<?xml version='1.0'?>
<model name="transfer_function" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- transfer function for Lorenz force actuator-->
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="per_s2">
<unit exponent="-2" units="second"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="J_per_C2">
<unit units="joule"/>
<unit exponent="-2" units="coulomb"/>
</units>
<units name="Js_per_C2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="coulomb"/>
</units>
<units name="Js2_per_C2">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-2" units="coulomb"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="m_per_s2">
<unit units="metre"/>
<unit exponent="-2" units="second"/>
</units>
<units name="J_per_m">
<unit units="joule"/>
<unit exponent="-1" units="metre"/>
</units>
<units name="J_per_m2">
<unit units="joule"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="J2_per_m4">
<unit exponent="2" units="joule"/>
<unit exponent="-4" units="metre"/>
</units>
<units name="Js_per_m2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="J2s2_per_m4">
<unit exponent="2" units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-4" units="metre"/>
</units>
<units name="Js2_per_m2">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="Js_per_C_m">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-1" units="coulomb"/>
<unit exponent="-1" units="metre"/>
</units>
<component name="main">
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="0.1" name="omega" units="per_s"/>
<variable initial_value="1" name="omega_ref" units="per_s"/>
<variable name="logOmega" units="dimensionless"/>
<variable initial_value="0" name="E_1" units="J_per_C2"/>
<variable initial_value="2000" name="E_2" units="J_per_m2"/>
<variable initial_value="3.5" name="R_1" units="Js_per_C2"/>
<variable initial_value="0.4" name="R_2" units="Js_per_m2"/>
<variable initial_value="0.15" name="L_1" units="Js2_per_C2"/>
<variable initial_value="0.018" name="L_2" units="Js2_per_m2"/>
<variable initial_value="10" name="Bl" units="Js_per_C_m"/>
<variable name="x_1" units="J_per_m2"/>
<variable name="x_2" units="J2_per_m4"/>
<!--var a_1: J2s2_per_m4;
var a_2: J2s2_per_m4;-->
<!--var omega_1: per_s;
var omega_2: per_s;-->
<variable name="omega_3" units="per_s"/>
<!--var omega_sq_1: per_s2;
var omega_sq_2: per_s2;-->
<variable name="logOmega_3" units="dimensionless"/>
<variable name="G_real" units="Js_per_C2"/>
<variable name="G_imag" units="Js_per_C2"/>
<variable name="amplitude" units="Js_per_C2"/>
<variable initial_value="1" name="amplitude_ref" units="Js_per_C2"/>
<variable name="phase" units="dimensionless"/>
<variable initial_value="1" name="phase_ref" units="dimensionless"/>
<variable name="phase_degrees" units="dimensionless"/>
<variable name="logAmplitude" units="dimensionless"/>
<!--a_1 = 2{dimensionless}*L_2*E_2-sqr(R_2);
a_2 = sqr(R_2)-4{dimensionless}*L_2*E_2;-->
<!--omega_sq_1 = (2{dimensionless}*E_2*L_2-sqr(R_2)+R_2*sqrt(a_2))/(2{dimensionless}*sqr(L_2));
omega_sq_2 = (2{dimensionless}*E_2*L_2-sqr(R_2)-R_2*sqrt(a_2))/(2{dimensionless}*sqr(L_2));-->
<!--omega_1 = sqrt(omega_sq_1);
omega_2 = sqrt(omega_sq_2);-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>omega_3</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>E_2</ci>
<ci>L_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>logOmega_3</ci>
<apply>
<log/>
<apply>
<divide/>
<ci>omega_3</ci>
<ci>omega_ref</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>omega</ci>
</apply>
<cn cellml:units="per_s2">1</cn>
</apply>
<apply>
<eq/>
<ci>logOmega</ci>
<apply>
<log/>
<apply>
<divide/>
<ci>omega</ci>
<ci>omega_ref</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x_1</ci>
<apply>
<minus/>
<ci>E_2</ci>
<apply>
<times/>
<apply>
<power/>
<ci>omega</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>L_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x_2</ci>
<apply>
<plus/>
<apply>
<power/>
<ci>x_1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<times/>
<ci>omega</ci>
<ci>R_2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>G_real</ci>
<apply>
<plus/>
<ci>R_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>R_2</ci>
<apply>
<power/>
<apply>
<times/>
<ci>omega</ci>
<ci>Bl</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>x_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>G_imag</ci>
<apply>
<times/>
<ci>omega</ci>
<apply>
<plus/>
<ci>L_1</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>Bl</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x_1</ci>
</apply>
<ci>x_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>amplitude</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<ci>G_real</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>G_imag</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phase</ci>
<apply>
<arctan/>
<apply>
<divide/>
<ci>G_imag</ci>
<ci>G_real</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phase_degrees</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>phase</ci>
<cn cellml:units="dimensionless">180</cn>
</apply>
<pi/>
</apply>
</apply>
<apply>
<eq/>
<ci>logAmplitude</ci>
<apply>
<log/>
<apply>
<divide/>
<ci>amplitude</ci>
<ci>amplitude_ref</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>
