Mixed discipline systems

1MODELING AND SIMULATION OF DYNAMIC SYSTEMS PHAM HUY HOANG HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY MIXED DISCIPLINE SYSTEMS Pham Huy Hoang INTRODUCTION MIXED DISCIPLINE SYSTEM: MIXED DISCIPLINE SYSTEM – COUPLING SYSTEM OF SINGLE-DISCIPLINE SYSTEMS 2Pham Huy Hoang ELECTROMECHANICAL SYSTEMS ARMATURE-CONTROLLED DC MOTOR Voltage is electric potential energy per unit charge (J/C = V) - referred to as "electric potential”. Electromotive force (emf) voltage (electromotance): - is that which tends to cause current (actual electrons and ions) to flow; - is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals; - is generated by a magnetic force (Faraday’s law). Pham Huy Hoang Faraday's Law Any change in the magnetic environment* of a coil of wire will cause a voltage (emf) to be "induced" in the coil. * The change of magnetic field strength, relative displacement between the magnet field and the coil. ELECTROMECHANICAL SYSTEMS 3Pham Huy Hoang Pham Huy Hoang ELECTROMECHANICAL SYSTEMS The back emf voltage across a DC motor: θω &eeb KKe == The torque developed by the motor: iKT t= eb : back emf voltage. θ : angular displacement of the rotor of the motor : angular velocity of the rotor T : torque applied to the rotor Ke : emf constant (Vs/rad) Ki : torque constant (Nm/A) ωθ =& 4Pham Huy Hoang )1( 0 ae a aaa eeb ab a aaa abaLaR vK dt diLiR KKe ve dt diLiR vevv =++ == =++ =−++ θ θω & & aV aR aL ai be rJ dJ dB LT ωθθ =&, ELECTROMECHANICAL SYSTEMS Pham Huy Hoang aV aR aL ai be rJ dJ dB LT ωθθ =&, )2(θθ θθ &&& &&& JBTiK iKT JBTT JJJ dLat at dL dr =−+ = =−+ += ELECTROMECHANICAL SYSTEMS 5Pham Huy Hoang aV aR aL ai be rJ dJ dB LT ωθθ =&,       =             − +               +               =++ =−+ a L aa t a ae d a aeaa a a Latd v T iR K iLK B i J vKiR dt diL TiKBJ θθθ θ θθ 0 00 00 0 ... &&& & &&& ELECTROMECHANICAL SYSTEMS Pham Huy Hoang BK ,a V aR aL ai be rJ dJ dB LT ωθθ =&, ELECTROMECHANICAL SYSTEMS 6Pham Huy Hoang ELECTROMECHANICAL SYSTEMS FIELD-CONTROLLED DC MOTOR )1(fffff vdt di LiR =+ fv fR fL constia = 0=be rJ dJ dB LT ωθθ =&, fi ftiKT = Pham Huy Hoang )2(θθ θθ &&& &&& JBTiK iKT JBTT JJJ dLft ft dL dr =−+ = =−+ += fv fR fL constia = 0=be rJ dJ dB LT ωθθ =&, fi ftiKT = ELECTROMECHANICAL SYSTEMS 7Pham Huy Hoang fv fR fL constia = 0=be rJ dJ dB LT ωθθ =&, fi ftiKT =       =             − +               =+ =−+ fv LT fifR tKdB fifL J fvfifRdt fdifL LTfitKdBJ θθ θθ & && &&& 0.0 0 ELECTROMECHANICAL SYSTEMS Pham Huy Hoang fv fR fL constia = 0=be rJ dJ dB LT ωθθ =&, fi ftiKT = ELECTROMECHANICAL SYSTEMS 8Pham Huy Hoang ELECTROMECHANICAL SYSTEMS MAGNETO-ELECTRO-MECHANICAL SYSTEMS Lenz’s law: increasing current in a coil will generate a counter emf which opposes the current. (The emf always opposes the change in current). The relation of this counter emf to the current is the origin of the concept of inductance. Pham Huy Hoang Magnetic Force and Lorentz force law: - The force is perpendicular to both the velocity v of the charge q and the magnetic field B (N/A = Ns/C = Tesla). - The magnitude of the force is F = qvB sinθ (θ is the angle between the velocity and the magnetic field). ELECTROMECHANICAL SYSTEMS 9Pham Huy Hoang -The magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero. - The direction of the force is given by the right hand rule. ELECTROMECHANICAL SYSTEMS Pham Huy Hoang v 1R1 i 2R C 2i L a y 1k 2k 1c 2c 1x 2x 1m 2m b ELECTROMECHANICAL SYSTEMS yKemfforceiveElectromot iKforceMagnetic &2 21 :)( : 10 Pham Huy Hoang 011 11 12 0 222 2 0 1 0 2 0 111 =−∫+++∫− =∫−∫+ x a bKdti C iR dt diLdti C vdti C dti C iR tt tt & v 1R1 i 2R C 2i L a y ELECTROMECHANICAL SYSTEMS Pham Huy Hoang 0 )()( 0)()( )]()([)( 2212221222 22122122 22 212 2 21 2 212 2 21 2 2111 12 1122122111121 =+−+− =−−−− ∑ = =+−++−++       =−+−++−− ∑ = xkxkxcxcxm xmxxcxxk xmF abiKxbkxbkkxbcxbccxm b xbmbxxcxxkbxcxkaiK JM OO &&&& &&&& && &&&& && &&& α 1k 2k 1c 2c 1x 2x 1m 2m b ELECTROMECHANICAL SYSTEMS 11 Pham Huy Hoang Pham Huy Hoang 12 Pham Huy Hoang Pham Huy Hoang 13 Pham Huy Hoang