lab 8. speed control of a d.c. motor - auburn...
TRANSCRIPT
Lab 8. Speed Control of a D.C. motor
The Motor Drive
Motor Speed Control Project1. Generate PWM waveform2. Amplify the waveform to drive the motor3. Measure motor speed4. Measure motor parameters5. Control speed with a computer algorithm
microcontroller
12 v dcMotor
acTachometer
Amplifier9 v
PowerSupply
SignalConditioning(Frequency
or Amplitude)
Buehler 12 volt permanent-magnet dc motor with tachometer output
Electrical Connections
yellow/green -- tachometer output
blue/red -- motor winding
Note: Tachometer wires may not have two colors on some units.
Exploded view
Motor electro-mechanical modelsRa – armature winding resistanceLa – armature winding inductanceia – armature currentVt – terminal voltageea – back emf
Tm – developed torqueTL – torque needed for loadω – rotational speedB – friction coefficientJ – moment of inertia
Motor Electrical Dynamics
ma
aa
aat
Ke
edtdiLiRv
ω=
++⋅=
ea = “back emf” (electromotive force) generated within armature windings
Note: back emf = 0 at standstilland increases linearly with motor speed
Mechanical Dynamics Analogous to Electrical Circuits!
Equations for these systemshave similar form.
Motor Mechanical Dynamics
am
Lm
iKT
TBdtdJT
⋅=
+⋅+⋅= ωω
Tm = developed torque increases with currentJ = motor moment of inertiaB = motor friction coeffientω = angular velocity of the motorTL = torque required to drive the load
Laplace Transformed Equations
Electrical
Mechanical
)()()()( sKssILsIRsV aaaat Ω⋅+⋅+⋅=
)()()()( sTsBssJsIK La +Ω⋅+Ω⋅=⋅
Steady state analysis (s=0)
Electrical steady state
Mechanical steady state
Solve for speed
Ω⋅+⋅= KIRV aat
La TBIK +⋅=⋅ Ω
tma
Lma
a VKBR
KTKBR
R⋅
++⋅
+−= 22Ω
Motor speed vs. load torque Speed is related to load torque and terminal voltage
Ω
LT
tV increasingspeed 1
operating points
load 1 load 2
speed 2
Transient response experiment
Measure Vmotor, VR, and Vtach
Imotor = VR (because R = 1)
Experimental results
Current reaches 1 amp during startup!
What we now know: For a given load, motor speed is proportional to voltage applied to
its terminals Use of a PWM signal allows the average voltage of the signal to
be varied by varying duty cycle
We have a 12v dc motor (max. terminal voltage is 12v) A 3 volt signal will be insufficient to produce full speed, PLUS … Motor may draw amps of current, whereas digital chip outputs can
typically supply only milliamperesIdea: Use a single transistor switch to
amplify the digital PWM signalto drive the motor
+=
211TT
TVV digitalavgT1 = “ON” timeT2 = “OFF” time
Basic Transistor Switch
(ideal models)
Switching an Inductive Load(motor winding) Inductor voltage-current law:
When current iC is switched off, diC/dt is large and negative Inductor voltage is large and
negative Collector voltage > Vcc
Q may be destroyed!
Switching an Inductive Load(need to protect switch Q) Use anti-parallel diode D!!!
reverse biased when Q is ON gives alternate current path when Q
switches OFF (when inductor voltage becomes negative)
protects Q Collector voltage is clamped to Vcc+Vdiode
a.k.a. freewheeling diode
Drive design model
Drive Design parameters
Maximum load current, ILOAD
Transistor current gain, hFE
Transistor voltage VBE(sat) in saturation mode
Microcontroller output voltage, Vhigh
Design Equations
Requirement for base current in the ON state
Calculate base series resistance, R
FE
LOADB h
II >>
EE Board variable power supplyPositive SupplyVP+ output voltage & current limit
VP+ ON
Waveforms Power Supply Window
ActualVP+ Current
Connect grounds of multiple power supplies
Lab Procedure Verify proper PWM signal generation Measure ac tachometer output (yellow/green
leads) at multiple non-zero speeds Plot motor speed vs. PWM signal duty cycle Repeat for several PWM signal frequencies,
over a range of values Find the “best” frequency (produces most linear
plot)
Choice of devices
Transistor (Q) 2N3904 is cheap but under-rated for current 2N2222 has higher current rating Both may be destroyed if motor is stalled
Diode (D) 1N4001 is a rectifier diode: a bit slow, has large
diameter leads 1N4148 (or 1N914) is a switching diode: faster,
but has low current rating (but is not expensive)
2N2222 NPN transistor dataAbsolute Maximum RatingsSymbol Parameter Value Unit
VCEO Collector-emitter voltage (base open) 40 VVCBO Collector-base voltage (emitter open) 75 VVEBO Emitter-base voltage (collector open) 6 V
IC Collector current 1 A
Electrical CharacteristicsSymbol Parameter Conditions min max Unit
hFE Dc current gain IC = 150 mA, VCE = 1 V 50VCE(sat) Collector-emitter
saturation voltageIC = 150 mA, IB = 15 mA 0.3 V
VBE(sat) Base-emitter saturation voltage
IC = 150 mA, IB = 15 mA 0.6 1.2 V
Source: Fairchild Semiconductor
2N3904 NPN transistor dataAbsolute Maximum RatingsSymbol Parameter Value Unit
VCEO Collector-emitter voltage (base open) 40 VVCBO Collector-base voltage (emitter open) 60 VVEBO Emitter-base voltage (collector open) 6 V
IC Collector current 200 mA
Electrical CharacteristicsSymbol Parameter Conditions min max Unit
hFE Dc current gain IC = 100 mA, VCE = 1 V 30VCE(sat) Collector-emitter
saturation voltageIC = 50 mA, IB = 5 mA 0.3 V
VBE(sat) Base-emitter saturation voltage
IC = 150 mA, IB = 5 mA 0.95 V
Source: Fairchild Semiconductor
1N4148 switching diode dataAbsolute Maximum RatingsSymbol Parameter Value Unit
VRRM Maximum repetitive reverse voltage 100 VIO Average rectified forward current 200 mAIF Dc forward current 300 mAIC Collector current 200 mA
Electrical CharacteristicsSymbol Parameter Conditions min max Unit
VF Forward voltage IF = 100 mA 1 VIR Reverse leakage VR = 20 V 0.025 µAtrr Reverse recovery time IF = 10 mA, VR = 6 V, Irr
= 1 mA, RL = 100 ohm4 ns
Source: Fairchild Semiconductor