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02_PreviewReview_for_CHE361W12

# 02_PreviewReview_for_CHE361W12 - CHE 361 PREVIEW MODELING...

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CHE 361: PREVIEW MODELING EQUATIONS - Ordinary Differential Equation Models from Mass and Energy Balances A. Develop equations: rate of accumulation and other rates B. Operating point: steady-state and deviation variables C. Linearization D. Laplace transforms E. Concept of a transfer function F. Solution of ODE models using numerical methods: Euler, Runge-Kutta and integration packages - linear vs. non-linear models. The "state-space" formulation for dynamics: state derivatives ˙x = f ( x , u ) nonlinear A x B u linear ODEs outputs y = g ( x ) nonlinear C x D d linear combination PROCESS CHARACTERISTICS - TRANSFER FUNCTION A. Classical first-order systems { K p , τ p , θ } and time behavior B. Classical second-order systems { K p , τ , ζ , θ } underdamped, critically damped and overdamped and time behavior C. Block diagram relationships: Overall transfer function, interacting systems D. Concepts of poles and zeros in the complex plane, RHP vs LHP , Im and Re axes. slow vs. fast poles, "effective" second or first order systems E. Time delay and the Pade’ approximation, lead-lag elements PHYSICAL DEVICES AND DATA ACQUISITION A. Standard instrumentation signal levels B Transmitters: linear vs. nonlinear steady-state calibration and gain C. Final control elements: control valve design and operations D. Sensor dynamics: e.g. G m (s) and use of K m in Fig 1 1 . 7 versus 1 1 . 8 PROCESS IDENTIFICATION / BEHAVIOR = Models Obtained from Experimental Data A.

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02_PreviewReview_for_CHE361W12 - CHE 361 PREVIEW MODELING...

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