1
Implementation of adaptive control
algorithm based on SPOC form
Winter 2011
Supervisor:
Submitted by:
Dr. Ilan Rusnak
Ofer Rosenberg
Roy Mainer
2
Project Background
• Why do we need adaptive control?
• What is an SPOC form?
• What was accomplished in previous projects?
▫ Implementations of linear systems identification
algorithms – in simulations and based on
recorded data – not real time
▫ Different algorithms returned different results
when applied on the same system. Which is
correct?
3
Project Goals
• Implementation of SPOC form adaptive control
algorithm – in REAL TIME
• Observation and measurement
• Conclusions
4
System Hierarchy
Linear
motion
system
Dspace
interface
Matlab +
Simulink
5
Project Development Steps:
• Introduction to the linear motion system and the
Dspace interface.
• Understanding and repeating the results of
previous related projects.
• Implementation of the SPOC algorithm in
Simulink.
• Test the algorithm on both simulation and real
time.
• Gathering results and conclusions.
6
The SPOC Simulink blocks
implementation
Constant5
Ce
eye(3)
Constant
diag(ones(1,2),1)
Constant1
In1
-K-
Constant3
Product2
zeros(3)
1
Qe
Math
Product3
Function
Matrix
Concatenation1
uT
Matrix
Multiply
Matrix
Multiply
Matrix
Multiply
-CuT
Gain
Constant2
eye(3)
Ke
Matrix
Multiply
Add1
1
eye(9)
[1x9]
Add2
Product7
Inv
Add4
Product4
Math
Function1
1.2e-9
Ke
Re
-K-
Add3
Product5
P0
Product
Gain1
P0
1
z
1
Aed
Matrix
Concatenation2
2
eye(3)
Constant4
-KGain2
In2
Product1
1
Matrix
Concatenation3
Matrix
Multiply
2
Matrix
Multiply
Matrix
Concatenation
Ke
Product10
Matrix
Multiply
Matrix
Multiply
Product9
Add5
X0
1
Out1
1
z
X0
Product8
y
Add6
7
The SPOC Simulink blocks
implementation - continued
• Using matrix building blocks and algebra we
implement the SPOC algorithm.
• Process noise estimation vector (Qe block) is
constant.
8
Simulation and Real Time
• Once the SPOC block was complete, our work was
divided to two parts – simulation and real time.
• Simulation:
▫ Mainly based on simulated inputs and transfer
functions.
• Real Time:
▫ Linear systems transfer function estimated in real time
and recorded.
• Both methods estimate the transfer function during
run time!
9
Main System Simulink Diagram
(simulation)
UU
To Workspace3
Scope
In1 Out1
YY
YY
To Workspace4
State Space
Plant
SPOC
Subsystem
UU
In1
Out1
UU
In2
Sine Wave
states
Sine Wave1
X0
Add
Divide4
Sine Wave2
Kdc
SW
denominator
numerator
Acker
Gain
denom
num
0
denom
Constant8
1
When
openloop
gain=0
X states
In1
Out1
In2
In3
KX
Kc
Out2
ACKER
Subsystem
denom
num
Kc
In1
In2 Out1
In3
KDC
Subsystem
num
To Workspace1
denum
To Workspace2
Kdc
10
Main System Simulink Diagram
(simulation) - continued
• A 3rd order linear system requires an input
comprised of at least 3 non dependent signals.
• Input is fed to both the transfer function (also 3rd
order) and the SPOC block.
• Transfer function output is recorded and fed to the
SPOC block.
• The SPOC block outputs are the state space vector,
the numerators and denominators vectors.
• Other blocks: Acker and KDC are used to gain
stability by moving the poles to pre determined
locations and normalizing the system’s gain
respectively.
11
Simulation Results
Numerator Coefficients
Denominator Coefficient
Numerator Coefficients
Denominator Coefficients
2.5
0
b1
b2
b3
2
-0.5
-1
1.5
-1.5
-2
1
-2.5
0.5
a1
a2
a3
-3
0
0
10
20
30
40
50
60
time [sec]
70
80
90
100
-3.5
0
10
20
30
40
50
60
time [sec]
70
80
90
100
12
Simulation Results – continued
• Simulated transfer function:
• Estimated transfer function:
• Success!
