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Nonlinear Systems

# Nonlinear Systems - Nonlinear Systems Modeling some...

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Nonlinear Systems Modeling: some nonlinear effects Standard state equation description Equilibrium points Linearization about EPs Simulation and insight Equilibrium point design

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Some nonlinear effects Aerodynamic drag on a vehicle Rotodynamic pump Nonlinear spring effect Nonlinear geometry Check valve modeling
Aerodynamic drag effect Typical aerodynamic drag on a passenger vehicle can be modeled by a drag force, Ra , given by 2 * * * ) 2 / ( r f D V A C Ra ρ = where ρ is mass density of air, C D is drag factor due to vehicle shape, A f is frontal (projected) area, and Vr is vehicle speed

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Rotodynamic pump A typical model for the outlet port of a rotodynamic pump is given by 2 2 3 * * Q k N k P 2 - = where P is outlet port pressure, N is shaft speed, and Q is outlet port flow.
Hardening spring A typical relation for the characteristic of a hardening spring is given by where F is the spring force and δ is the spring deflection from free length.

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