EE3530-2

EE3530-2 - Chapter 2 Dynamic Models Dynamic Model:...

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hapter 2 Dynamic Models Chapter 2 Dynamic Models Dynamic Model: mathematical escription of the process How to model a dynamic system? description of the process. Typically, a set of differential equations. First Principal (principals in physics) Experimental methods These equations can be Nonlinear Time Varying and Infinite Dimensional. Mechanical Systems : Various forms of Newton’s Law Linear motion: F=ma In this course, we consider a special class of approximations: Linear Time Invariant (LTI) rocesses Rotational Motion: Electric Circuits: irchhoff’s current law (KCL) TI θ = && processes. Models can be given in other forms: Transfer functions descriptions nd graphical forms etc Kirchhoff s current law (KCL) Kirchhoff’s voltage law (KVL) and graphical forms, etc
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Cruise Control Model Equations of motion: ub x m x −= && & if we are only interested in speed ( ) : b u or x x mm vx u += = & & 0 Given an input by d assume the solution is st s bu vv uU e V e = & t 0 and assume the solution is vV = 00 Then 1 ( ) st st b sV e U e m 0 Hence 1/ Vm b = 0 U s m + This is called Transfer Function. Obtained by replacing d/dt by s
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A Two-Mass System: Suspension Model Equations of motion: Rearranging:
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EE3530-2 - Chapter 2 Dynamic Models Dynamic Model:...

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