Chapter 4 Multi-rate Design for Wireless NCS
4.2 Analysis of time delay in HNCS
In general, the induced network time delay presents different characteristics depending on both the network hardware and protocols; moreover, it varies owing to network loading, scheduling policies, and the number of nodes. Research on HNCS is much more difficult than those on general delayed systems where the time delay is usually assumed to be constant or bounded. In this study, the total time delay in HNCS is categorized into three types as they occur at (1) the gateway node, (2) the network channel, and (3) the remote site. The summed time delay at each node actually includes
all the network node preprocessing time, the controller computation time, the encoding time, the waiting time, the total queuing time, and the blocking time (Lian et al., 2002).
The total time delay, also called the round-trip delay, is the required period for a packet to travel from the client node to the remote node and back to the original client node. The proposed networked control architecture combines both the time-driven and the event-driven processes and the typical NCS structure is the same as shown in Fig.
2.9(a).
4.2.1 Delay time analysis
The RTT is measured from the client node to the control center station through the gateway, and back to the original client node. In this experimental setup, a notebook computer with Intel® Pentium CPU 1.60 GHz was tested with 496 MB of RAM, Intel(R) PRO/Wireless 2200BG Network Connection Card, and with Windows XP Professional Version 2002 OS with Service Pack 2. For the CAN bus, the experimental results indicate that the time delay in the CAN bus is relatively small as compared to that of the wireless network, as shown in Fig. 4.5.
0 2 4 6 8 10 12 14 16 18 20
1 1.5 2 2.5 3 3.5 4
Sec.
Time Delay (ms)
(a) (b)
Fig. 4.5 Measurement of the delay time on CAN network (a) the transmit time for a node-to-node and (b) the RTT between the gateway and the client
The time delays on both IEEE 802.11g ad-hoc wireless network and the CAN network (transmitted with different sampling rates and various environments) were measured as shown in Fig. 4.6, and the results are summarized in Tables 4.1- 4.2.
(a) (b)
Fig. 4.6 Measurements of time delay in (a) a simple environment and (b) a complex environment
Table 4.1 The averaged delay time of the hybrid networks in a simple environment (unit: ms）
Sampling Time No. 1 No. 2 No. 3 No. 4
5 ms 2.807961 11659.09 2.474295 5574.375 10 ms 4453.212 5489.112 2910.771 3.897898 20 ms 20.2813 470.5569 23.0162 5590.872
Table 4.2 The averaged delay time of the hybrid networks in a complex environment.
(unit: ms )
Sampling Time No. 1 No. 2 No. 3 No. 4
5 ms 22797.18 15326.39 4855.466 22797.18 10 ms 7818.727 16693.98 8716.06 12349.45 20 ms 21.59492 21.16303 10726.56 535.6239 50 ms 37.0036 45.71434 44.39008 49.5021
The results indicate that different environments and sampling rates greatly affect the delay time of HNCS. Results also indicate that an increasing network load and longer messages lengths also cause a significant increase in the delay time. Furthermore, the delay time increases dramatically in a more complex environment with a faster sampling time. Too many wireless devices use a 2.4 GHz unlicensed band in our daily
living environment. Owing to the limited bandwidth in wireless networks, most ad-hoc networks use a contention-based protocol for controlling channel access resource.
Performance of wireless ad-hoc networks is thus poor because of network congestion with abundant medium contest. The previously mentioned definition of a transmission is then implemented using TCP. Due to network congestion, traffic load balancing, or other unpredictable network behavior, TCP detects these problems, requests the retransmission of lost packets, and rearranges out-of-order packets to reduce the occurrence of other problems. TCP sometimes incurs relatively long delays while waiting for out-of-order messages or retransmissions of lost messages. Therefore, the probability that the time delay in a complex environment is dramatically changed increases when it is under the same sampling time. Comparing the results of the CAN bus and wireless systems, it is obvious that no matter the environment is simple or complex, the time delay in wireless systems remains to be the bottleneck during the transmission for HNCS.
4.2.2 Stability of HNCS
Experiments were conducted for the present HNCS and the position controller was located on the control center station. The coefficients of PI controller were tuned as
K
p=0.0001 and Ki=0.00000001. The system identification result from the pseudo random binary signal (PRBS) response for the present AC permanent magnet synchronous motor is obtained as
5 2
10 (0.029 1.6105) ( ) s(0.0001s 0.019s 1)
p
G s s
For the wireless 802.11g with a 54 Mbps transmission rate, the measured time delay is shown in Fig. 4.7. The results indicate that although the time delay effect in the wireless network is in a stochastic nature, it is basically bounded. For the client of the servo motor, the sampling time is 20 ms with a square wave command input and the upper/lower commands are 30000/15000 pulse of the encoder readout. As shown in Fig. 4.8, the communication congestion occurs around 4.5 seconds and note that the PI control cannot maintain a stable HNCS with a fixed sampling time under such
applying the first-order Padé approximation to the time delay are shown in Fig. 4.9.
When tm is greater than 100 ms, the Nyquist plot encloses -1, and the system becomes unstable.
Fig. 4.7 The bounded time delay effect measured in HNCS
unbounded time-delay effect (after 4.5 s)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 -1.5
-1 -0.5 0 0.5
tm=0ms tm=20ms tm=40ms
tm=60ms tm=80ms tm=100ms tm=120ms tm=140ms
j Im L
Re L
Fig. 4.9 Nyquist plots with different time delay
Fig. 4.10 Structure of the multi-rate design method