PWM speed regulation of a DC motor

BASICS OF AUTOMATIC REGULATION
PWM speed regulation of a DC motor
The scheme presents speed regulation of a DC motor (DCM) with the possibility of controlling the direction
of spinning.
Changing the direction of spinning is done in a way that the motor is connected in a „H - bridge“, and the
actual change is controlled with a coder T.
PWM ( pulse width modulation) is done by using a integrated circle LM 339 ( 4 x comparator) of which only
two are used. The first comparator is used as a astable multivibrator which oscillates at a frequency set by
ressistance R1 and the capacitor C1, and the second comparator (OP2) is used for adjusting the „Duty
Cycle“ of PWM signal which we lead on the base of the transistor that connects the „H – Bridge“ to the
mass.
Comparator 1 (OP1) works as a comparator with a hysteresis which oscillates thanks to the fact that
different currents pass trough the diodes D1 and D2, and it can be seen from the I – U characteristic of the
PN diode on image 2.
It's very important that the ressistance R1 is multiple times larger of ressistances R2( R1/R2 = 10 in this case),
because then the current that runs trough diode D2 ID2 is multiple times larger and of course according to
that the voltage drop on diode UD2 becomes larger then the drop on UD1. If the situation was opposite there
wouldn't be any oscillations ; that is the comparator OP1 wouldn't get out of negative saturation.
On capacitor C1 we get sawtooth voltage in a range from 0,65V ( UD2 ) to 5,15V ( 1/3 Vcc voltage of
powering. Vcc = 16V! VCC* R3/( R2 + R3 )). That sawtooth voltage is brought on the inverted input of
comparator ( OP2 ) , while on the non inverted input we bring voltage from potentiometer P which we use
to control the speed of spinning ( Duty Cycle 0 – 100% ).
On output OP2 we get a PWM signal which we run trough ressistance R6 to the base of the Darlington
transistor made of transistors T5 and T6 and by doing that we connect the mass to the lower branch of H –
Bridge ( emitters T2 and T4 ).
We connect the DCM in the diagonal of H – bridge which we control by coder T over inverter In1 and In2 (
1/2 CD4001)
Bases of transistors T1 and T4 are connected as well as the bases of transistors T2 and T3
so that one direction of spinning is controlled by transistors T1 and T4 while transistors T2 and T3
are blocked and vice versa.
In order to calculate the frequency of PWM signal, we must know
that the capacitor C1 is charged
according to the exponential law and that in the starting moment
(t=0) voltage on capacitor Uc0, and
value of ressistance is R1 ( UDD – Uc0 ). The capacitor empties in a
moment because the ressistance
of the diode D1 is very low. If we apply knowledge of mathematics we get the
following:
Udd = Uc + Ur / d
dUdd = dUr + dUc
Ur = R ⋅ i / d
dUr = Rdi
PWM speed regulation of a DC motor
Q = CUc / d
dQ = CdUc
idt = CdUc
idt
dUc =
C
0 = dUr + dUc
High School MATE BLAŽINE LABIN 1
BASICS OF AUTOMATIC REGULATION
0 = R ⋅ di + i ⋅ dt / C
− ln(i ) + ln(k ) =
1
t
RC
k
t
ln( ) =
i
RC
dt
− Rdi = i
C
di dt
− =
/∫
i RC
di
dt
−∫ =∫
i
RC
e
t / RC
i = k ⋅e
=
k
i
−t /( RC )
In moment t = 0 the current of charging is I = Ur/R = (Udd –Uco)/R so by using these values we get:
(Udd – Uco)/R = k*e0so k becomes k = (Udd – Uco)/R so by that the current is in fuction of time
i=
Udd − Uco − t /(RC )
e
R
Voltage on the capacitor:
At the current moment t=0
Uc = Uco so the constant equals:
∫ idt = C ∫ dUc
U − Uco − t /( RC )
⋅e
dt = CUc + k
R
− t /( RC )
U − Uco
= CUc + k
(− RC ) ⋅ e
R
− t /( RC )
− C (U − Uco) ⋅ e
= CUc + k
∫
− C (U − Uco) ⋅ 1 = CUco + k
k = −C ⋅ U
By applying shown values we get the expression for the voltage on the capacitor:
− C (U − Uco) ⋅ e
− (U − Uco) ⋅ e
− t /( RC )
− t /( RC )
= CUc − CU
= Uc − U
and finally we get the voltage on the capacitor in the function of time:
Uc = U − (U − Uco) ⋅ e
e
− t /( RC )
=
− t /( RC )
U − Uc
/ ln
U − Uco
PWM speed regulation of a DC motor
we look for a value of time for voltage value of voltage Uc.
−
t
U − Uc
= ln(
)
RC
U − Uco
High School MATE BLAŽINE LABIN 2
BASICS OF AUTOMATIC REGULATION
U − Uco
t = RC ln(
)
U − Uc
If we apply the next values, and the values are the voltage on the capacitor Uco = 0,65V, voltage that the
capacitor will be filled with Uc = 5,15V and the voltage of the whole set which fills the capacitor
U = 16v, we get the time need for the capacitor to fill up.
3
− 9 16 − 0,65
t = 220 ⋅ 10 ⋅ 22 ⋅ 10 ln(
) = 1,68ms
16 − 5,15
And the frequency of the PWM pulse f = 596 Hz.
PWM speed regulation of a DC motor
High School MATE BLAŽINE LABIN 3