Fuel Cell Reformer Control Karel Schnebele May 5, 2006 - PowerPoint PPT Presentation

Fuel Cell Reformer Control Karel Schnebele May 5, 2006

Presentation Outline � Introduction � Development of the state space model � Modeling the system � SISO control � Multivariable control � RGA analysis and pairing � Disturbance rejection � Directional sensitivity

Introduction � Purpose: create final project � Model � Steam reformer for residential fuel cell plant � From Jahn and Schroer, 2005

Development of State Space Model: Model Component Relationships Single lines depict heat transfer (solid is conduction, dashed is radiation), double lines depict the burner gas flow, and triple lines depict the reformate gas flow.

Development of State Space Model: Dynamic Equations ⋅ dT ( ) ( ) ( ) = − − − − ⋅ − W C k T T k T T c n T T B W GW G W WA W A p , B W A dt ⋅ ( ) ( ) ( ) dT = − − − + ⋅ ⋅ − G C k T T k T T k c n T T F G BG B G GW G W FG p , F F G dt ( ) ⋅ dT ( ) ( ) ( ) = − − ⋅ − − − − − 4 4 B C k T T c n T T k T T k T T B B FB F B p , B B W BR B R BG B G dt ( ) ⋅ ⋅ ⋅ dT ( ) ( ) = − + ⋅ − − ⋅ − ⋅ − E C k T T c n T T r n c n T T F H O , i H O E RE R E p , F R E p , H O E H O 2 2 dt 2 2 ( ) ⋅ ( ) − ⋅ − − − c n T T k T T CH p , CH E CH EA E A 4 4 4 ( ) ⋅ dT ( ) ( ) = − − − + ⋅ − 4 4 R C k T T k T T c n T T F , R BR B R RE R E p F FG R dt ⋅ ⋅ ⋅ ⋅ ( ) ( ) − Δ ⋅ Δ − Δ ⋅ Δ − ⋅ − − ⋅ − h n h n c n T T c n T T 0 1 H O CH 0 1 p , H O R E p , CH R E 2 4 2 4

Development of State Space Model: Changing nCH4i 1300 Tw Tg initial methane flow=15 SLPM 1200 Tb Te steam to carbon ratio=3.5 1100 Tr excess air ratio=5 1000 Temperature (K) 900 1600 Tw 800 Tg Tr =754.7771 Tb 1400 Te =993.785 700 Te Tb =487.445 Tg =368.1042 Tr 600 Tw =151.937 1200 Temperature (K) 500 1000 400 0 100 200 300 400 500 600 700 800 900 time (sec) initial methane flow rate=10 SLPM 800 Tr =898.7824 Te =1208.8189 steam to carbon ratio=3.5 Tb =577.0143 Tg =428.0062 600 Tw =172.8318 excess air ratio=5 400 0 100 200 300 400 500 600 700 800 900 time (sec)

Development of State Space Model: Changing Steam to Carbon Ratio 1300 Tw 1200 Tg Tb initial methane flow rate=10 SLPM Te 1100 steam to carbon ratio=4 Tr 1000 excess air ratio=5 Temperature (K) 900 1400 Tw 800 1300 Tg Tr =709.2319 Tb 1200 Te =916.397 Te 700 Tb =464.8156 Tr Tg =352.8994 1100 600 Tw =146.5796 Temperature (K) 1000 500 900 400 800 0 100 200 300 400 500 600 700 800 900 Tr =807.7388 time (sec) Te =1069.7957 700 Tb =517.3146 initial methane flow rate=10 SLPM Tg =388.0229 600 Tw =158.9264 steam to carbon ratio=3 500 excess air ratio=5 400 0 100 200 300 400 500 600 700 800 900 time (sec)

Development of State Space Model: Changing Excess Air Ratio 1400 Tw Tg 1300 Tb Te initial methane flow rate=10 SLPM 1200 Tr 1100 steam to carbon ratio=3.5 Temperature (K) 1000 excess air ratio=5 900 1300 800 Tw Tr =907.7055 Tg 1200 Te =1124.999 700 Tb Tb =666.8927 Te Tg =487.5032 1100 600 Tw =213.1884 Tr 1000 500 Temperature (K) 900 400 0 100 200 300 400 500 600 700 800 900 time (sec) 800 Tr =754.7771 initial methane flow rate=10 SLPM Te =993.785 700 Tb =487.445 steam to carbon ratio=3.5 Tg =368.1042 600 Tw =151.937 excess air ratio=4 500 400 0 100 200 300 400 500 600 700 800 900 time (sec)

Development of State Space Model: Specified values � Reformer temp = 700 deg C � Steam to carbon ~ 3.5 � Methane flow rate ~ 10 SLPM

Development of State Space Model: Output Temperatures 1200 Tw Tg 1100 Tb Te 1000 Tr 900 Methane flow rate = 9.5 SLPM Temperature (K) Steam to carbon=3.0076 800 Excess air ratio=5 Tr =700.003 Te =897.0203 700 Tb =460.524 Tg =350.0323 600 Tw =145.5671 500 400 0 100 200 300 400 500 600 700 800 time (sec)

Development of State Space Model: States, Inputs, and Outputs − ⎡ ⎤ ⎡ ⎤ x T T 1 W Ws ⎢ ⎥ ⎢ ⎥ − x T T ⎢ ⎥ ⎢ ⎥ 2 G Gs ⎢ ⎥ ⎢ ⎥ = − States = x T T 3 B Bs ⎢ ⎥ ⎢ ⎥ − ⎢ x ⎥ ⎢ T T ⎥ 4 E Es ⎢ ⎥ ⎢ ⎥ − ⎣ ⎦ ⎣ ⎦ x T T 5 R Rs λ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ u excess air ratio ( ) g y T = = = 1 1 1 B Inputs = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Outputs = ⎣ ⎦ ⎣ ⎦ u nv ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ g y T 2 2 2 R

