Presentation of Event Triggered Adaptive Differential Modulation

Presentation of Event Triggered Adaptive Differential Modulation

1. Introduction
Event Triggered Adaptive Dierential Modulation:
A New Method for Trac Reduction in Networked
Control Systems
Upeka Premaratne
Department of Electronic and Telecommunication Engineering
The University of Moratuwa
September 11, 2014
Upeka Premaratne ETADM

2. Introduction
Outline
1
Introduction
2
Stability Theory
3
ETADM
4
NG-ETADM
5
Extremum Seeking Control
6
Conclusions
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3. Introduction
Contribution
Event Triggered Adaptive Dierential Modulation (ETADM)
IA new method for reducing network trac by combining the
trac reduction eects of event based sampling and speech
coding
The next generation version of ETADM
ICurrently cannot be disclosed due to the patenting process
Extremum Seeking Control with Sporadic Communication
IA new method for extremum seeking control with sporadic
packet transmission instead ofper iterationpacket transmission
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4. Introduction
Introduction
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5. Introduction
Introduction
Q
A
connect the plant(s), controller and sensors in a control
system instead of a dedicated connection.
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6. Introduction
Introduction
Q
A
connect the plant(s), controller and sensors in a control
system instead of a dedicated connection.
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7. Introduction
History
Serial networks have a long history in industrial automation
IUsed for discrete event systems with Programmable Logic
Controllers (PLCs)
IRS232, RS485, DNP3, Modbus, CAN-bus etc.
Emergence of TCP-IP based packet switched networks
IMore bandwidth
IHigher bandwidth eciency than TDMA based serial networks
IModbus over TCP-IP and IEC61850 (electric substation
automation)
Continuous control loops
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8. Introduction
Why Networked Control Systems?
Advantages (Miorandi et al. 2007, Lee et al. 2007)
Bandwidth eciency
Lower infrastructure costs
Flexibility
Disadvantages (Zampieri 2008, Donkers et al. 2011)
Limited information feedback (bandwidth and packet size)
Medium access restrictions
Delay, delay variation and packet drops
Security
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9. Introduction
Motivation and Research Problem
Motivation
Packet drops, delay and delay variation are caused by network
bottlenecks (e.g. queues) (Agarwal 1991)
IAect performance and stability of NCS (Cloosterman et al.
2008, Quevedo and Nesic 2011)
Historically solved by using dedicated (isolated) network
(Pollet 2002, Paukatong 2005, Chandia et al. 2007)
IOften not a viable due to internetworking and wireless networks
No control over external network trac sources
The Objective
Develop a method for reducing trac generated by the
control system such that it remains stable with minimum
degradation in performance.
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10. Introduction
Motivation and Research Problem
Motivation
Packet drops, delay and delay variation are caused by network
bottlenecks (e.g. queues) (Agarwal 1991)
IAect performance and stability of NCS (Cloosterman et al.
2008, Quevedo and Nesic 2011)
Historically solved by using dedicated (isolated) network
(Pollet 2002, Paukatong 2005, Chandia et al. 2007)
IOften not a viable due to internetworking and wireless networks
No control over external network trac sources
The Objective
Develop a method for reducing trac generated by the
control system such that it remains stable with minimum
degradation in performance.
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11. Introduction
Stability Theory
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12. Introduction
Event Triggered Adaptive
Dierential Modulation
Upeka Premaratne ETADM

13. Introduction
Event Triggered Adaptive Dierential Modulation
From Publication
Premaratne, Halgamuge and Mareels,Event Triggered Adaptive
Dierential Modulation: A New Method for Trac Reduction in
Networked Control Systems, IEEE Transactions on Automatic
Control, 58 (7), pp. 1696-1706, 2013.
Contribution
A hybrid trac reduction method that combines event based
sampling and speech coding techniques for nonlinear control
systems that satisfy the small gain condition. It is robust to
occasional packet drops.
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14. Introduction
Event Based Sampling
Sampling a variable when a threshold is exceeded instead of
periodic sampling
IMET, MBET
If the rate of change of the signal is bounded, reduces the
eective sampling rate
Sporadic trac
Heuristic parameters
MBET has no proof of stability for packet drops (closest
result in Hirche and Buss 2004)
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15. Introduction
Memoryless Event Triggering
Triggering Mechanism
IFjv[k]j eTTHEN
T ransmit(v[k])
END
Schematic Sampler MET Network
Signal Reconstruction
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16. Introduction
Memoryless Event Triggering 30 32 34 36 38 40 42 44 46 48 50
-4
-2
0
2
4
6
8
10
12
14
x 10
-3
t (s)
Amplitude


