Modeling - PowerPoint PPT Presentation

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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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Modeling

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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

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

Modeling Guidlines

• 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

Common Physical Laws

• 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

More Physical Laws

Electric Circuits

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

impedance

RLC network

KVL:

Or start in s-domain and solve for TF directly

Zf

Iin=0

Zi

Vin=0

Gain = inf

Ideal Op amp:

Mesh analysis

Mesh 2

Mesh 1

Write equations around the meshes

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

Determinant

Nodal analysis

i3

i1

Kirchhoff current law at these two nodes

i2

i4

i1 - i2 - i3=0

i3 - i4 =0

Kirchhoff current law

conductance

Sum of injected current into each node

Sum of admittance at each node

Admittance between node i and node j