DC Motor Control docx

DC Motor Control: Theory and Implementation By Chung Tan Lam CIMEC Lab. I. Introduction A DC motor speed drive The mathematical model of dc motor (permanent magnet type) can be expressed by these equations where a V : Armature voltage [V] a i : Armature current [A] e T : Electromagnetic torque [N.m] L T : Load torque [N.m] a L : Armature inductance [H] a R : Armature resistance [ Ω ] K : Coupling coefficient [N.m/A] J : Momen of inertia [Kg.m 2 ] m B : Damping coefficient The block diagram of a cascade closed-loop speed control of the dc motor is shown below. DC MOTOR MODEL 1 CASCADE SPEED CONTROL OF A DC MOTOR DRIVE Typical dynamic responses are also shown. The motor is initially at standstill and at no load when a step command in speed is applied; when steady-state conditions are reached, a reversal of speed is commanded followed by a step load application. The system is highly nonlinear due to the introduction of saturation needed to limit both the current delivered and the voltage applied to the motor. The system is in the saturation mode when the errors are large; as a consequence, the controller functions as a constant current source, that is torque, resulting in the ramping of the speed since the load in this example is a pure inertia. The inclusion of saturation limits on the PI integrator is therefore necessary to provide antiwindup action. The presence of the signum function in the torque expression is required in order to insure that the load is passive whether the speed is positive or negative (as is the case here). 2 1. DC Motor Transient Running Operation This demo simulates the running of a DC motor with constant field or pm excitation (5 hp 240V 1200 rpm) rated torque Tr = 30 N.m BLOCK DIAGRAM MODEL OF A DC MOTOR 3 MOTOR TRANSIENT RUNNING OPERATION Electrical system equation: va = Ra.ia + La.dia/dt + ea where ea = K.wm Mechanical system equation: Te = J.dwm/dt + Tl.signum(wm) + f(wm) where Te = K.ia Simulation Results MOTOR SPEED [rad/s] 4 MOTOR CURRENT [A] 2. DC Motor with bipolar PWM excitation This demo simulates the running of a DC motor with PWM (bipolar) excitation (5 hp 240V 1200 rpm) rated torque Tr = 30 N.m 5 DC Motor With Bipolar PWM Excitation DC Motor Model Simulation Results 6 Voltage Average Applied To Motor MOTOR SPEED (rad/s) Motor Current (A) 3. DC Motor with unipolar PWM excitation 7 This demo simulates the running of a DC motor with PWM (unipolar) excitation (5 hp 240V 1200 rpm) rated torque Tr = 30 N.m DC Motor Model Simulation Results 8 Voltage Average Applied To Motor Motor Speed (Rad/S) Motor Current (A) 4. Automatic Starter of a DC Motor 9 This demo simulates the starting of a DC motor with automatic starter (5 hp 240V 1200 rpm) rated torque Tr = 30 N.m The starter is simulated by a speed-dependent effective armature resistance using a look-up table. Mathematical model of the dc machine          = = ++= ++= ae ma Lm m e aaa a aa KiT Ke TB dt d JT eiR dt di LV ω ω where a V : Armature voltage [V] a i : Armature current [A] e T : Electromagnetic torque [N.m] L T : Load torque [N.m] a L : Armature inductance [H] a R : Armature resistance [ Ω ] K : Coupling coefficient [N.m/A] J : Momen of inertia [Kg.m 2 ] m B : Damping coefficient Simulation Results 10 [...]... winding with dc motors, and are the phase values for a BLDC motor Brushless dc motors (BLDC) are usually 3 phase synchronous motors used in a configuration to be treated as dc drives Also note, it is assumed that dc motors being discussed have a permanent magnet field supply Wound field motors are not part of this discussion MOTOR RESISTANCE For the winding resistance use an ohmmeter For a DC motor measure... torque[lb-in]/acceleration[rad/sec2]=lb-in-sec2 17 BLDC MOTORS- The tests described thus far must be modified for a bldc motor A bldc motor must be tested with its servo amplifier The step input will be a step in dc voltage to the servo amplifier input The voltage step should be large enough to