Modeling and simulation of dynamic systems - Pham Huy Hoang

MODELING AND SIMULATION<br /> OF DYNAMIC SYSTEMS<br /> <br /> MIXED DISCIPLINE SYSTEMS<br /> <br /> PHAM HUY HOANG<br /> HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY<br /> <br /> INTRODUCTION<br /> <br /> MIXED DISCIPLINE SYSTEM:<br /> MIXED DISCIPLINE SYSTEM – COUPLING SYSTEM OF<br /> SINGLE-DISCIPLINE SYSTEMS<br /> <br /> Pham Huy Hoang<br /> <br /> 1<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> ARMATURE-CONTROLLED DC MOTOR<br /> Voltage is electric potential energy per unit charge<br /> (J/C = V) - referred to as "electric potential”.<br /> Electromotive force (emf) voltage (electromotance):<br /> - is that which tends to cause current (actual<br /> electrons and ions) to flow;<br /> - is the external work expended per unit of charge<br /> to produce an electric potential difference across<br /> two open-circuited terminals;<br /> - is generated by a magnetic force (Faraday’s<br /> law).<br /> <br /> Pham Huy Hoang<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> Faraday's Law<br /> Any change in the<br /> magnetic<br /> environment* of a coil<br /> of wire will cause a<br /> voltage (emf) to be<br /> "induced" in the coil.<br /> * The change of<br /> magnetic field<br /> strength, relative<br /> displacement<br /> between the magnet<br /> field and the coil.<br /> Pham Huy Hoang<br /> <br /> 2<br /> <br /> Pham Huy Hoang<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> The back emf voltage across a DC motor:<br /> &<br /> eb = K eω = K eθ<br /> <br /> The torque developed by the motor:<br /> T = Kt i<br /> <br /> eb : back emf voltage.<br /> θ : angular displacement of the rotor of the motor<br /> & = ω : angular velocity of the rotor<br /> θ<br /> T : torque applied to the rotor<br /> Ke : emf constant (Vs/rad)<br /> Ki : torque constant (Nm/A)<br /> Pham Huy Hoang<br /> <br /> 3<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> ia<br /> <br /> Ra<br /> <br /> La<br /> <br /> &<br /> θ ,θ = ω<br /> Jr<br /> <br /> eb<br /> <br /> Va<br /> <br /> TL<br /> <br /> Jd<br /> Bd<br /> <br /> vRa + vLa + eb − va = 0<br /> di<br /> Raia + La a + eb = va<br /> dt<br /> &<br /> eb = K eω = K eθ<br /> Raia + La<br /> <br /> dia<br /> &<br /> + K eθ = va<br /> dt<br /> <br /> (1)<br /> Pham Huy Hoang<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> ia<br /> <br /> Ra<br /> <br /> La<br /> <br /> &<br /> θ ,θ = ω<br /> eb<br /> <br /> Va<br /> <br /> Jr<br /> <br /> TL<br /> <br /> Jd<br /> <br /> Bd<br /> <br /> J = Jr + Jd<br /> &<br /> &<br /> T + TL − Bdθ = Jθ&<br /> T = Kt ia<br /> &<br /> &<br /> Kt ia + TL − Bdθ = Jθ& (2)<br /> Pham Huy Hoang<br /> <br /> 4<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> ia<br /> <br /> Ra<br /> <br /> La<br /> <br /> &<br /> θ ,θ = ω<br /> eb<br /> <br /> Va<br /> <br /> Jr<br /> <br /> TL<br /> <br /> Jd<br /> <br /> Bd<br /> <br /> &<br /> &<br /> Jθ& + Bdθ − Kt ia = TL<br /> di<br /> &<br /> La a + Raia + K eθ = va<br /> dt<br /> &<br /> &<br /> θ&<br /> θ<br />  J 0    Bd 0    0 − Kt  θ  TL <br />  <br />  <br />  0 0  ..  +  K L   .  + 0 R  i  = v <br /> <br />  i   e<br /> a  i  <br /> a  a   a <br />  a<br />  a<br /> Pham Huy Hoang<br /> <br /> ELECTROMECHANICAL SYSTEMS<br /> <br /> ia<br /> <br /> Va<br /> <br /> Ra<br /> <br /> La<br /> <br /> &<br /> θ ,θ = ω<br /> eb<br /> <br /> Jr<br /> K, B<br /> <br /> TL<br /> <br /> Jd<br /> Bd<br /> <br /> Pham Huy Hoang<br /> <br /> 5<br /> <br />