Development of State Space Model: Matrices = + & x ' Ax ' Bu ' = + y ' Cx ' Du ' ∂ ∂ f f = = i i B A ∂ ∂ ij ij u x j j ∂ ∂ g g = = i D i C ∂ ij ∂ ij u x j j

Development of State Space Model: Matrices ⎡ ⎤ − × − 4 0 . 001593 7 . 098 10 0 0 0 ⎢ ⎥ − 0 . 002115 0 . 004911 0 . 0018443 0 0 ⎢ ⎥ ⎢ ⎥ = − − A 0 . 034462 0 . 020455 0 . 058625 0 0 . 008232 ⎢ ⎥ − ⎢ ⎥ 0 0 0 0 . 00472 0 . 004436 ⎢ ⎥ × − − 4 ⎣ ⎦ 0 0 1 . 4285 10 0 . 004675 0 . 007322 − − ⎡ ⎤ 0 . 02424 25 . 888 ⎢ ⎥ 0 . 14687 156 . 0762 ⎢ ⎥ ⎡ ⎤ ⎡ ⎤ 0 0 0 0 1 0 0 = ⎢ ⎥ = − − = ⎢ ⎥ D B 2 . 0898 2032 . 8766 ⎢ ⎥ C ⎣ ⎦ ⎢ ⎥ 0 0 ⎣ ⎦ 0 0 0 0 1 − − 0 . 05429 57 . 6894 ⎢ ⎥ ⎢ ⎥ − − ⎣ ⎦ 0 . 075294 80 . 0119

Development of State Space Model: Final Subsystem Uniform Random Number2 1 -C- lambda 5 Constant4 Constant1 1 Tb x' = Ax+Bu y = Cx+Du -C- State-Space1 2 Constant2 nv 2 Tr -C- -C- Constant3 Product Constant Uniform Random Number3

Development of State Space Model: Subsystem in Large System Tb lambda Tb excess air ratio burner temp nv Tr Tr methane flow rate Subsystem3 reformer temp

Model Development Temperature responses to excess air ratio change of 0.5 465 705 700 460 695 Tb (deg C) 455 Tr (deg C) 690 450 Lead-lag 685 First order 445 680 440 675 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Time (sec) Time (sec) 8 Methane Flow Rate to Burner (SLPM) 5.6 7.5 5.4 Excess Air Ratio 7 5.2 6.5 5 6 4.8 5.5 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Time (sec) Time (sec)

Temperature responses to a methane flow rate change of 0.5658 SLPM 465 705 700 460 695 455 Tb (deg C) Tr (deg C) 690 Lead-lag 450 685 First order 445 680 440 675 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Time (sec) Time (sec) 6 7.3 Methane Flow Rate to Burner (SLPM) 7.2 5.5 7.1 Excess Air Ratio 7 5 6.9 6.8 4.5 6.7 6.6 4 6.5 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Time (sec) Time (sec)

Model Parameters First order equation: Lead-lag equation: ⎛ ⎞ τ + s 1 kp ⎜ ⎟ = = n g kp g ⎜ ⎟ τ + p τ + p s 1 ⎝ ⎠ s 1 p p Δ Δ y y = = kp kp Δ Δ u u τ = τ n τ time when 63.2% of change occurs iterate to find , p p Process Transfer Functions ( ) ( ) + + ⎡ ⎤ 500 sec 1 520 sec 1 s s − ° − ° 28 . 548 C 19 . 39 C ⎢ ⎥ ( ) ( ) ⎡ ⎤ ⎡ ⎤ + u 1 y 1 400 sec s 400 sec s 1 = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ − ° − ° 45 . 506 C 35 . 69 C ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ u 2 y 2 ( ) ( ) ⎢ ⎥ + + ⎣ ⎦ 730 sec s 1 710 sec s 1

Process vs Model Model and process responses to setpoint change in excess air ratio 465 705 700 460 695 Tb (deg C) 455 Tr (deg C) 690 450 685 445 680 440 675 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Time (sec) Time (sec) 6 8 Methane Flow Rate to Burner (SLPM) 7.5 Excess Air Ratio 5.5 7 6.5 5 6 4.5 5.5 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Time (sec) Time (sec)

Process vs Model Model and process responses to setpoint change in methane flow rate 465 705 700 460 695 455 Tb (deg C) Tr (deg C) 690 450 685 445 680 440 675 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Time (sec) Time (sec) 6 7.3 Methane Flow Rate to Burner (SLPM) 7.2 5.5 7.1 Excess Air Ratio 7 5 6.9 6.8 4.5 6.7 6.6 4 6.5 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Time (sec) Time (sec)

SISO Controller Development: IMC-based PID control strategy PI controller w/ disturbance rejection PI controller w/ filter term for for first order transfer functions lead-lag transfer functions ⎛ + ⎞ ⎛ + ⎞ ⎛ ⎞ 1 ⎜ ⎟ = 1 1 ⎜ ⎟ ⎜ ⎟ = g kc 1 ⎜ ⎟ g kc 1 ⎜ ⎟ ⎜ ⎟ τ c ⎝ ⎠ τ τ + s c ⎝ ⎠ ⎝ ⎠ s s 1 I I F τ p − λ = 2 τ kc = p kc λ kp λ kp τ λ − λ 2 τ = τ τ = τ 2 τ = p I p F n τ I p