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solenoid_dcpmm

# solenoid_dcpmm - LINEARIZED ENERGY-STORING TRANSDUCER...

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LINEARIZED ENERGY-STORING TRANSDUCER MODELS Energy transduction in an electro-mechanical solenoid may be modeled by an energy-storing multiport. i IC F x . e = λ . Energy transduction in an electric motor may be modeled by a gyrator. G Y i F e = λ . x . But the fundamentals of energy transduction are the same in both. How can these different models be reconciled? Linearizing the nonlinear multiport constitutive equations reveals their relation. Linearized solenoid model page 1 © Neville Hogan

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L INEARIZED SOLENOID MODEL A gyrator relates power variables (effort and flow) A multiport energy storage element relates power and energy variables (effort and momentum, flow and displacement) Solenoid model constitutive equations: λ = i L e –(x/x c ) 2 F = i 2 L x e –(x/x c ) 2 x c 2 Differentiate the electrical constitutive equation with respect to time. e = d λ dt λ = i L e –(x/x c ) 2 d λ dt = L e –(x/x c ) 2 di dt 2 i L x e –(x/x c ) 2 x c 2 dx dt Linearized solenoid model page 2 © Neville Hogan
Consider small deviations about an operating point: nominal position x o nominal current i o Define L o _ _ L e –(x o /x c ) 2 and G o _ _ 2 i o L x o e –(x o /x c ) 2 x c 2 Linearized solenoid model page 3 © Neville Hogan

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solenoid_dcpmm - LINEARIZED ENERGY-STORING TRANSDUCER...

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