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