利用自适应编码调制的无线网络控制系统的分析和设计

1、 916 ACTA AUTOMATICA SINICA Vol. 35 (k T (k Q (k + T (k R (k V (k 2 T (k P (k + T (k P (k + T (k Q max max T T k (k + 1 R 1 + ( 1 (k Q k h h k 1 k1 max T (n Z1 (n T (n Z1 (n + 1 T (k (Z1 + Z2 (k n=k h 1 n=k max h k1 1 n=k max h v T (k (T (T T v (k+ T (n Z2 (n + 2v T (kT (k ( I x (k + v k1 n=k x (k +

2、 2v T (k M x (k x (k 1x T (k K T T Kx 2v T (k S x (k x k 2v T (k N x (k x k k 1 max 1 h n=k max h (n + (n + 1 k1 max 1 h n=k max h (n 1 T v T (k 1 + 2 + T 2 + 3 + 3 + max 1 1 T + 1 M Z1 M T + ( 1 SZ1 S + h k1 max 1 T + 1 N Z2 N + 1 (T (T T + 1 T v (k v T (k M + T (n Z1 n=k h 1 Z1 M Tv (k + Z1 (n k1

3、1 n=k max h k 1 1 n=k max h 1 v T (k S + T (n Z1 Z1 S Tv (k + Z1 (n 1 v T (k N + T (n Z2 Z2 N Tv (k + Z2 (n (14 T 1 + 2 + T 2 + 3 + 3 + 1 1 T M Z1 M T + ( 1 SZ1 S + max +1 h max +1 h (15 The loop equation for the electrical circuit is u(t = ea = L dia + Ria + eb dt (16 1 T N Z2 N + 1 (T (T T + 1 T 0

4、 2 The mechanical torque balance based on Newton s law is J d + B + Tl = Te = Kia dt (17 Therefore, (10 yields V (k 0, and the WNCS (7 is asymptotically stabilized. Remark 4. By dening new Lyapunov functions and making use of more matrix variables to achieve delay dependence, a new condition is obta

5、ined for the controller design of WNCS (7. The merit of the proposed conditions is that they can deal with larger ED and get better performance for system (7. By letting x1 = ia and x2 = , the electromechanical dynamics of the DC motor can be described by the following state-space descriptions x 1 x

6、 2 = = R Kb 1 x1 x2 + u L L L (1 4 Simulation K B x1 x2 J J In this section, we use the Matlab linear matrix inequality toolbox and Simulink to illustrate the eectiveness and advantage of our proposed method. All simulations use the network settings given in Table 1. Table 1 System parameters values

7、 Value 1 024 bits 0.864 ms 3 0.03 1ms 50 packets where the parameters of the motor are shown in Table 2. Table 2 J L R B K Kb Inertia Inductance Resistance Damping coecient Torque constant Back-EMF constant DC motor parameters 42.6E-6 Kgm2 170E-3 H 4.67 47.3E-6 Nms/rad 14.7E-3 Nm/A 14.7E-3 Vs/rad Pa

8、rameter Frame size ACK timeout tout Retry limit m Error coding threshold Fixed link delay Buer size A DC motor speed control system31 is introduced based on WNCS utilizing adaptive coded modulation schemes. First, we give the controller for WNCS applying ACM schemes by Theorem 1. Here, the result in

9、 27 is used, and it is an adaptive code with eight 4-D trellis codes utilizing the eight nested 2-D signal constellations. The overall encoder is applied in the International Telecommunications No. 7 YANG Li et al.: Analysis and Design of Wireless Networked Control system Utilizing 917 Union s ITU-T

10、 V.34 modem standard. Using the curve tting with the least squares method, we get the thresholds n , which are listed in Table 3. Table 3 n 1 2 3 4 5 6 7 8 Codes and calculated n (dB for target BER0 = 103 Mn 4 8 16 32 64 128 256 512 an 896.0704 404.4353 996.5492 443.1272 296.6007 327.4874 404.2837 3

11、10.5283 bn 10.7367 6.8043 8.7345 8.2282 7.9270 8.2036 7.8824 8.2425 n 7.1 11.8 14.0 17.0 20.1 23.0 26.2 29.0 Fig. 5 Responses of state x2 5 Conclusion If we choose Ts = 0.0083 ms, and h = 0.7 s, the transmission rate will be 0.24E+6 bps, 0.36E+6 bps, 0.48E+6 bps, 0.60E+6 bps, 0.72E+6 bps, 0.84E+6 bp

12、s, and 0.96E+6 bps. According to (1 and (2, the total region of ED will be 0.0095 s, 1.7419 s. Based on Theorem 1, we can get the following controller gain K = 0.0446 0.0231 In this paper, we have modelled the WNCS with ACM scheme as a discrete-time system with time-varying input delay. The concept

13、of ED is presented to capture the characteristics of varying rate, interference, and routing in wireless transmission channel. Delay-dependent sucient conditions on the stability of the closed-loop WNCS and the state feedback controller are derived in terms of linear matrix inequalities by using a r

14、ecent result on the discrete time delay. Simulation result shows the eectiveness and advantage of the proposed method. References 1 Yue D, Han Q L, Chen P. State feedback controller design of networked control systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 2004, 51(11: 640644

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19、random packet losses. IEEE Transactions on Systems, Man, Cybernetics, Part B: Cybernetics, 2007, 37(4: 916924 10 Xie Jin-Song, Fan Bing-Quan, Young Sam Lee, Yang Jin. Guaranteed cost controller design of networked control systems with state delay. Acta Automatica Sinica, 2007, 33(2: 170174 11 Yang D

20、e-Dong, Zhang Hua-Guang. Robust H networked control for uncertain fuzzy systems with time-delay. Acta Automatica Sinica, 2007, 33(7: 726730 On the other hand, if there is no ACM used in WNCS, the total region of ED will be 0.0465 s, 2.3222 s. The following controller can be obtained K = 0.5568 0.570

21、4 The responses of the resulting closed-loop system with and without ACM scheme are shown in Figs. 4 and 5, where the initial condition is x (0 = 0.08; 0.1. It is easy to see that the system performance is improved when there exists ACM scheme in WNCS. The settling time, when ACM is applied (5 s for

22、 x1 and 10 s for x2 , is less than that without ACM (17 s for x1 and 40 s for x2 . Moreover, the overshoot of the states with ACM schemes are less than the ones without ACM. Fig. 4 Responses of state x1 918 ACTA AUTOMATICA SINICA Vol. 35 12 Liu G P, Xia Y Q, Rees D, Hu W S. Design and stability crit

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35、G Li Received her bachelor and master degrees from the Department of Electrical Engineering, Yanshan University, in 2004 and 2006, respectively. She is currently a Ph. D. candidate at Yanshan University. Her research interest covers time-delay systems and networked control systems. E-mail: yangli135 0 GUAN Xin-Ping Received his master degr