1. Implementation of adaptive control algorithm based on SPOC form
Winter 2011
Supervisor: Dr. Ilan Rusnak
Submitted by: 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?
2) רקע: פרויקט המשך לגיל קנאשטי שבנה המערכת ומימש אלגוריתמי זיהוי אשר אחד מהם היה spoc (במטלב ולא בזמן אמת)
מהי בקרה אדפטיבית?
מהו Spoc?

3. Project Goals
Implementation of SPOC form adaptive control algorithm – in REAL TIME
Observation and measurement
Conclusions
3) מטרתנו לבצע שיערוך בזמן אמת ולהעריך את יכולת הזיהוי ואיכותו.

4. System Hierarchy
Matlab + Simulink
Dspace interface
Linear motion system
4) כאן ניתן לראות את המערכת אשר חילקנו למערכת ההינע הלינארית, ממשק ה Dspace אשר מורכב מפאנל וכרטיס במחשב וכן תוכנת cintrol desk ששימשה אותנו להקלטת המשוב ומשתני המצב וכלי הסימיולינק בו מימשונו את ה SPOC והמטלב בו נעזרנו להקלטות.

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.
5) כאן ניתן לראות את שלבי הפרויקט: הבנה של המערכת שיש לנו ביד מגיל (הנע לינארי) ופונקציית תמסורת של מנוע זרם ישר.
שחזור והבנה של תוצאות קודמות.
מימוש SPOC בסימיולינק
בדיקת האלגוריתם בסימולציה ואח"כ בזמן אמת
איסוף תוצאות והסקת מסקנות

6. The SPOC Simulink blocks implementation
ואת שלושת מקדמי המונה ושלושת מקדמי המכנה סה"כ וקטור באורך 9 כיוון שהמערכת מסדר 3 כפי ששערנו מה שהסתבר כטעות.

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.
7) רעש התהליך Qe ורעש המדידה Re הם פרמטרים אשר אנו פותרים באמצעותם את אי הודאות באמצעות מסנן קלמן. כאן Qe קבוע בעתיד אנו משנים אותו למשתנה וממותג בפעולה בRT .

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!
8) לאחר שמומש הבלוק של SPOC חולקה העבודה לסימולציה וזמן אמת:
בסימולציה יצרנו plant במרחב המצב מסדר 3 מהסיבות שהסברנו קודם וחיברנו את בלוק ה SPOC כך שישערך (יזהה)את פ' התמסורת אותה יצרנו.
בזמן אמת יצרנו לראשונה זיהוי של האלג' את פ' התמסורת של המערכת בזמן אמת ללא הקלטה של האות (וקטור משתני המצב).

9. Main System Simulink Diagram (simulation)

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

12. Simulation Results – continued
Simulated transfer function:
Estimated transfer function:
Success!

13. Main System Simulink Diagram (real time)

14. 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.

15. Process noise estimation vector
The ratio Qe/Re affects the estimated coefficients convergence speed.
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

17. Numerator Coefficients convergence – zoomed

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
Transfer function converged successfully.
system might be of higher order.
Convergence time
Very fast, 23 [sec] without Qe switching.
Also fast, 30 [sec] with proper Qe.
Noise
Noiseless
Dramatic decrease in noise after Qe switching.
Influence of closed loop
None
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.

20. 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

21. Tubes http://www.youtube.com/watch?v=aFKcutmu7Jg&featu re=g-upl
SPOC OPEN ZOOM
re=g-upl
SPOC OPEN LOOP
ture=g-upl
SPOC ACKER GAIN 0.5 ZOOM
ture=g-upl
SPOC ACKER GAIN 0.5
ure=g-upl

22. 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 ( )
"Linear Control System Analysis and Design with Matlab 5th. Ed" \ John j. D'azzo, Stuart N. Sheldon ( )
“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".

23. Dr. Ilan Rusnak Koby Kochai Orly Vigderzon Gil Kanashty
Special thanks
Dr. Ilan Rusnak
Koby Kochai
Orly Vigderzon
Gil Kanashty

24. Ofer Rosneberg Roy Mainer
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.

26. 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.
המערכת מורכבת ממנוע DC מסילה ומשוב (מיקום) באמצעות אינקודר. המנוע מקבל אות מהמחשב דרך יחידת הדיספייס (המרת D/A) ומגבר ההספק
המנוע מבוקר ע"י בקר הממוש בסימיוליק ומבוסס על פרויקט קודם
כתוצאה מלימוד שעשינו על מנוע זרם ישר אנו מניחים בפרויקט כי המערכת היא מסדר שלישי

28. Acker Block

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