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Modeling and simulation of dynamic systems - Pham Huy Hoang

Modeling and simulation of dynamic systems is Pham Huy Hoang 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. | MODELING AND SIMULATION OF DYNAMIC SYSTEMS MIXED DISCIPLINE SYSTEMS PHAM HUY HOANG HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY INTRODUCTION MIXED DISCIPLINE SYSTEM: MIXED DISCIPLINE SYSTEM – COUPLING SYSTEM OF SINGLE-DISCIPLINE SYSTEMS Pham Huy Hoang 1 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 ELECTROMECHANICAL SYSTEMS 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. Pham Huy Hoang 2 Pham Huy Hoang ELECTROMECHANICAL SYSTEMS The back emf voltage across a DC motor: & eb = K eω = K eθ The torque developed by the motor: T = Kt i eb : back emf voltage. θ : angular displacement of the rotor of the motor & = ω : angular velocity of the rotor θ T : torque applied to the rotor Ke : emf constant (Vs/rad) Ki : torque constant (Nm/A) Pham Huy Hoang 3 ELECTROMECHANICAL SYSTEMS ia Ra La & θ ,θ = ω Jr eb Va TL Jd Bd vRa + vLa + eb − va = 0 di Raia + La a + eb = va dt & eb = K eω = K eθ Raia + La dia & + K eθ = va dt (1) Pham Huy Hoang ELECTROMECHANICAL SYSTEMS ia Ra La & θ ,θ = ω eb Va Jr TL Jd Bd J = Jr + Jd & & T + TL − Bdθ = Jθ& T = Kt ia & & Kt ia + TL − Bdθ = Jθ& (2) Pham Huy Hoang 4 ELECTROMECHANICAL SYSTEMS ia Ra La & θ ,θ = ω eb Va Jr TL Jd Bd & & Jθ& + Bdθ − Kt ia = TL di & La a + Raia + K eθ = va dt & & θ& θ J 0 Bd 0 0 − Kt θ TL 0 0 + K L . + 0 R i = v .