Input Signal
Reconstruction
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17. Introduction
Memory Based Event Triggering
Triggering Mechanism
IFjv[k]vMj eTTHEN
vm=v[k]
T ransmit(vm)
END
Schematic Sampler MBET ZOHNetwork
Signal Reconstruction
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18. Introduction
Memory Based Event Triggering 25 25.2 25.4 25.6 25.8 26 26.2 26.4 26.6
-0.02
-0.01
0
0.01
0.02
t (s)
y(t)


Signal
Reconstruction
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19. Introduction
Speech Coding Techniques
Exploit high dependency of adjacent samples
IVariables (state variables and outputs) in dynamical systems
exhibit similar high dependence
A dierence can be transmitted instead of the entire sample
IAdaptive Delta Modulation for linear systems (Gomez-Estern
et al. 2007, 2011, Canudas-de-Wit et al. 2009)
IEcient for TDMA but not for packet switched protocols due
to large packet overhead
IDierence adaptation (step adaptation) for better transient
response
Cannot use statistical properties to further reduce bandwidth
like in human speech (Un and Cho 1982, Schroeder and Atal
1985)
IObtaining statistical properties of control systems is unrealistic
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20. Introduction
Adaptive Delta Modulation ADM
Encoder
Step Size
Channel
S[k]
Lossy
Integrator
v[k] 34.934.95 35 35.0535.135.1535.2
-3
-2
-1
0
1
2
3
4
5
x 10
-3
t (s)
Amplitude


Input Signal
Reconstruction
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21. Introduction
ETADM
How can we combine event based sampling and speech coding
techniques?ADM
Encoder
v[k]
Step Size Transmit if z[k]¹0
Event
Triggering
S[k]
Lossy
Integrator
v[k]
Event Based Sampler
z[k] Communication Network
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22. Introduction
ETADM
How can we combine event based sampling and speech coding
techniques?ADM
Encoder
v[k]
Step Size Transmit if z[k]¹0
Event
Triggering
S[k]
Lossy
Integrator
v[k]
Event Based Sampler
z[k] Communication Network
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23. Introduction
ETADM - Sample Output 4.9 4.95 5 5.05 5.1 5.15 5.2
-3
-2
-1
0
1
2
3
4
5
x 10
-3
t(s)
Amplitude


Input Signal
Reconstruction
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24. Introduction
Stability Theory
For a plant with continuous dynamics described by a set of ODEs
_x=f(x; u; w)
x2R
nx
is the system state,u2R
nu
the control input and
w2R
nw
an exogenous disturbance.nx; nu; nw2Z
+
The control signal with the network induced erroreis given by,
u=(x) +e
Assume Input to State Stability (ISS) w.r.t. inputseandwfor
_x=f(x; (x) +e; w)
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25. Introduction
Network Induced Error Bounds
The network induced errore=e+ex+euwill consist of
edue to delay2[0; max]
exdue to the reconstruction ofx
eudue to reconstruction ofu
u=(x(t)) +e(t) +ex(t) +eu(t);
e(t) =(x(t))(x(t))
=
Z
t
t
_
ds=
Z
t
t
@
@x
f(x; (x) +ex+eu; w)ds;
ex(t) =(x(t))(x(t));
eu(t) =

(x(t))(x(t)):
Now it is only a matter of nding the upper bounds (Teel 1998).
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26. Introduction
Stability Proof in Paper
Theorem 1
Proof of stability due to delay, error due to reconstruction ofxand
ufrom Razhumikhin type theorems.
Theorem 2
Proof of reconstruction error bound of ADMjeADMj smax(smax
is the maximum step size).
Theorem 3
Proof that reconstruction is possible only when the event triggering
thresholdeT=smin(sminis the minimum step size)
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27. Introduction
Example - Ship Roll Stabilizer Wave Disturbance
Communication
Network
Stabilizing Fin
Hull Dynamics
Ko
s +a.s+b
2
Gain
-K
SamplingSamplesReduction (%)Atten. (dB)
Periodic100000(benchmark) -33.601
MET 96509 3.49 -17.959
MBET 11724 88.28 -12.487
ETADM 20236 79.76 -20.221
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28. Introduction
Robustness to Packet Drops
The lossy integrator output (i.e., reconstructed signal) is given by,
xi[k] =
k
X
i=1
K
ki+1
S[i] +K
k
xi[0]:
SinceK <1, there existsn < ksuch that for the quantization
errorqe,
K
kn+1
Smaxqe:
TakingN:=kn+ 1,
xi[k]
k
X
i=kN+1
K
ki+1
S[i]:
For a reasonable estimate onlyNprevious samples are needed.
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29. Introduction
Error Attenuation 4.9 4.905 4.91 4.915 4.92 4.9254.93 4.935 4.94 4.945 4.95
0.011
0.0115
0.012
0.0125
0.013
t(s)
Amplitude


