<?xml version='1.0' encoding='UTF-8'?>
<model name="BG3" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<!-- Bond graph model of a coupled electrical-mechanical system (voice coil)-->
<!-- electrical units-->
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="C_per_s">
<unit units="coulomb"/>
<unit exponent="-1" units="second"/>
</units>
<units name="C_per_s2">
<unit units="coulomb"/>
<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>
<!--TF units-->
<units name="Js_per_C_m">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-1" units="coulomb"/>
<unit exponent="-1" units="metre"/>
</units>
<!--mechanical 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="Js_per_m2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="Js2_per_m2">
<unit units="joule"/>
<unit exponent="2" units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<component name="Environment">
<variable name="u_in_e" public_interface="out" units="J_per_C"/>
<variable initial_value="0" name="t" public_interface="out" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_in_e</ci>
<apply>
<times/>
<cn cellml:units="J_per_C">50</cn>
<apply>
<sin/>
<apply>
<times/>
<cn cellml:units="per_s">50</cn>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<ci>t</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Voice_coil_equations">
<!-- State variables-->
<variable name="t" public_interface="in" units="second"/>
<variable initial_value="0" name="v_1_e" units="C_per_s"/>
<variable name="a_1_e" units="C_per_s2"/>
<variable initial_value="0" name="q_C_m" units="metre"/>
<variable initial_value="0" name="v_2_m" units="m_per_s"/>
<variable name="a_2_m" units="m_per_s2"/>
<variable name="u_in_e" public_interface="in" units="J_per_C"/>
<variable name="u_R_e" units="J_per_C"/>
<variable name="u_L_e" units="J_per_C"/>
<variable name="u_1_e" units="J_per_C"/>
<variable name="u_2_m" units="J_per_m"/>
<variable name="u_C_m" units="J_per_m"/>
<variable name="u_R_m" units="J_per_m"/>
<variable name="u_L_m" units="J_per_m"/>
<!-- Constitutive parameters -->
<variable initial_value="1" name="E_1" units="J_per_C2"/>
<variable initial_value="100" name="E_2" units="J_per_m2"/>
<variable initial_value="5" name="R_1_e" units="Js_per_C2"/>
<variable initial_value="0.4" name="R_2_m" units="Js_per_m2"/>
<variable initial_value="0.2" name="L_1_e" units="Js2_per_C2"/>
<variable initial_value="0.01" name="L_2_m" units="Js2_per_m2"/>
<!-- TF parameters: this depends on the number of coil turns and the magnetic flux.-->
<variable initial_value="6" name="Bl" units="Js_per_C_m"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_1_e</ci>
</apply>
<ci>a_1_e</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_C_m</ci>
</apply>
<ci>v_2_m</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_2_m</ci>
</apply>
<ci>a_2_m</ci>
</apply>
<apply>
<eq/>
<ci>u_in_e</ci>
<apply>
<plus/>
<ci>u_R_e</ci>
<ci>u_L_e</ci>
<ci>u_1_e</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_2_m</ci>
<apply>
<plus/>
<ci>u_C_m</ci>
<ci>u_R_m</ci>
<ci>u_L_m</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>u_R_e</ci>
<apply>
<times/>
<ci>R_1_e</ci>
<ci>v_1_e</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_L_e</ci>
<apply>
<times/>
<ci>L_1_e</ci>
<ci>a_1_e</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_1_e</ci>
<apply>
<times/>
<ci>Bl</ci>
<ci>v_2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_2_m</ci>
<apply>
<times/>
<ci>Bl</ci>
<ci>v_1_e</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_C_m</ci>
<apply>
<times/>
<ci>E_2</ci>
<ci>q_C_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_R_m</ci>
<apply>
<times/>
<ci>R_2_m</ci>
<ci>v_2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_L_m</ci>
<apply>
<times/>
<ci>L_2_m</ci>
<ci>a_2_m</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="Environment" component_2="Voice_coil_equations"/>
<map_variables variable_1="u_in_e" variable_2="u_in_e"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
</model>