cause the motor to reach rated speed With bldc motors it is not possible to measure the high frequency phase current in a WYE connected motor Thus... If it is a WYE connected BLDC motor, the armature resistance is the line-to-line resistance Thus divide the resistance (l-l) by 2 to get the phase resistance The ohmic value will also be very small MOTOR VOLTAGE CONSTANT K e To measure K e of the motor, put the motor shaft in a machine lathe and rotate the shaft at some speed [rpm] such as 1000rpm With a dc motor, use a DC voltmeter to measure the... te C P U R e s e t V C C _ IO JP2 U SB 5V 2 1 1 of 1 MEASURING MOTOR PARAMETERS These are the motor parameters that are need: K e (volts-sec/rad) Motor voltage constant K T (lb-in/amp) Motor torque constant Ra (ohms) Motor armature resistance La (Henries) Motor inductance J m ( lb − in − sec 2 ) Motor inertia Load inertia reflected to the motor armature shaft J load ( lb − in − sec 2 ) J Total ( lb −... can thus be calculated as done previously MOTOR INDUCTANCE L This procedure assumes a model as a series equivalent R L circuit To measure the motor inductance uses a very low voltage ac source to the motor winding The resistance and inductance will be very small values For a magnetic flux field dc motor, apply the ac voltage to the armature winding For a BLDC motor apply the ac voltage to one pair of... torque of the motor rotor These two parameters are described as follows: ACCELERATION – This parameter is determined by putting a step in current into the motor winding to bring the motor up to rated speed The motor will accelerate exponentially The acceleration is a measure of the rate of change of velocity over a period of time To make this test, a dc tachometer should be connected to the motor shaft... voltage to one pair of the three wires In both cases measure the voltage and the current Remember that the BLDC motor is usually connected in WYE Thus the readings will be line-to-line You want the phase values for the voltage, so divide the voltage by 2 The impedance of the dc motor or the BLDC motor phase winding is thenImpedance = Armature voltage or phase voltage [volts] = [ohms] line current [amps]... used to measure the current or torque and velocity Commercial bldc servo amplifiers have two dc output test points One output is a dc voltage proportional to velocity with a given calibration The voltage can be directly connected to a strip chart as described previously to measure the motor acceleration, A second test output provides a dc voltage proportional to torque or a percentage of rated torque... Volts[v] Ke = or speed [rad / sec] speed [rpm] With a BLDC motor use an ac voltmeter to measure the voltage between any 2 wires of the 3 motor wires and then convert the line-to-line voltage to the phase voltage value by dividing the line-to-line voltage by 3 = 1.73 15 K e ( phase) = K e (line − to − line) 1.73 MOTOR TORQUE CONSTANT K T The motor torque constant ( K T ) can be computed from the voltage...   sec  MOTOR INERTIA J m Motor rotor inertia can be measured by making an experiment The inertia can be calculated from the equation [ ]  rad  Acceleration torque [lb − in] = Inertia lb - in - sec 2 x acceleration  2   sec  Also (rearranging terms) accel torque Inertia = lb − in − sec 2 acceleration [ ] DC MOTORS To do this test it is necessary to measure the acceleration of the motor rotor . cascade closed-loop speed control of the dc motor is shown below. DC MOTOR MODEL 1 CASCADE SPEED CONTROL OF A DC MOTOR DRIVE Typical dynamic responses are also shown. The motor is initially at standstill. torque Tr = 30 N.m 5 DC Motor With Bipolar PWM Excitation DC Motor Model Simulation Results 6 Voltage Average Applied To Motor MOTOR SPEED (rad/s) Motor Current (A) 3. DC Motor with unipolar PWM. single winding with dc motors, and are the phase values for a BLDC motor. Brushless dc motors (BLDC) are usually 3 phase synchronous motors used in a configuration to be treated as dc drives. Also