MOTOR SPEED CONTROL
M51971L/FP
MITSUBISHI <CONTROL / DRIVER IC>
Hint for designing a stabilized speed control
system
(Method for determining the filter constants (CF1, CF2 and RF) at
pin
)
The filter constants at pin
must be determined to satisfy the
system stability.
1. Transfer Function of the Motor Speed Control
System
8
The motor speed control system is a negative feedback system
including a control circuit and a motor.
As the condition necessary for stable negative feedback, the phase
must be generally 180 or less in the frequency area where the
gain of open-loop transfer function (GC(S) GM(S)) is 1 or more.
2. Transfer Function of Motor
If the motor armature current and angular velocity are assumed to
be la and
ωv, respectively, the following equation is established.
Tg = KT la = (SJ+D) ωv (1)
Where: Tg : Torque generated in the motor
KT : Proportional constant between the torque genera-
ted in the motor and the armature current
J : Inertia moment of Motor and load
D : Coefficient of viscosity friction
If the number of poles in the tacho-generator is assumed to be P,
the relation of
ω = P ωv exists between tacho-generator angular
frequency
ω and motor angular velocity ωv and, therefore, the
motor transfer function (transfer function including motor and
tacho-generator) GM(S) takes a single-pole transfer function as
follows:
Where:
la
ω
=
D (1+S
)
P KT
D
J
=
1 +
KM
ωM
S
GM(S) =
(2)
(3)
D
P KT
KM =
J
D
ωM =
(4)
(5)
3. Transfer Function of Control Circuit Using the
M51971
If input information is assumed to be given continuously (the tacho-
generator frequency is assumed to be infinitely high), the transfer
function from the input at pin
to the output at pin
is as follows:
4
9
(input frequency at pin )
(output voltage at pin )
GC(M51971)(S)
(6)
4
9
=
CF1 + CF2
T
τ ( I C + I d )
8
x
S(1 + S/
ωF2)
1 + S/
ωF1
Where :
T
τ : Timer pulse width 1.10 x Rτ x Cτ
l C : Charging current at pin
l d : Discharging current at pin
8
~
RF CF2
1
ωF1
RF CF1 CF2
CF1 +CF2
ωF2
If the gain of the circuit connected to the back of pin
of the
M51971 is assumed to be KCP, transfer function GC(S) for the
entire circuit is as follows:
9
GC(S) = KCP
(7)
CF1 + CF2
T
τ ( I C + I d )
8
x
S(1 + S/
ωF2)
1 + S/
ωF1
x
≡
Control circuit
- GC (S)
Motor
GM (S)
Motor speed control system
log
G
M
(j
ω
)
log
ω
ωM
Approximate motor transfer function
log
G
C
(j
ω
)
log
ω
ωF1
Approximate transfer function of control circuit
ωF2