process_models

# process_models - Dynamic Process Models 1 Conversion...

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Unformatted text preview: Dynamic Process Models 1. Conversion between model types 2. Nonlinear model linearization 3. State-space models 4. Transfer function models 5. Matlab/Simulink examples Conversion Between Model Types First Principles Model Linearization State-Space Model Transfer Function Model Laplace transform Realization Linear Nonlinear Theoretical Process Models ● Conservation equations » Fundamental basis for model development » Mass, energy and momentum conservation » Nonlinear ODEs ● Constitutive equations » Semi-empirical relations required to complete model » Reaction rates, heat transfer rates, etc. » Nonlinear algebraic equations ● Parameter estimation » Needed to determine unknown parameters » Reaction rate constants, heat transfer coefficients, etc. » Yields parameter values that best fit available data ● Focus of ChE 361 Nonlinear Model Linearization ● Nonlinear ODE model ● Find steady-state point ● Linearize about steady-state point ● Yields linear ODE model in deviation form ● Covered in ChE 361 R u R x u x f dt dx ∈ ∈ = ) , ( ) , ( u x f = ' ' ' ' ) , ( ' ) , ( ) , ( bu ax u u f x x f u x f dt dx u x u x + ≡ ∂ ∂ + ∂ ∂ + 2245 Isothermal CSTR Example ● Nonlinear ODE model ● Find steady-state point ) , ( ) ( 2 2 Af A A A Af A k C C f kC C C V q dt dC B A =-- = → 1 2 3 1 ) 1 )( 2 ( ) 2 )(...
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process_models - Dynamic Process Models 1 Conversion...

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