Input Signal
Reconstruction
The error has approximately equal area above and below the
input signal
IA Fourier series exists
IThe error harmonics are attenuated by a linear plant
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30. Introduction
Next Generation ETADM
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31. Introduction
Extremum Seeking Control with
Sporadic Packet Transmission
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32. Introduction
Extremum Seeking Control
Extremum Seeking Control is the process of stabilizing a plant
at anoptimum operating point.
It requires minimala prioriknowledge of the plant.
Capable of tracking changes in the plant.
IExample: Maximizing the torque output of an engine for
variations in the fuel air mixture of an engine
Has been used in dierent forms throughout history (LeBlanc
1922, Drapper and Li 1954) but formalized only after 2000
(Krstich and Wang 2000, Teel 2001, Tan et al. 2006, Nesic et
al. 2013)
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33. Introduction
Continuous Time ESC dx/dt = f(x,u)
y = g(x,u)
High Pass
Filter
Low Pass
Filter
Sensor
+
ε/(b*s)
b*sin(ωt)
u
n
Sinusoidal dither correlated with the plant output
Zero correlation at an optimum point
Non-zero correlation for a gradient
The integrator osets the input in the direction of the gradient
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34. Introduction
ESC Dynamical System Framework (Teel 2001) dx/dt = f(x,u)
y = g(x,u)
Controlleru
k+1
=F[uk,G(uk)]
An iterative optimization algorithm calculatesuk+1
ISteepest gradient (Teel 2001)
IShubert's algorithm (Nesic 2013)
Needs a sample of the output of the plant foreach iteration
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35. Introduction
Algorithm Comparison
Continuous Time ESC
Integrator output is constant at an optimum point
The dither and correlator are tightly coupled
ICan this be decoupled?
IIs there an alternative to correlation?
Indirect evaluation of constraints
ESC Dynamical System Framework
Any iterative algorithm can be used.
IIs it possible to implement an algorithm with sporadic
communication instead ofper iterationcommunication?
?????
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36. Introduction
The Solution dx/dt = f(x,u)
y = f(x,u)
DetectorSensor
Communication
Network Update u
k
C : f(u[i])<f(u
k)
u[i]
Dither
u[i]=u
k+a[i]
Sync Clock Sync Clock
Replace correlation with detection
Replace the integrator with a ditherupdate(uk+1=uk+a[i])
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37. Introduction
The Luus-Jaakola Algorithm
1: u[i]2R
nu
withu02 Fandr[i] =r02R
nu
2: (u0)
3: d[i]2R
nu
4: u[i] =uk+diag(d[i])r[i]
5:ifu[i]2 Fthen
6:fCheck if constraints are satisedg
7: (u[i])
8:if((u[i])< (uk))_(reset)then
9: fUpdate if abetter optimum valueis foundg
10: (uk+1) =(u[i]).
11: uk+1=u[i].
12:end if
13:end if
14: r[i+ 1] =F(r[i])(if(u)is multimodal)
15:
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38. Introduction
Unconstrained Implementation Sample
and Hold+
Uniform Dither
Detector
Control
Input
Discrete Time SignalUpdate Input (from Network)
u[i]
u
k
a[i]
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39. Introduction
Inequality Constraints and Well-posed Equality Constraints
Inequality Constraints
For every ditheru[i]check if inequality constraints are satised
If satised update a second sample and hold
Well-posed Equality Constraints
Modify the signal
Ane constraintsu1+u2+u3= 1andu13u2u3= 3
result inu1=u2+ 2andu3=2u21(onlyu2needs to be
dithered)
Nonlinear constraintu1= 2u
2
2
+u
2
3
results inu1by dithering
u2andu3.
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40. Introduction
Constrained Implementation Sample
and Hold
Sample
and Hold
Q=B[F(·)]
(Inequality)
+
Uniform
Dither
Detector
Control
Input
Discrete
Time Signal
Update Input
(from Network)
Update Input
u[i]
u
k
Y(·)YC(·,·)
YR(·)
û[i]
u[i]
u[i]
a[i]
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41. Introduction
Inequality Constraint Example
Minimize
(u) = 1:0316285 + 4u
2
12:1u
4
1+ 0:333u
6
1+u1u24u
2
2+ 4u
4
2
with_x=(u)5xandu1u20opt. at (-0.0898, 0.7126)u
1
u
2