13
Main System Simulink Diagram (real
time)
RTI Data
0
ENCODER
MASTER SETUP
Clock1
DS1104ENC_SETUP
1
shut down
at simulation
end
start simulation
with 0 inputs
for 10 sec.
One
Switch1
Mult
Switch2
4
5
3
UU
UU_norm
error
1
error
Divide4
pos_error
input gain
20
v el_error
DAC
to motor
Kp
0
limit
YY
0.012
Enc position
Zero
Enc delta position
1
DS1104ENC_POS_C1
YY
enc_scale_factor
Constant
SPOC
Subsystem
2
YY
Sine Wave1
YY
UU
Sine Wave
Add5
Multiport
Switch
Sine Wave2
Inv_Gain
Manual
Switch
In1
Out1
Kcx_gain
0/0.1/0.5/1
error
In2
0
Constant2
1
Sine Wave3
X0
states
xo
Switch
denominator
numerator
Pulse
Generator
num
denum
states_out
8
Chirp Signal
denum_out
7
states
In1
Out1
Kcx
In2
In3
Out2
ACKER
Subsystem
kc
1
Kcx_out
10
Kc_out
denum
num_out
6
Constant1
num
kc
0
Clock
0
In1
In2 Out1
In3
KDC
Subsystem
9
inv_gain_out
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Main System Simulink Diagram (real
time) - continued
• Based on the simulation schematic.
• Input switching to allow multiple choices and
stop the motor from reaching the rail end.
• Gain blocks based on previous empiric results.
• Dspace designated blocks:
• Inputs are fed to motor through Dspace D/A.
• Outputs (motor position on rail) is fed through
position feedback.
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Process noise estimation
vector
•
•
•
New Qe1
1e-6*diag([1 1 1
0 0 0 0 0 0 ]) + 1e-8*diag([ 0 0 0
110
•
0 1 1])
Clock
0
1e-6*diag([1 1 1
0 0 0 0 0 0 ]) + 1e-4*diag([ 0 0 0
The ratio Qe/Re affects the
estimated coefficients convergence
speed.
110
•
0 1 1])
Switch
Qe1
•
•
Re – Measurement noise
Qe – Process noise
Results show that high ratio
improves estimation speed while low
ratio reduces noise.
In simulation we have no
measurement noise so no need to
switch.
Convergence time is approximately
20 [sec] in real time.
After 20 [sec] the Qe vector is
switched to lower the ratio and
reduce the noise.
16
Real Time Results
Numerator Coefficients
Denominator Coefficient
Numerator Coefficients
Denominator Coefficients
250
150
200
100
a1
a2
a3
50
150
b1
b2
b3
100
0
-50
50
-100
0
-150
-50
-200
-100
-150
-250
0
10
20
30
time [sec]
40
50
60
-300
0
10
20
30
time [sec]
40
50
60
17
Numerator Coefficients convergence –
zoomed
Numerator Coefficients
250
200
150
b1
b2
b3
100
50
0
-50
-100
-150
5
10
15
20
time [sec]
25
30
18
Real Time Results – continued
• Estimated transfer function:
• Success?
▫ We have no reference to compare with…
19
Conclusions
Results table
Conclusions summary
Comparison
Parameter
Simulation
Real Time
Accuracy
Perfect
Convergence time
Very fast, 23 [sec]
without Qe
switching.
Noiseless
Transfer function
converged
successfully.
system might be of
higher order.
Also fast, 30 [sec]
with proper Qe.
Noise
Influence of closed
loop
None
Dramatic decrease
in noise after Qe
switching.
Influences the
estimation result
• Linear system was expected to
be of 3rd order. Results show it
is probably of higher order.
• High ratio of Qe/Re improves
convergence speed, while
lower ratio reduces noise.
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Articles Links
• The links will be opened from technion computers or any computer
who is registered to IEEE Xplore Digital Library.
