Temperature Modelling and Control of the Biomass Pretreatment Process Remus Mihail Prunescu NPCW-17 26 January 2012
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Agenda 𝜕 𝜌𝑐𝑇
𝜕𝑡+ 𝛻𝑇 𝜌𝑐𝒖𝑇 = 𝛻𝑇 Γ𝑐𝛻𝑇 + 𝑆𝑇
Temperature
Modelling
Questions?
Classical and Advanced Control*
Project Description
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𝑢𝑅𝑛 = Δ𝑡[ 1 − 𝜃 𝑣𝑇
𝑛+1 + 𝜃𝑣𝑇𝑛] The Inbicon Demonstration Plant
Process Description I
Bio-Ethanol (144 kg) C5 Molasses (371 kg) Bio-Pellets (435 kg)
End Products
Pretreatment
Thermal Reactor Steam
Wheat Straw (1 ton)
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The Thermal Reactor Process Description II
𝐴 = 𝜋𝑟2
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Preliminary Analysis Temperature Modelling I
𝑓 𝑥 = 𝑎0 + 𝑎𝑛 cos𝑛𝜋𝑥
𝐿+ 𝑏𝑛 sin
𝑛𝜋𝑥
𝐿
∞
𝑛=1
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Computational Fluid Dynamics i Temperature Modelling II
Heat Convection-Diffusion Equation:
𝜕(𝜌𝑐𝑇)
𝜕𝑡+ 𝛻𝑇 Γ𝑐𝑢𝑇 = 𝛻𝑇 Γ𝑐𝛻𝑇 + 𝑆𝑇
𝜌𝑐𝜕𝑇
𝜕𝑡+ 𝜌𝑐𝑢𝑥
𝜕𝑇
𝜕𝑥=
𝜕
𝜕𝑥𝜅𝜕𝑇
𝜕𝑥+
𝜕
𝜕𝑦𝜅𝜕𝑇
𝜕𝑦+ 𝑆𝑇
: : ∫
𝜃
𝑎𝑃𝑛+1𝑇𝑃
𝑛+1 = 𝑎𝑃𝑛𝑇𝑃
𝑛 + 𝑎𝐸𝑛𝑇𝐸
𝑛 + 𝑎𝑊𝑛 𝑇𝑊
𝑛 +
+𝑎𝑆𝑛𝑇𝑆
𝑛 + 𝑎𝑁𝑛𝑇𝑁
𝑛 + 𝑎𝐸𝑛+1𝑇𝐸
𝑛+1 + 𝑎𝑊𝑛+1𝑇𝑊
𝑛+1 +
+𝑎𝑆𝑛+1𝑇𝑆
𝑛+1 + 𝑎𝑁𝑛+1𝑇𝑁
𝑛+1 + 𝑆𝑢
𝑎𝑃,𝑁,𝑆,𝐸,𝑊 = 𝑓(𝜃, 𝐷, 𝐹)
𝑎2 + 𝑏2 = 𝑐2
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Computational Fluid Dynamics ii Temperature Modelling II
𝑎𝑃𝑛+1 + 𝑎𝑁
𝑛+1
𝑎𝑃𝑛+1
𝑇𝑃𝑛+1 = 𝑎𝑃
𝑛 − 𝑎𝑁𝑛
𝑎𝑃𝑛
𝑇𝑃𝑛 +
+𝑎𝐸𝑛𝑇𝐸
𝑛 + 𝑎𝑆𝑛𝑇𝑆
𝑛 + 𝑎𝑊𝑛 𝑇𝑊
𝑛 + 𝑎𝐸𝑛+1𝑇𝐸
𝑛+1 +
+𝑎𝑆𝑛+1𝑇𝑆
𝑛+1 + 𝑎𝑊𝑛+1𝑇𝑊
𝑛+1 +
+𝑆𝑢 + 2𝑇𝑛 𝑎𝑁𝑛 + 𝑎𝑁
𝑛+1
𝑆𝑢
Boundary Conditions:
𝐄𝐓 𝑥 𝑇𝑛+1 = 𝐀𝐓𝑥 𝑇
𝑛 + 𝐁𝐓𝑢𝑇𝑛
State Space Model:
𝑥 + 𝑎 𝑛 = 𝑛
𝑘𝑥𝑘𝑎𝑛−𝑘
𝑛
𝑘=0
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Simulation Results Temperature Modelling III 𝑒𝑥 = 1 +
𝑥
1!+
𝑥2
2!+
𝑥3
3!+ ⋯
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PID Control (Results) Classical and Advanced Control I
𝐶 𝑠 = 𝐾𝑃 +𝐾𝐼
𝑠+ 𝐾𝐷𝑠
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LQRi (Results) Classical and Advanced Control II
𝑢 = −𝐾𝑥
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MPC (Results) Classical and Advanced Control III
minΔ𝑈𝑘
Φ =1
2 𝑦 𝑘+1+𝑗|𝑘 − 𝑟𝑘+1+𝑗|𝑘 𝑄
2𝑁−1
𝑗=0
+1
2 Δ𝑢𝑘+𝑗|𝑘 𝑆
2𝑁−1
𝑗=0
𝑢min < 𝑢𝑘+𝑗|𝑘 < 𝑢max
Δ𝑢min < Δ𝑢𝑘+𝑗|𝑘 < Δ𝑢max
1 + 2 = 3
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:-??!??-:
Questions? Something grey and funny that fits on a line :-?
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