H Metrology Measurement Science and Technology ETH Zurich, Switzerland Institute of Machine Tools and Manufacturing H H H Contact the Author H © Copyright H d0000722; rev02 Cooperation H H Example Direct-Current Motor with Permanent-Magnet Karl H. Ruhm Key Words direct current, DC, motor, permanent-magnet, model, differential equation, derivation, torque, speed Abstract The sub-model of a DC motor concerning torque and speed is an ordinary linear differential equation of second order with one derivation in the input quantity. Introduction Depending on the demands, the model of a DC-motor with permanent-magnet generally is a multivariable system (multiple input, multiple output; MIMO). Here we will consider only the dependence of speed (t) [s–1] by the load torque ML(t) [N m]. So we treat only a monovariable system (single input, single output; SISO). 1 Differential Equation RA d 1 cF 2 2 1 RA 1 d (t) (t) (t) ML (t) ML (t) [s 3 ] 2 L A dt LA LA dt dt mit 2 d s 1 rotational speed ( 2n / 60) ML Nm torque RA electrical resistance LA H VA 1s inductivity Nms2 massmoment of inertia cF machine value Wb V s magnetic flux MINIMOTOR SA This is a linear ordinary differential equation (ODE) with two derivations of the output quantity (t) and one derivation of the input quantity ML(t). 2 Signal Effect Diagram This differential equation and its solution are shown in the signal effect diagram as follows: M L (t) d dt . ω(0) – 1 Θ – Σ – – ω(0) . .. ω(t) ω(t) RA LA ω(t) 2 1 cF2Φ2 Θ LA B1312 RA Θ LA Reliance Electric If one is interested, not to have the derivation operation of an input quantity in the diagram, which may cause problems with the implementation in a simulation program, a modification will lead to a differentiator-free realisation (Supplement → Module "Differentiator-Free Realisation"). Alternate Versions There is a German version of this document: → d0000XXX Modifications Rev. Date Modification 00 02.11.2006 First Edition 02 21.06.2012 Minor Additions 2