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Wireless Distributed Control Networks 10 th Nov 2005Jayant Srinivasan

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Introduction Information among distributed sensors, controllers and actuators needs to be exchanged over a communication network to achieve a certain control objective. Eg. Automated Highway Systems.

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Break up of lecture The first half of the lecture will deal with design considerations for Networked Control Systems. In keeping with the course, the latter half will deal with particular emphasis on Wireless Network design for distributed control.

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What is a Networked Control System (NCS)? Feedback Control Loops wherein the control loops are closed through a real-time network are called networked control systems. The introduction of control network bus architectures can improve the efficiency, flexibility, and reliability of these integrated applications, reducing installation, reconfiguration, and maintenance time and costs.

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Caveat!! Although the NCS draws from elements of networking and control theory, the design of the communication protocols and interacting control system should not be treated as disparate! Network issues such as bandwidth, quantization, survivability, reliability and message delay should be considered simultaneously with controlled system issues like stability, performance, fault tolerance and adaptability.

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Effect of Time Delay Arise from time sharing of the communication medium as well additional functionality required for physical signal coding & communication processing. Degrades systems performance and can cause instability.

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Timing Components In an NCS, T delay = T device + T network T delay = T pre + T wait + T tx + T post T pre = preprocessing time at source T wait = waiting time at source T post = post processing time T tx = propogation delay

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Timing Components (contd) Waiting Time at source nodes –Refers to the time a message might spend in the queue at the senders buffer. –Is mainly affected by network protocols, message connection type and network traffic load. Consider,

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Timing Components (contd) Transmission time –Most deterministic parameter in the system –T tx = N x T bit + T prop N – Message length in Bits T bit – bit time T prop – propogation time between any two devices – is negligible for a small scale network – is negligible for a small scale network Processing time –Refers to the sum of both pre and post processing times. –is device dependent, i.e depends on the no. of input/output modules, processing units, computational load, functionality, etc. –Can cause significant delay if not synchronized with the request frequency!

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Network and Control Performance Analysis During design of an NCS, a performance chart, like the one shown below can be derived. This performance chart provides a clear way of selecting the optimal sampling period.

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The Network QoS must be analyzed before implementing control systems with network architectures –Main evaluation measures of QoS are time delay statistics, network efficiency, network utilization and the number of lost or unsent messages. The control QoP (Quality of Performance) must be specified to help evaluate control system performance. –Two criteria are generally used to evaluate control system design and performance, they are:

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A digital control approach is used to analyze the system as the all the application signals over the common bus network are discretized. In order that system stability and control performance be maintained, two control measures can be used to determine the best sampling period: phase margin and control system bandwidth. –Primary effect of sampling time delay is additional phase lag. –The phase lags are further classified as: Phase lag due to discretization, Phase lag due to time delay (of other components),

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A rule of thumb followed in digital control to guarantee control QoP is: The adjacent figure is a simulation study of the impact of sampling effect and time delay on control QoP. –ω bw = 2.5 Hz –Max Sampling period, T s = 20 ms –Const time delay = 2 ms

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P B can now be calculated based on the previous figure. –If the statistics of the additional time delay are known, then, Δφ = Δφ s = ωT s /2 & Δφ d = Δφ d s + Δφ d = ωT d s /2 + ωT d Where, Δφ d represents the phase lag of digital control with time delay and Δφ is the phase lag without delay. Where, Δφ d represents the phase lag of digital control with time delay and Δφ is the phase lag without delay. Now, in order that the system with delay perform as well as the system without delay, Now, in order that the system with delay perform as well as the system without delay, Δφ = Δφ d Δφ = Δφ d which means that, T s = T d s + 2T d, and T s T bw /20, Thus, P B = T d s = T s 2T d = 16ms assuming a constant delay of 2ms.

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The point P C can also be calculated as: P C = T ttt / ln 2 where, T ttt = Total Transmission Time T ttt = Total Transmission Time If considering the device processing time, P C will increase and can be modified as: P C = (T proc + T ttt )/2 P C = (T proc + T ttt )/2

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Simulation Study with Network Delay only Ethernet DeviceNet

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Simulation Study with both Network and Device Delays

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Lessons learnt Verified and located the degradation points Messages with small sampling periods also increase network loads Device processing time must be minimized to guarantee the determinism of Device processing time must be minimized to guarantee the determinism of transmission time as well as reduce the end-to-end delays.

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Wireless Network for Distributed Control Part 2: Wireless Network Design for Distributed Control

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Issues Problems specific to Wireless Networks –Increased Delay –Lossy medium Tradeoff between communication and controller performance – –The more the controller knows about the system, the better the control performance is. – – However, this increases the communication burden on the network.

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Approach As advocated in the general case for NCS, As advocated in the general case for NCS, we cast the joint control and communication design problem in a broader framework of cross-layer design. Such an approach allows each layer of the network protocol stack to be optimized relative to the end-to-end controller performance. – –will specifically investigate the interaction of the physical layer design, the MAC protocol choice, and the controller sampling period

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Cross Layer Design Framework Given the context, the goal of the Network, Link and MAC layers is to optimize control performance. Performance is a complicated function of the packet delay distribution, the probability of packet loss and the data resolution associated with the network.

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Wireless Network Model Wireless Link Model – –Each transmitter is assigned a unique ID number and this ID number is attached to the data. (ID uses log 2 M bits, for M txs) – –BCH codes for error correcting and a16 bit CRC for error detection, errors can have a disastrous effect on the system. – –a packet will be discarded if it has not been successfully received by the end of the sample period.

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From the control perspective, the previous model is further simplified into: –Where v q,i is the covariance in quantization. –P s is the probability of successful transmission. The time delay distribution and the probability of packet loss are determined by the MAC protocols, total number of retransmissions and probability of successful transmission P s. P s for each packet can be easily calculated given the link design, wireless channel gain and transmit power.

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Control System model and Controller Design all the plants in our model are continuous time linear time-invariant systems and we can represent the nth system with the following state space equations: – –Where x (t) is the system state, w (t) is the disturbance acting on the plant, u (t) is the control force, y (t) is the measured output and v (t) is the measurement noise. The Linear quadratic cost function is used as our performance measure

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Simulations TDMA with different link designs

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Performance evaluation of different MAC schemes

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Cross Layer Design principles Cross Layer Design: the Link, MAC and Application Layer

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Conclusions and Discussion Joint design over all the network layers gives significant performance gains. Uncoded link can be optimal under some circumstances. Identification of parameters that are shared between layers is key.

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References [1] Submitted to IEEE Conference on Decision and Control, 2004 [1] Xiangheng Liu and Andrea Goldsmith, "Wireless Network Design for Distributed Control." Submitted to IEEE Conference on Decision and Control, 2004 [2] [2] M.S. Branicky, et. al. Scheduling and feedback co-design for networked control systems, Proc. IEEE Conf. on Decision and Control, pp. 1211-1217, Dec. 2002. [3] F. Lian, et. al. Network Design Consideration for Distributed Control Systems, IEEE Trans. on Control Systems Technology, pp. 297- 307,Mar. 2002.

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