3 351 1st order system, part 1

3 351 1st order system, part 1 - Response of a System to an...

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1 1 (Chapter 3 in F&B) Response of a System to an Input 2 General Concept system signal output How does your mechanical, measurement, electrical, or other physical system respond to an input? Examples thermometer responding to temperature cantilever responding to tap membrane responding to pressure change strain gauge responding to strain
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2 3 Review: Ordinary Differential Equations 1 11 0 1 mm dx d x d x b b ... b b x F(t ) dt dt dt ++ + + = A function F(t) , in terms of a variable x(t) : order = m This is an ordinary differential equation (ODE) – it has one independent variable, x . The dependent variable is F . The order of the ODE is the order of the highest derivative . dx yC dt = 1 st order 2 2 dy g dt = 2 nd order Fk x = 0 th order Discussion What physical systems do these equations describe? dV IC dt = 4 System Model 1 0 1 d x b b ... b b x dt dt dt + + = A forcing function F(t) , in terms of a physical variable x(t) : produces a system response y(t) : 1 0 1 nn d y d y aa . . . a a y dt dt dt + + where m n . Most systems can be modeled by zero, 1 st , or 2 nd order linear ODEs, or reasonably well approximated by them.
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3 5 0 th Order Systems 6
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3 351 1st order system, part 1 - Response of a System to an...

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