Wireless Distributed Control Wireless Distributed Control NetworksNetworks

1010thth Nov 2005 Nov 2005 Jayant SrinivasanJayant Srinivasan

IntroductionIntroduction

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

Break up of lectureBreak up of lecture

The first half of the lecture will deal with The first half of the lecture will deal with design considerations for Networked design considerations for Networked Control Systems.Control Systems.

In keeping with the course, the latter half In keeping with the course, the latter half will deal with particular emphasis on will deal with particular emphasis on Wireless Network design for distributed Wireless Network design for distributed control.control.

What is a Networked Control What is a Networked Control System (NCS)?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.

Caveat!!Caveat!!

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

Effect of Time DelayEffect of Time Delay

Arise from time sharing of the Arise from time sharing of the communication medium as well additional communication medium as well additional functionality required for physical signal functionality required for physical signal coding & communication processing. coding & communication processing.

Degrades system’s performance and can Degrades system’s performance and can cause instability.cause instability.

TimingTiming ComponentsComponents

In an NCS,In an NCS,

TTdelaydelay== TTdevice device + T+ Tnetworknetwork

TTdelaydelay= T= Tprepre+ T+ Twaitwait+ T+ Ttxtx+ T+ Tpostpost

TTpre pre = preprocessing time at source = preprocessing time at source

TTwait wait = waiting time at source = waiting time at source

TTpostpost = post processing time = post processing time

TTtx tx = propogation delay = propogation delay

Timing Components (cont’d)Timing Components (cont’d)Waiting Time at source nodesWaiting Time at source nodes– Refers to the time a message might spend in the queue at the sender’s Refers to the time a message might spend in the queue at the sender’s

buffer. buffer.

– Is mainly affected by network protocols, message connection type and Is mainly affected by network protocols, message connection type and network traffic load. network traffic load.

Consider, Consider,

Timing Components (cont’d)Timing Components (cont’d)Transmission timeTransmission time– Most deterministic parameter in the systemMost deterministic parameter in the system– TTtxtx = N x T = N x Tbitbit + T + Tpropprop

N – Message length in BitsN – Message length in Bits

TTbitbit – bit time – bit time

TTpropprop – propogation time between any two devices – propogation time between any two devices

– – is negligible for a small scale networkis negligible for a small scale network

Processing timeProcessing time– Refers to the sum of both pre and post processing times. Refers to the sum of both pre and post processing times. – is device dependent, i.e depends on the no. of input/output is device dependent, i.e depends on the no. of input/output

modules, processing units, computational load, functionality, etc. modules, processing units, computational load, functionality, etc. – Can cause significant delay if not synchronized with the request Can cause significant delay if not synchronized with the request

frequency!frequency!

Network and Control Performance AnalysisNetwork and Control Performance AnalysisDuring 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.

The Network QoS must be analyzed before The Network QoS must be analyzed before implementing control systems with network architecturesimplementing control systems with network architectures– Main evaluation measures of QoS are time delay statistics, Main evaluation measures of QoS are time delay statistics,

network efficiency, network utilization and the number of lost or network efficiency, network utilization and the number of lost or unsent messages. unsent messages.

The control QoP (Quality of Performance) must be The control QoP (Quality of Performance) must be specified to help evaluate control system performance.specified to help evaluate control system performance.– Two criteria are generally used to evaluate control system Two criteria are generally used to evaluate control system

design and performance, they are:design and performance, they are:

A digital control approach is used to analyze the system A digital control approach is used to analyze the system as the all the application signals over the common bus as the all the application signals over the common bus network are discretized. network are discretized.

In order that system stability and control performance be In order that system stability and control performance be maintained, two control measures can be used to maintained, two control measures can be used to determine the best sampling period: determine the best sampling period: phase margin phase margin and and control system bandwidth.control system bandwidth.– Primary effect of sampling time delay is additional phase lag.Primary effect of sampling time delay is additional phase lag.– The phase lags are further classified as:The phase lags are further classified as:

Phase lag due to discretization,Phase lag due to discretization,

Phase lag due to time delay (of other components), Phase lag due to time delay (of other components),

A rule of thumb followed in A rule of thumb followed in digital control to guarantee digital control to guarantee control QoP is:control QoP is:

The adjacent figure is a The adjacent figure is a simulation study of the impact simulation study of the impact of sampling effect and time of sampling effect and time delay on control QoP.delay on control QoP.