• Real-Time Simultaneous State Estimation and Parameters
Identification of Linear Drive System with the SPOC based
Algorithm
• http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=00532255
• http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=721052
• http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4793065
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Tubes
 SPOC OPEN ZOOM
• http://www.youtube.com/watch?v=aFKcutmu7Jg&featu
re=g-upl
 SPOC OPEN LOOP
• http://www.youtube.com/watch?v=KeURm9FxpgA&fea
ture=g-upl
 SPOC ACKER GAIN 0.5 ZOOM
• http://www.youtube.com/watch?v=nv7UwoHDDZI&fea
ture=g-upl
 SPOC ACKER GAIN 0.5
• http://www.youtube.com/watch?v=He0nM6c7g14&feat
ure=g-upl
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Bibliography
• “Real-Time Simultaneous State Estimation and
Parameters Identification of Linear Drive
System with the SPOC based Algorithm” \ Dr. Ilan Rusnak (article)
• "Feedback Control of Dynamic Systems 6th Ed." \ Gene F. Franklin, J
David Powell, Abbas Emami-Naeini (681.516)
• "Linear Control System Analysis and Design with Matlab 5th. Ed" \ John j.
D'azzo, Stuart N. Sheldon (681.511)
• “Control for Unstable Nonminimum Phase Uncertain Dynamic Vehicle” \
Dr. Ilan Rusnak (article)
• “State Observability and Parameters Identifiability of Stochastic Linear
Systems” \ Dr. Ilan Rusnak (article)
• “Simultaneous State Observability and Parameters Identifiability of
Discrete Stochastic Linear Systems” \ Dr. Ilan Rusnak
• Internet and especially Wikipedia
• Project book by Gil Kanashty:
."‫• "יישום אלגוריתמי זיהוי של מערכות ליניאריות על מערכת מעבדתית‬
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Special thanks
Dr. Ilan Rusnak
Koby Kochai
Orly Vigderzon
Gil Kanashty
24
Thanks for watching
Ofer Rosneberg
Roy Mainer
25
Adaptive Control (Wikipedia)
• “Adaptive Control is the control method used
by a controller which must adapt to a controlled
system with parameters which vary, or are
initially uncertain”.
• For example, as an aircraft flies, its mass will
slowly decrease as a result of fuel consumption;
a control law is needed that adapts itself to such
changing conditions.
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SPOC Algorithm
• SPOC – States and Parameters Observability
Canonical Form.
• SPOC algorithm is another method of estimating
the transfer function of a system.
• By representing the observer canonical form of a
3rd order linear system, we can isolate the
condition for stability.
• That condition can be solved using Kalman
filter.
27
Linear Motion System
•
•
•
•
Our linear motion system is based on
a DC motor, traveling back and forth
across the rail.
The DC system has speed and even
acceleration feedback.
The motor is controlled by the
computer via the Simulink
implemented controller.
This system was believed to be of 3rd
order.
28
Acker Block
2
In2
(1
0
0)
col 1
(0
1
0)
Matrix
Multiply
2
col 2
Matrix
Concatenation4
2
Product13
Out2
Matrix
Multiply
Terminator
Product12
Product14
kx
[ 1 1.2 0.47 0.06]
To Workspace2
pvv -required closed
loop polynomial
Product11
Ce1
We changed the coefficients
of the polynom.
The algorithem didn't
work for fast poles!
Scope1
eye(3)
[0 0 1]
Constant6
Product6
plv
1
In1
Inv
Divide1
num
Matrix
Multiply
3
Product17
In3
Matrix
Multiply KX
Product18
KX
To Workspace1
num
num
Matrix
Multiply
Out1
Product15
num
Matrix
Multiply
Product16
2
controlability matrix
kxx
1
29
Real-Time Simultaneous State Estimation and Parameters
Identification of Linear Drive System with the SPOC based
Algorithm
30
Real-Time Simultaneous State Estimation and Parameters
Identification of Linear Drive System with the SPOC based
Algorithm - continued
31
Real-Time Simultaneous State Estimation and Parameters
Identification of Linear Drive System with the SPOC based
Algorithm - continued