Notes-2A

# Notes-2A - Chapter 2 Modeling and Simulation Dynamic Model...

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Chapter 2 Modeling and Simulation Dynamic Model: mathematical description of the process. Typically, a set of differential equations. These equations can be Nonlinear Time Varying and Infinite Dimensional. In this course, we consider a special class of approximations: Linear Time Invariant (LTI) processes. Models can be given in other forms: Transfer functions descriptions and graphical forms, etc How to model a dynamic system? First Principal (principals in physics) Experimental methods Mechanical Systems : Various forms of Newton’s Law Linear motion: F=ma Rotational Motion: Electric Circuits: Kirchhoff’s current law (KCL) Kirchhoff’s voltage law (KVL) TI θ = &&

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Models of Electric Circuits Kirchhoff’s current law (KCL): The algebraic sum of currents leaving a junction or node equals the algebraic sum of currents entering that node. Kirchhoff’s voltage law (KVL): The algebraic sum of all voltages taken around a closed path in a circuit is zero.
2.1 Modeling Based on First Principles Electrical Systems: RLC circuit KCL to node 1: KCL to node 2: KVL to loop 3: 1.KCL 2.KCL 3.KVL 1 1 1 1 () i vt vt dv t Ci t dt R =− 22 21 2 dv t v t t g v t dt R 12 di t L dt 2 o vt =

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Bridged Tee Circuit Select node 4 as the reference and the voltages v 1 , v 2 , and v 3 at nodes 1, 2, 3 as the unknowns. Then At node 2 the KCL is Transfer function: And at node 3 the KCL is 13 and io vv == 2 1212 1 2 2 2 11 1 2 2 () ( ) 1 [ ( ) ] 1 o i Vs CCRR s R RCs CCRRs RC ++ + = + +
Another Electric Circuit

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## This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Notes-2A - Chapter 2 Modeling and Simulation Dynamic Model...

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