Implementation of adaptive control algorithm based on SPOC form Winter 2011 Supervisor: Dr. Ilan Rusnak Submitted by: Ofer Rosenberg Roy Mainer

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?

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.

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.

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

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.

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 .

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).

Main System Simulink Diagram (simulation)

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.

Simulation Results Numerator Coefficients Denominator Coefficient

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

Main System Simulink Diagram (real time)

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.

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.

Real Time Results Numerator Coefficients Denominator Coefficient

Numerator Coefficients convergence – zoomed

Real Time Results – continued Estimated transfer function: Success? We have no reference to compare with…

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.

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

Tubes http://www.youtube.com/watch?v=aFKcutmu7Jg&featu re=g-upl 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

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".

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

Ofer Rosneberg Roy Mainer Thanks for watching Ofer Rosneberg Roy Mainer

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.

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.

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

Acker Block

Real-Time Simultaneous State Estimation and Parameters Identification of Linear Drive System with the SPOC based Algorithm

Real-Time Simultaneous State Estimation and Parameters Identification of Linear Drive System with the SPOC based Algorithm - continued

Real-Time Simultaneous State Estimation and Parameters Identification of Linear Drive System with the SPOC based Algorithm - continued