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# Modeling - PowerPoint PPT Presentation

Modeling. Use math to describe the operation of the plant, including sensors and actuators Capture how variables relate to each other Pay close attention to how input affects output Use appropriate level of abstraction vs details

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## PowerPoint Slideshow about 'Modeling' - xiujuan-ye

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Presentation Transcript

• Use math to describe the operation of the plant, including sensors and actuators

• Capture how variables relate to each other

• Pay close attention to how input affects output

• Use appropriate level of abstraction vs details

• Many types of physical systems share the same math model  focus on models

• Focus on important variables

• Use reasonable approximations

• Write mathematical equations from physical laws, don’t invent your own

• Eliminate intermediate variables

• Obtain o.d.e. involving input/output variables  I/O model

• Or obtain 1st order o.d.e.  state space

• Get I/O transfer function

• Circuit: KCL: S(i into a node) = 0

KVL: S(v along a loop) = 0

RLC: v=Ri, v=Ldi/dt, i=Cdv/dt

• Linear motion: Newton: ma = SF

Hooke’s law: Fs = KDx

damping: Fd = CDx_dot

• Angular motion: Euler: Ja = St

t = KDq

t = CDq_dot

Voltage-current, voltage-charge, and impedance relationships for capacitors, resistors, and inductors

impedance

KVL:

Zf

Iin=0

Zi

Vin=0

Gain = inf

Ideal Op amp:

Mesh 2

Mesh 1

Sum of impedance around mesh 1

Sum of applied voltages around the mesh

Sum of impedance common to two meshes

Sum of impedance around mesh 2

i3

i1

Kirchhoff current law at these two nodes

i2

i4

i1 - i2 - i3=0

i3 - i4 =0

conductance

Sum of admittance at each node

Admittance between node i and node j