Transcript Lecture 10 Wireless Distributed Control Networks

Wireless Distributed Control
Networks
10th Nov 2005
Jayant Srinivasan
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.
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.
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.
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.
Effect of Time Delay
Arise from time sharing of the
communication medium as well additional
functionality required for physical signal
coding & communication processing.
Degrades system’s performance and can
cause instability.
Timing Components
In an NCS,
Tdelay= Tdevice + Tnetwork
Tdelay= Tpre+ Twait+ Ttx+ Tpost
Tpre = preprocessing time at source
Twait = waiting time at source
Tpost = post processing time
Ttx = propogation delay
Timing Components (cont’d)
Waiting Time at source nodes
– Refers to the time a message might spend in the queue at the
sender’s buffer.
– Is mainly affected by network protocols, message connection
type and network traffic load.
Consider,
Timing Components (cont’d)
Transmission time
– Most deterministic parameter in the system
– Ttx = N x Tbit + Tprop
N – Message length in Bits
Tbit – bit time
Tprop – propogation time between any two devices
– 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!
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.
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:
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),
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.
– ωbw= 2.5 Hz
– Max Sampling period,
Ts = 20 ms
– Const time delay = 2 ms
PB can now be calculated based on the previous figure.
– If the statistics of the additional time delay are known,
then,
Δφ = Δφs = ωTs/2 &
Δφd = Δφds + Δφd = ωTds/2 + ωTd
Where, Δφd 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,
Δφ = Δφd
which means that,
Ts = Tds + 2Td , and
Ts ≈ Tbw/20,
Thus, PB = Tds = Ts − 2Td = 16ms
assuming a constant delay of 2ms.
The point PC can also be calculated as:
PC = Tttt/ ln 2
where,
Tttt = Total Transmission Time
If considering the device processing time, PC will
increase and can be modified as:
PC = (Tproc + Tttt)/2
Simulation Study with Network Delay only
Ethernet
DeviceNet
Simulation Study with both Network and Device Delays
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
transmission time as well as reduce the
end-to-end delays.
Part 2: Wireless Network Design for
Distributed Control
Wireless Network for Distributed Control
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.
Approach
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 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.
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 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
further simplified into:
– Where vq,i is the covariance in quantization.
– Ps 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 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
Simulations
TDMA with different link designs
Performance evaluation of different MAC schemes
Cross Layer Design principles
Cross Layer Design: the Link, MAC and Application Layer
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.
References
[1] Xiangheng Liu and Andrea Goldsmith, "Wireless Network Design for
Distributed Control." Submitted to IEEE Conference on Decision and
Control, 2004
[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. 297307,Mar. 2002.