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 :-?