Fractional Order Relay Feedback Experiments for MIMO Process Identification and Decoupling

1. Fractional Order Relay Feedback Experiments for MIMO Process Identification and Decoupling ZhuoLi PhD Student, EECS, UC Merced Member of the MESA Lab zli32@ucmerced.edu

2. Outlines • Background • Identification • The relay feedback technique • relay meets fractional calculus • relay meets fractional order systems • Decoupling • The experiment platform • When decoupling meet fractional order systems • Some random thinking

3. Background

4. MEMS Micro-electro-mechanical systems Inside an accelerometer http://memsblog.wordpress.com/2011/01/05/chipworks-2/

5. Nano fabrication, wafer processing Demand: High precision High yield Repeatability Efficiency Massive production Fabrication of SiCnano-pillars by inductively coupled SF6/O2 plasma etching J H Choi1,2, L Latu-Romain2, E Bano1, F Dhalluin2, T Chevolleau2 and T Baron2 2012J. Phys. D: Appl. Phys.45 235204 Challenges: Difficult to sense High nonlinearity Multi variable Synchronization

6. Mission for control engineers • Temperature • Pressure • Gas flow • RF power • etc …… • Advanced modeling techniques • Advanced control technologies

7. The relay feedback technique

8. The time line Astrom & Hugglund Relay feedback tuning Ramirez, R. W Use FFT for relay K.K Tan Modified Relay Z-N Critical Oscillation P feedback Luyben Using relay for identification W Li Relay with time delay CC Yu Biased relay J Lee et. al Relay with FO integrator behind A Leva Waller Two channel Relay 2011 1984 1985 1997 1987 1942 1996 1991 1992 1993 Astrom, 1984, Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins Luyben, 1987, Derivation of Transfer Functions for Highly Nonlinear Distillation Columns Li, 1991, An improved auto tune identification method ……

9. Varieties of relay feedbacks

10. The frequency response Im -180 Re Ideal Relay Relay with hysteresis 2 channel relay -90 Relay plus time delay Relay plus an integrator

11. When relay feedback meets with fractional order integrator

13. Block diagrams Relay with integer order integrator -H + - Relay with fractional order integrator

14. Varieties of relay feedbacks

15. The frequency response Im -180 Re Ideal Relay Relay with hysteresis 2 channel relay Relay plus an FO integrator -90 Relay plus time delay Relay plus an integrator

16. The frequency response Im -180 Re Ideal Relay Relay with hysteresis 2 channel relay Relay plus an FO integrator -90 Relay plus time delay Relay plus an integrator

18. Simulation Eg.1

19. Simulation Eg.2 R. K. WOOD and M. W. BERRY Model “Terminal composition control of a binary distillation column” 8

20. Advantages • Wider phase range • Phase can be predetermined , • Non-zero initial part (efficient) Save a quarter cycle time ! Think about some slow processes e.g. distillation column Relay with time delay Relay with FO integrator

21. When relay feedback meets with fractional order system

22. Equations for relay identification

23. Simulation

24. Experimental implementation Raw Data from Platform on slide 27 Identified by curve fitting Using Dr.Podlubny’smlf Identified by relay feedback Order scanning

25. Future work • Other model structures • Using relay transient

26. The experiment platform

27. The development highlights Peltier • Thermoelectric modules • H-bridge, heating/cooling • IR thermo meters • Two inputs four outputs • Real-time control • Product of multiple failures Metal plate IR Thermometers Power Peltier I2C Bus Arduino MOSFET Serial PC (Matlab) Side product

28. The hardware configuration Heat sink Peltier Load Electric power Heat

29. A video demo

30. The four modes

31. Performance testing • PID control with anti-windup • Testing with actuator only having cooling capability Set point Control signal Temperature

32. The non-minimum phase temperature data Fitting using fractional order model Commemorate order Fitting using second order model [K T1 T2 T3] = [2716 -877 349.3 -6.1] [K T1 T2 T3] = [1.7048 198.8152 53.7816 -39.3604]

33. Decoupling

35. The conventional techniques

36. Conventional Decoupling • Ideal decoupling • Simple decoupling • Inverted decoupling

37. Example – simplified decoupling • System • Decoupler • D

38. Example – modified simplified • System • Decoupler • D

39. What if the process is fractional order

40. Fractional order decoupler

41. Random thinkings

42. Another example Credit: Dr.RichardMigan Zhuo Li

43. Some diffusion data

44. Temperature in a sealed room – bounded diffusion • Half order plus delay • Using NILT/Mittagleffler • [K T L] = 2.1232 22.8021 9.7312 • Fitting error (least mean squares): 0.0700 • Half order plus delay • Using NILT/Mittagleffler • [K T L] = 6.0031 5.2222 14.7917 • Fitting error (least mean squares): 0.2214

45. Thank you