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Zhuo Li PhD Student, EECS, UC Merced Member of the MESA Lab zli32@ucmerced.edu 6/12/2013

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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 2

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Background 3

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

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Nano fabrication, wafer processing 5 Demand: High precision High yield Repeatability Efficiency Massive production Challenges: Difficult to sense High nonlinearity Multi variable Synchronization Fabrication of SiC nano-pillars by inductively coupled SF 6 /O 2 plasma etching J H Choi 1,2, L Latu-Romain 2, E Bano 1, F Dhalluin 2, T Chevolleau 2 and T Baron 2 2012 J. Phys. D: Appl. Phys. 45 235204

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

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The relay feedback technique 7

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1942 Z-N Critical Oscillation P feedback 1984 Astrom & Hugglund Relay feedback tuning Luyben Using relay for identification 1997 Waller Two channel Relay 1987 1996 K.K Tan Modified Relay CC Yu Biased relay 1992 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 identication method …… Ramirez, R. W Use FFT for relay 1985 1991 W Li Relay with time delay 8 The time line A Leva 1993 2011 J Lee et. al Relay with FO integrator behind

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Varieties of relay feedbacks 9 Relay typeProcess phasePhase pre-knowDescribing functionPhase shift range IdealYesOne point No3 rd and 4 th quadrant Yes3 rd and 4 th quadrant Same as above--- YesOne point ---- TC relayYes3 rd quadrant Biased ideal relayYesOne point Biased with hysteresis No-3 rd and 4 th quadrant

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

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When relay feedback meets with fractional order integrator 11

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

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Varieties of relay feedbacks 14 Relay typeProcess phasePhase pre-knowDescribing functionPhase shift range IdealYesOne point No3 rd and 4 th quadrant Yes3 rd and 4 th quadrant Same as above--- YesOne point ---- TC relayYes3 rd quadrant Yes3 rd and 4 th quadrant Biased ideal relayYesOne point Biased with hysteresis No-3 rd and 4 th quadrant

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

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

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Simulation Eg.1 AToTError (%)L Ideal0.0970.391.62318.860.099 Hysteresis0.3831.5521.62418.790.201 Delay0.8463.6121.63218.40.135 Integrator0.72.8531.58920.530.126 TC0.1950.7432.1839.160.099 FO int0.1330.5361.62718.650.102

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Simulation Eg.2 AToTError (%)L 0.10.8534.4213.419.731.03 0.31.095.713.5319.011.06 0.51.57.8613.5418.911.1 0.72.2912.113.5518.871.18 0.93.8120.513.5718.721.29 1.17.174213.6418.312 1.310.881.814.811.43.25 1.411.911116.471.351.05 1.512.514819.6317.562.1 1.612.719624.9849.561.43 1.712.824330.5182.687.62 1.812.823529.4476.3113.2

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Advantages 20 Relay with time delayRelay with FO integrator Save a quarter cycle time ! Think about some slow processes e.g. distillation column

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When relay feedback meets with fractional order system 21

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Equations for relay identification For integer order systemsFor fractional order system (Proposed method) Equations for IO are special cases of those for FO 22

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Simulation 23 Ideal relay With delay With integrator With hyst 0.7049 1.23691.0962 0.9002 2.4520 8.19606.2240 4.1150 13.9949 14.219814.0771 14.0679 Error 16.2% 14.85%15.71% 15.76% L 0.9314 1.09450.8251 1.1830

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Experimental implementation 24 Order scanning Raw Data from Platform on slide 27

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Future work Other model structures Using relay transient 25

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The experiment platform 26

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The development highlights Thermoelectric modules H-bridge, heating/cooling IR thermo meters Two inputs four outputs Real-time control Product of multiple failures 27 Power I 2 C Bus Arduino Serial PC (Matlab) PC (Matlab) IR Thermometers MOSFET Side product

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The hardware configuration 28 Load Heat sink Peltier Electric power Heat

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A video demo 29

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The four modes Power on cooling – heat pumpingPower off cooling – annealing/natural dissipation Power on heating – electrical heatingPower off heating – thermo cycle 30

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

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

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Decoupling 33

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The conventional techniques 35

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Conventional Decoupling Ideal decoupling Simple decoupling Inverted decoupling 36

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Example – simplified decoupling

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Example – modified simplified

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What if the process is fractional order 39

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Fractional order decoupler 40

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Random thinkings 41

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Another example 42 Credit: Dr.Richard Migan Zhuo Li

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Some diffusion data 43

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Temperature in a sealed room – bounded diffusion 44

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Thank you 45

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46 Hided

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