– ωωbwbw= 2.5 Hz= 2.5 Hz

– Max Sampling period, Max Sampling period,

TTss = 20 ms = 20 ms

– Const time delay = 2 msConst time delay = 2 ms

PPBB can now be calculated based on the previous figure. can now be calculated based on the previous figure. – If the statistics of the additional time delay are known, If the statistics of the additional time delay are known,

then,then,

ΔφΔφ = = ΔφΔφs s = = ωωTTss/2 &/2 &

ΔφΔφdd = = ΔφΔφddss + + ΔφΔφdd = = ωωTTdd

ss/2 + /2 + ωωTTdd

Where, Where, ΔφΔφd d represents the phase lag of digital control represents the phase lag of digital control with time delay and with time delay and ΔφΔφ is the phase lag without delay. is the phase lag without delay.

Now, in order that the system with delay perform as Now, in order that the system with delay perform as well as the system without delay, well as the system without delay,

ΔφΔφ = = ΔφΔφdd which means that, which means that,

TTss = T = Tdds s + 2T+ 2Td d , and, and

TTss ≈ T ≈ Tbwbw/20, /20,

Thus, PThus, PBB = T = Tddss = T = Tss − 2T − 2Td d = 16ms= 16ms

assuming a constant delay of 2ms. assuming a constant delay of 2ms.

The point PThe point PCC can also be calculated as: can also be calculated as:

PPCC = T = Ttttttt/ ln 2/ ln 2

where,where,

TTtttttt = Total Transmission Time = Total Transmission Time

If considering the device processing time, PIf considering the device processing time, PCC will will

increase and can be modified as:increase and can be modified as:

PPCC = (T = (Tprocproc + T + Ttttttt)/2)/2

Simulation Study with Network Delay onlySimulation Study with Network Delay only

Ethernet

DeviceNet

Simulation Study with both Network and Device DelaysSimulation Study with both Network and Device Delays

Lessons learntLessons learnt

Verified and located the degradation Verified and located the degradation pointspoints

Messages with small sampling periods Messages with small sampling periods also increase network loadsalso increase network loads

Device processing time must be minimized Device processing time must be minimized to guarantee the determinism of to guarantee the determinism of transmission time as well as reduce the end-to-end delays.

Wireless Network for Distributed Control

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

IssuesIssues

Problems specific to Wireless NetworksProblems specific to Wireless Networks– Increased DelayIncreased Delay– Lossy mediumLossy medium

Tradeoff between communication and Tradeoff between communication and controller performancecontroller performance– The more the controller knows about the

system, the better the control performance is.– However, this increases the communication

burden on the network.

ApproachApproach

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

Cross Layer Design FrameworkCross Layer Design Framework

Given the context, the goal of Given the context, the goal of the Network, Link and MAC the Network, Link and MAC layers is to optimize control layers is to optimize control performance. performance.

Performance is a complicated function of the packet delay distribution, the probability of packet loss and the data resolution associated with the network.

Wireless Network ModelWireless Network Model

Wireless Link ModelWireless Link Model

– Each transmitter is assigned a unique ID number and this ID number is attached to the data. (ID uses log2M 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.

From the control perspective, the previous model is From the control perspective, the previous model is further simplified into:further simplified into:

– Where vWhere vq,i q,i is the covariance in quantization.is the covariance in quantization.

– PPss is the probability of successful transmission. 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 Ps.

Ps for each packet can be easily calculated given the link design, wireless channel gain and transmit power.

Control System model and Controller DesignControl 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<n>(t) is the system state, w<n>(t) is the disturbance acting on the plant, u<n>(t) is the control force, y<n>(t) is the measured output and v<n>(t) is the measurement noise.

The Linear quadratic cost function is used as our performance measure

SimulationsSimulations

TDMA with different link designs

Performance evaluation of different MAC schemesPerformance evaluation of different MAC schemes

Cross Layer Design principlesCross Layer Design principles

Cross Layer Design: the Link, MAC and Application Layer

Conclusions and DiscussionConclusions and Discussion

Joint design over all the network layers Joint design over all the network layers gives significant performance gains.gives significant performance gains.

Uncoded link can be optimal under some Uncoded link can be optimal under some circumstances.circumstances.

Identification of parameters that are Identification of parameters that are shared between layers is key. shared between layers is key.

ReferencesReferences

[1] [1] Xiangheng Liu and Andrea Goldsmith, "Wireless Network Design for Distributed Control." Submitted to IEEE Conference on Decision Submitted to IEEE Conference on Decision

and Control, 2004and 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.