DC Motor Control

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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...

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Nội dung Text: DC Motor Control

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 Va : Armature voltage [V] ia : Armature current [A] Te : Electromagnetic torque [N.m] TL : Load torque [N.m] La : Armature inductance [H] Ra : Armature resistance [ Ω ] : Coupling coefficient [N.m/A] K J : Momen of inertia [Kg.m2] Bm : 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  dia Va = La dt + Ra ia + ea  T = J dω m + B + T e m L dt  ea = Kω m T = Ki e a where Va : Armature voltage [V] ia : Armature current [A] Te : Electromagnetic torque [N.m] TL : Load torque [N.m] La : Armature inductance [H] Ra : Armature resistance [ Ω ] : Coupling coefficient [N.m/A] K : Momen of inertia [Kg.m2] J Bm : Damping coefficient Simulation Results 10
MOTOR SPEED MOTOR CURRENT 11
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(H-Bridge Driver + 2 output +4 input + 4 Indicator LED’s) HV QD HV IR F 5 4 0 C6 + 2 R3 104 O u tp u t1 T1 10 HO1 IR F 5 4 0 1 J1 2 C4 1 0 0 0 u F -6 4 V 1 O u t1 GND 1 2 3 VS1 M1 3 M2 4 In p u t1 QC 5 3 GND1 IR F 5 4 0 6 2 In p u t2 R4 C3 7 GND2 10 104 8 O u tp u t2 LO 1 T2 1 T o H - B r id g e D r iv e r IR F 5 4 0 2 O u tp u t 1 O u t1 14 3 O u t2 O u t2 13 1 HO1 12 HV Vs1 11 LO 1 10 3 HO2 9 HV Vs2 8 LO 2 7 In p u t4 6 J2 In p u t3 5 QB In p u t2 4 IR F 5 4 0 1 2 In p u t1 GND 3 R5 2 C u rrA m p O u tp u t2 2 10 3 HO2 O u tp u t1 1 1 4 In p u t3 5 GND3 6 J3 In p u t4 7 3 VS2 GND4 8 QA IR F 5 4 0 O u tp u t 2 2 R6 10 LO 2 1 3 F1 FUSE C u rrA m p R2 R1 + C5 0 .0 1 -1 W 0 .0 1 -1 W T it le 3 .3 u F -6 4 V H - B r id g e P o w e r M O S F E T S iz e D ocum ent N um ber R ev A A -0 2 1 D a te : W ednesday , M ay 11, 2005 Sheet 1 of 1 13
Power MOSFET Module VCC C N 10 R e s e t_ S W R LY 1 6 VCC RB6 VC C 5 5 6 RB7 4 3 CN1 2 2 9 E XTV C C MC LR 2 1 1 10 1 R1 IC D 2 R eset 10K R ESET# VCC CN2 VCC R e m o te C P U R e s e t V C C _ IO 4 JP2 RX R C 7 /R X 3 U SB 5V R6 R eset U1 TX R C 6 /TX 2 2 1 10K SW 1 P O R TV C C 1 1 40 M C LR R B7 M C LR R B 7 /P G D JP3 2 39 AN0 R B6 R A 0 /A N 0 R B 6 /P G C E x t. 5 V 3 38 R S232 R A4 AN1 R B5 R A 1 /A N 1 R B 5 /P G M 2 1 VC C 4 37 E XT5 V AN2 R B4 R A 2 /A N 2 R B4 5 36 AN3 R B 3 /C A N R X R A 3 /A N 3 R B 3 /C A N R X S t a rt 6 35 R A4 R B 2 /C A N T X RA4 R B 2 /C A N T X SW 2 C2 7 34 VC C AN4 R B 1 /I N T 1 R A 5 /A N 4 R B 1 / IN T 1 (11,12,13,14): Only for USB Controller 104 8 33 R E 0 /R D R B 0 /I N T 0 R E 0 / R D / A N 5 R B 0 / IN T 0 9 32 VCC R E 1 /W R R E 1 / W R /A N 6 VDD (10): V+=12 or 24VDC depend on Extended board 10 31 C1 CN6 R E 2 /C S R E 2 /C S /A N 7 GND 11 30 104 D B7 VD D R D 7 /P S P 7 12 29 D B6 GND R D 6 /P S P 6 5 J1 J2 8 5 13 28 SDO D B5 R C 5 /S D O VCC OUT OSC1 R D 5 /P S P 5 4 14 27 SDI D B4 R C 4 /S D I OSC2 R D 4 /P S P 4 3 1 14 O SC 40 15 26 SCK R C 5 /S D O RC0 R C 7 /R X R C 3 /S C K D B0 RC0 R C 7 /R X 2 2 13 1 4 16 25 R C 4 /S D I RC1 R C 6 /T X D B1 NC GND RC1 R C 6 /TX 1 3 12 17 24 R C 3 /S C K R C 2 /P W M 1 R C 5 /S D O D B2 R C 2 /C C P 1 R C 5 /S D O 4 11 Y2 18 23 SPI R E 0 /R D R C 3 /S C K R C 4 /S D I D B3 R C 3 /S C K R C 4 /S D I 5 10 19 22 RC0 D B0 D B3 D B4 R D 0 /P S P 0 R D 3 /P S P 3 6 9 20 21 RC1 D B1 D B2 D B5 R D 1 /P S P 1 R D 2 /P S P 2 7 8 R C 2 /P W M 1 D B6 8 7 GND D B7 9 6 P IC 1 8 F 4 5 8 VCC CN3 AN0 R B 0 /I N T 0 10 5 V+ R B 1 /I N T 1 Power Management 11 4 R E S E T# R E 2 /C S 4 12 3 CANH V C C _ IO R E 1 /W R 3 13 2 CANL E XTV C C R B4 2 14 1 VCC U2 P O R TV C C R B5 1 VCC 1 8 R B 2 /C A N T X 2 TXD R s C O N 14 C O N 14 7 C A N _ IN 3 GN D CAN H R5 R4 R7 CN8 6 4 VC C C AN L 150 150 150 C 3 R B 3 /C A N R X 5 VCC CN4 R X D V re f 104 CN5 CN9 5 SDO R C 5 /S D O 4 4 M C P2551 SDI CANH R C 4 /S D I V+ V+ 4 4 3 3 SCK CANL R C 3 /S C K E XT5V E XT5 V Aux_Power 3 Aux_Power 3 2 2 R e s e t_ S W R e s e t_ S W 2 2 1 1 2 GND GND 1 1 JP1 120 VC C VC C SPI JU M P _1 R 2 C AN _O U T C N 11 C N 12 VC C VCC C N 15 1 E x t_ 5 V C N 14 3 3 AN 0 AN 1 V+ 3 2 2 3 AN 4 E XT5V 2 1 1 3 2 AN 3 GND 1 2 1 D1 1 LE D C5 AD0 C6 AD 1 CN7 C4 104 104 C9 AD 4 104 VCC C8 AD 3 104 C N 13 104 R3 3 330 AN2 2 T it l e 1 C A N _ U S B In t e rf a c e S iz e D ocum ent N um ber R ev C7 AD2 A4 U S B C A N C o n tro l e r - U S B C A N . o p j 1 .1 104 D a te : W e d n e s d a y , J u ly 2 8 , 2 0 0 4 Sheet 1 of 1 Motor Controller (PIC18F458 + 5AD’s + CAN Comm.) 14