-1 -0.5 0 0.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.5
1
1.5
2
2.5
3
3.5
4 0 20 40 60 80 100120140160180200
0
0.002
0.004
0.006
0.008
0.01
a) Disturbance
t
w
0 20 40 60 80 100120140160180200
-0.5
0
0.5
1
b) Control Inputs
t
u


u
1
u
2
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42. Introduction
Ill-posed (Manifold) Equality Constraints
For an ill-posed constraint (u)
Transform into a well posed space (if it exists)
u
2
1+ 2u
2
2= 1)u1= sin()andu2= cos()=
p
2
Taylor series approximation (a1) (from Manton 2002)
(uk+a) = (uk)
|{z}
=0
+a
T
r (uk) +
1
2
a
T
H[ (uk)]a+H.O.T
|{z}
0
Findasuch that
k(a)k= min
a




a
T
r (uk) +
1
2
a
T
H[ (uk)]a




!0
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43. Introduction
Ill-posed (Manifold) Equality Constraints (Contd..)
Perturb by radiusrand nd projection to (u)
Find the vector of angles
=

12: : : n1

T
2 FR
n1
such that,
k()k= min

k (uk+r)k !0
where
=
2
6
6
6
6
6
4
cos(1)
cos(2) sin(1)
: : :
cos(n1)
Q
n2
j=1
sin(j)
Q
n1
j=1
sin(j)
3
7
7
7
7
7
5
2R
n
Both the Taylor series approximation and projection method
are inquasireal time
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44. Introduction
Inequality Constraint Example
Minimize
(u) = (u11)
2
+ (u21)
2
with_x=(u)10x
and (u) = (u
2
1+u
2
21)
3
u
2
1u
3
2opt. at (1,1)0 5 10 15 20 25 30
-1
-0.5
0
0.5
1
1.5
t (s)
u(t)
a) Projection Method


0 5 10 15 20 25 30
-1
-0.5
0
0.5
1
1.5
t (s)
u(t)
b) Taylor Series Approximation


u
1
u
2
u
1
u
2
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45. Introduction
Multimodal Optimization
Decrement search radius using down counterc[i] =cmax
down to 1 with each iteration
a[i] =
c[i]
cmax
[original dither]
Tested on 11 benchmarkR
n
functions against Simulated
Annealing and Random Optimization
Algorithm
MeanR
n
Success (%)
2 3 4 5 10
LJES-GDD 96.68 91.66 65.44 52.02 5.27
RO (= 0:6) 82.11 75.73 35.44 1.84 0.00
RO (= 8:3) 37.37 29.65 25.41 17.54 1.34
RSA (Boltz) 88.67 63.13 30.75 18.53 0.07
RSA (Fast) 91.95 50.13 21.68 10.99 0.00
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46. Introduction
Pump Controller Implementation Pump
Flow SensorController
Flow TransportDriver
Network PumpSensor
DriverSwitch
Tx Node
Rx Node
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47. Introduction
Pump Controller Objective Function 0 0.10.2 0.30.4 0.50.60.7 0.80.9 1
0
0.5
1
1.5
2
2.5
3
3.5
Duty Cycle
Flow (l/min) 0 0.10.2 0.30.4 0.50.60.7 0.80.9 1
0
5
10
15
20
25
Duty Cycle
Obj. Func.


F1
F2
F3
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48. Introduction
Pump Controller Performance 5700 5750 5800 5850 5900 5950 6000 6050 6100
0
0.02
0.04
0.06
0.08
0.1
0.12
a) ESC Tracking
t (s)
Duty Cycle


5700 5750 5800 5850 5900 5950 6000 6050 6100
2
2.2
2.4
2.6
2.8
3
b) Pump Output
t (s)
Flow (l/min)
dither
u
k
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49. Introduction
Pump Controller Results
Controls a PWM (u) range from 1-255
Sensor output (y) from 0-25
Dithers amplitude range25
TS= 2sand run for 2h (3600 samples)
Objective function
(u) =yu=4
Generated 107 packets (reduction of 97.02%)
Need to incorporate robustness to packet drops and delay
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50. Introduction
Conclusions
For dynamical systems
IThe use of the passive lossy integrator in ETADM and
NG-ETADM results in systems that are robust to packet drops
compared to MBET
IThe periodic cycle structure of the error enables error
attenuation by a linear plant
For ESC
IUsing the Luus-Jaakola algorithm, sporadic packet transmission
can be implemented instead of per iteration transmission
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51. Introduction
Future Work and Open Problems
Information rate analysis of ETADM, MBET etc.
Trac models for NCS
IJitter models
ISelf similarity models for congestion management
Security of NCS
Improvements for the LJES
IEcient metaheuristics
IHandling packet drops and delay
IApplication to multiobjective optimization and dynamic games
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52. Introduction
Thank You!
Thank You!
Questions?
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