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02_Modelling_E2009 - 28150 Introduction to proces control 2...

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1 28150. Introduction to proces control 2. First principles process modelling Krist V. Gernaey 31 August 2009 28150 Learning objectives • At the end of this lesson you should be able to: – Create, in a structured step-wise fashion, a first-principles dynamic model for a process – Implement and simulate the model (exercises, next week!) 31 August 2009 28150 Outline • Introduction • Model development principles • Degrees of freedom analysis • A systematic model development approach • Modelling examples 31 August 2009 28150 Outline Introduction • Model development principles • Degrees of freedom analysis • A systematic model development approach • Modelling examples
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2 31 August 2009 28150 What is a model? • A model (M) for a system (S) and an experiment (E) is anything to which E can be applied in order to answer questions (P) about S (Minsky, 1965) S P M E 31 August 2009 28150 Different models • Physical model of a system – Pilot plant • Mathematical model of a system – Equations – Graphs • Linguistic model of a system – Example: If substrate is available, dissolved oxygen consumption of the biomass will increase 31 August 2009 28150 What is a first principles model? • A model developed using the principles of chemistry, physics and biology (conservation laws) • ’first engineering principles model’, ’theoretical model’, ’deterministic model’, ’white box model’ • Steady-state model versus unsteady-state model ( dynamic model ) 31 August 2009 28150 Model classification First engineering principles models Empirical (black Box )models Semi- empirical (grey box) models Process data Process knowledge Neural network, ARX, ARMAX, etc.
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3 31 August 2009 28150 Properties of first principles models • Model complexity must be determined (assumptions), depends on model purpose • Can be computationally expensive (not real-time) • May be expensive/time-consuming to obtain • Good for extrapolation, scale-up • Does not require experimental data to obtain (data required for validation and fitting) 31 August 2009 28150 Properties of black-box models • Large number of unknown parameters • Can be obtained quickly (e.g., linear regression) • Model structure is subjective • Dangerous to extrapolate 31 August 2009 28150 Properties of grey-box models • Compromise of first two approaches • Model structure may be simpler • Good versatility, can be extrapolated • Can be run in real-time 31 August 2009 28150 The use of a model Real world problem Mathematical problem Mathematical solution Interpretation of solution
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4 31 August 2009 28150 Outline • Introduction Model development principles • Degrees of freedom analysis • A systematic model development approach • Modelling examples 31 August 2009 28150 Model development principles Conservation of mass Conservation of component i { } { } out mass of rate in mass of rate mulation mass of accu rate - = + - = produced i component of rate out
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