control Systems with Delays. Lund, Sweden: PhD thesis, Dep. of Automatic Control, Lund Inst. of Techn., 1998. [4] L. A.Montestruque and P. Antsaklis: Stability of model-based networked control systems with time-varying transmission times. IEEE Trans. Autom. Control, Vol. 49, No. 9, Sep. 2004. pp. 1562–1572. [5] J. Nilsson, B. Bernhardsson, and B. Wittenmark: Stochastic analysis and control of real-time systems with random time delays. Automatica, Vol. 34, No. 1, Jan. 1998. pp. 57–64. [6] S. Soucek, T. Sauter, and G. Koller: Effect of delay jitter on quality of control in EIA-852- based networks. In Proc. IECON, Vol. 2, 2003, pp. 1431–1436. [7] Q. Li, G. Yi, C. Wang, L. Wu, and C. Ma: LMI-based stability analysis of networked control systems with large time-varying delays. In Proc. IEEE Int. Conf. Mechatronics Autom., 2006, pp. 713–717. [8] Y. Xia, G. P. Liu, and D. H. Rees: H control for networked control systems in presence of random network delay and data dropout. In Proc. Chin. Control Conf., 2006, pp. 2030-2034. [9] K. Natori and K. Ohnishi: A design method of communication disturbance observer for time-delay compensation, taking the dynamic property of network disturbance into account. IEEE Trans. Ind. Electron., Vol. 55, No. 5, May 2008, pp. 2152–2168. [10] G. P. Liu, Y. Xia, J. Chen, D. Rees, and W. Hu: Networked predictive control of systems with random network delays in both forward and feedback channels. IEEE Trans. Ind. Electron., Vol. 54, No. 3, Jun. 2007, pp. 1282– 1297. [11] Guo-Ping Liu, Yuanqing Xia, David Rees, Wenshan Hu: Design and Stability Criteria of Networked Predictive Control Systems With Random Network Delay in the Feedback Channel. IEEE Trans. On Systems, Man, and Cybernetics, Part C: Applications and Reviews, Vol. 37, No.2, 2007, pp. 173-184. [12] Xia, Y.; Liu, G.P.; Fu, M.; Rees, D.: Predictive control of networked systems with random delay and data dropout. IET Control Theory & Applications, Vol. 3, Iss. 11, 2009, pp. 1476–1486. [13] Wenshan Hu, Guoping Liu, and David Rees: Event-Driven Networked Predictive Control. IEEE Trans. Ind. Electron., Vol. 54, No.3, Jun. 2007, pp. 1603-1613. [14] R. A. Gupta and M. Y. Chow: Networked control system: Overview and research trends. IEEE Trans. Ind. Electron., Vol. 57, No. 7, Jul. 2010, pp. 2527-2535. [15] Wei Zhang, J.H.: Modeling end-to-end delay using pareto distribution". In Second International Conference on Internet Monitoring and Protection. ICIMP 2007, pp. 21-24. [16] L.L. Lam, Kai Su, C.W. Chan and X. J. Liu: Modeling of Round Trip Time over the Internet. Proceedings of the 7th Asian Control Conference, Hong Kong, China, 2009, pp. 292-297. 566 Nguyen Trong Cac, Nguyen Van Khang VCM2012 [17] V.Paxson, F.S.: Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Transactions on Networking, 1995.3(3): pp. 226-244. [18] Martin Ohlin, Dan Henriksson and Anton Cervin: TrueTime 1.5 – Reference Manual. Lund Institute of Technology, Sweden, Jan. 2007, pp. 7-107. [19] Rachna Dhand, Gareth Lee, Graeme Cole: Communication Delay Modelling and its Impact on Real-Time Distributed Control Systems. The Fourth Int. Conf. on Advanced Engineering Computing and Applications in Sciences, 2010, pp. 39-46. . tắt Trễ truyền thông trong các hệ thống điều khiển có nối mạng (NCSs) là ngẫu nhiên trong tự nhiên. Một hệ thống điều khiển thời gian thực phân tán được liên kết với nhau thông qua một mạng. nhà máy hoặc các thiết bị có thể bị hư hỏng, làm suy giảm hiệu suất của hệ thống. Để nghiên cứu bù trễ truyền thông đối với NCSs, trong bài báo này mô hình AR được đề xuất. Các kết quả mô phỏng. Trip Time over the Internet. Proceedings of the 7th Asian Control Conference, Hong Kong, China, 2009, pp. 292-297. 566 Nguyen Trong Cac, Nguyen Van Khang VCM2 012 [17] V.Paxson, F.S.: Wide-area