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MECH 466 - Lecture4-ModellingofElectricalandMechanicalSystems-2009W

Impulse since rs1 the transfer function can also be

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Unformatted text preview: pulse Since R(s)=1, the transfer function can also be Since R(s)=1, defined as the Laplace transform of impulse response: response: A system is assumed to be at rest. (Zero initial system condition) 2008/09 MECH466 : Automatic Control 7 2008/09 MECH466 : Automatic Control 8 2 Models of electrical elements Resistance Inductance i(t) i(t) Modeling example Input v1(t) i(t) i(t) i(t) i(t) R1 i(t) i(t) Capacitance R2 v2(t) Output C v(t) v(t) R v(t) v(t) v(t) v(t) L C Kirchhoff voltage law (with zero initial conditions) Kirchhoff Laplace transform 2008/09 By Laplace transform, By transform, MECH466 : Automatic Control 9 Modeling example (cont’d) i(t) i(t) 2008/09 MECH466 : Automatic Control 10 Example: Modeling of op amp R1 - Zf(s) (s) Input v1(t) R2 I(s) I(s) v2(t) Output Input Vi(s) (s) + Vd=0 - Zi(s) (s) C i =0 i vd Vo(s) Output (s) Transfer function Transfer Impedance Z(s): V(s)=Z(s)I(s) Impedance Z(s): V(s)=Z(s)I(s) Transfer function of the above op amp: Transfer (first-order system) (first2008/09 MECH466 : Automatic Control 11 2008/09 MECH466 : Automatic Control 12 3 Impedance computation Modeling example: op amp R2 Series connection Series I(s) I(s) i(t) R1 i(t) Z1(s) Z2(s) Input vi(t) (t) C - i =0 - i vd + V(s) V(s) vd=0 vo(t) Output (t) Parallel connection Parallel I(s) I(s) By the formula in previous two pages, By Z1(s) Z2(s) (first-order system) (first- V(s) V(s) 2008/09 MECH466 : Automatic Control 13 2008/09 MECH466 : Automatic Control 14 More exercises (in Philipps & Harbor’s book) Modeling exercise: op amp Find a transfer function from v1 to v2. Find C2 C1 R2 R1 Input vi(t) (t) i =0 + Vd=...
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