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Unformatted text preview: 1 Lec 3. System Modeling • Transfer Function Model • Model of Mechanical Systems • Model of Electrical Systems • Model of Electromechanical Systems • Reading: 3.13.3, 3.63.8 LTI Systems Given by Differential Equations LTI systems modeling practical systems are often given by ODE Take Laplace transform (assuming zero initial condition) Transfer function : 2 (Rational) Transfer Functions Roots of B ( s ) are called the zeros of H ( s ) ( z 1 ,…,z m ) Roots of A ( s ) are called the poles of H ( s ) ( p 1 ,…,p n ) System is called an nth order system Poles and zeros occur in complex conjugate pairs, e.g. if 2+ j 3 is a pole (or zero), so is 2 j 3. PoleZero plot: Standard Forms of (Rational) Transfer Function Ratio of polynomials: Factored (or product) form: Sum form (assume poles are distinct): p 1 ,…, p n : poles, r 1 ,…, r n : residues 3 A Geometric Interpretation of Residues Pole zero plot: Distance to zeros Distance to poles (except itself) Remark: if a pole is very close to a zero, its residue will be small.Remark: if a pole is very close to a zero, its residue will be small....
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This note was uploaded on 10/12/2010 for the course ECE 382 taught by Professor Staff during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 Staff

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