MEASURING MOTOR PARAMETERS These are the motor parameters that are need: K e (volts-sec/rad) Motor voltage constant Motor torque constant K T (lb-in/amp) 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 ) Total inertia= J m + J load J Total ( lb − in − sec 2 ) Note that the above values are stated for a 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 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 the armature resistance between the 2 armature wires. The ohmic value of the armature resistance will be very small, thus a high sensitivity ohmmeter will be needed. 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 armature voltage. The K e is then the voltage you read divided by the speed in rad/sec. Convert rpm to rad/sec as rev 2π radias min  rad  = x x 60 sec  sec   min rev Volts [v] 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 (line − to − line) K e ( phase) = 1.73 MOTOR TORQUE CONSTANT K T The motor torque constant ( K T ) can be computed from the voltage constant ( K e ) as- K e  volts(l −l )   lb − in   = 0.00684  rpm  KT   amp    The derivation for the above equation is Equate Electrical Power to Mechanical Power converted to Watts 2π T 3xExI = x N x x 1.356 60 12 Where T : lb-in I : Amps E : Volts rms(line-to-line) N :rpm Rearranging terms and simplifying: E T = 0.00684 x N I Where   volts rms (l −l ) E = K e =  Back emf constant,    N rpm   lb − in   T = K T = Torque constant, A   I Converting rpm to rad/sec       v x rev x 60 sec   v x 60   v ( l −l )   =  rad  = 9.554 rad  Ke  rev 2π x min   x 2π      min   sec   sec  Thus 16
K e 9.554 = 0.00684 K T 9.554 KT = Ke 0.00684    v ( l −l )   lb − in   = 1396.8K e  rad  KT   amp     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 lb − in − sec 2 Inertia = acceleration DC MOTORS To do this test it is necessary to measure the acceleration of the motor rotor and the acceleration 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. The output of the tachometer should be connected to a strip chart recorder. When a step input in current is applied to the motor winding, the chart recorder will plot the rate of change of the motor shaft velocity as a function of the tachometer output voltage. The tachometer calibration can be used to convert volts to rpm. The acceleration is therefore the change in velocity for the linear part of the exponential curve (sometimes refered to as the 66% response of the exponential change in velocity) divided by the time elapsed for the detected rate of change in velocity. The resulting calculation of the acceleration must have the dimensions changed to be in units of rad/sec2. TORQUE- An ammeter must be inserted in series with the motor input winding. When the step in input current is applied to the motor input, the maximum value of current should be noted. This current must be converted to torque. The torque is equal to the maximum value of current observed multiplied by the motor torque constant. Torque [lbin]= amps[a] x KT [lb-in/a]. The inertia is then the acceleration torque divided by the acceleration - Inertia= Accel 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 some other procedure must be 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. This calibrated voltage can also be recorded with a stripchart recorder to observe its maximum value for a step voltage input to the servo amplifier. The inertia 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 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 then- Armature voltage or phase voltage [volts] Impedance = = [ohms] line current [amps] The impedance = reacctance2 + resis tan ce 2 = [ohms] reactance[var s] = impedance 2 − resis tan ce 2 Solve for the reactance from this equation. Note that the phase resistance was measured previously and will be small in value. The inductance can than be calculated from Reactance[var s] = 2π x frequency x inductance The frequency is probably going to be from the ac source at 60 Hz. Thus reactance[var s] Inductance [henries] = 2π x frequency[Hz] 18
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