M51971FP Mitsubishi, M51971FP Datasheet - Page 12

• Manufacturer Part Number: M51971FP
• Description: MOTOR SPEED CONTROL
• Manufacturer: Mitsubishi

4. Necessity for stable control
Stable control requires the gain of G
characteristics of 180˚ or less in a frequency area of 1 or more.
The relation of the phase and the gain is determined according to
the Baud’s theorem when all poles and zero points of the transfer
function are placed at the left side of the complex sphere.
If G
of | G
must be -12dB/oct or more for stable control.
For the reason above, when the circuit constant is selected to
achieve
and G
established with respect to the frequency of
inclination of the gain of G
To make a precise control, the gain of open-loop transfer function
must be large in the entire area of frequency.
The variation of the motor rotating speed attenuates due to
disturbance at an inclination of -6dB/oct with the frequency of
or more.
The capability of rotating speed control in the frequency area from
at
| G
G
Improvement of control precision in the frequency area from
The K
(5).
5. Influence on the Stability of Tacho-generator
The control system that is controlled with tacho-generator frequ-
ency, i.e. period, is a kind of sample hold system controlled with
discrete information in the time axis.
Addition of extra phase delay to sample hold operation makes the
system more unstable.
More precise transfer function H*(j ) (G
above operation into account is as follows, when H(j )(G
G
tion is not taken into account:
F1
C
F2
F2
M
C
(j )
(j )) is assumed to be the transfer function where this opera-
Frequency
C
F1
to
(j
or less.
requires the following conditions.
(j )
| G
H*(j ) =
C
(
CP
M
F1
(j )
F2
F1
F2
•
C
(j ) is -6dB/oct, that is, the following formula must be
F2
G
(j
or C
•
M
)
F1
| G
>>
G
). The following formula is established with
M
is determined by the gain of open-loop transfer function
•
•
M
G
(j ) is almost equal to -6dB/oct with the frequency of
M
G
C
F1
M
(j ) follows the Baud’s theorem, in a frequency area
1
M
)
(j
M
sin ( /
(j
•
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
(j ) |
+ C
M
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
G
, and the inclination of the gain of each of G
F2
( /
M
F2
F2
(j
)
) | < 1 and when the inclination of the gain of
•
value must be set to satisfy formulae (4) and
G
G
M
1 the inclination of gain of G
M
G
)
) | <
(j
)
C
(j )
e
– j
F2
2
•
) | < 1
G
G
F2
F1
n = –
M
(j ) begins to be -12dB/oct.
H(j
C
• • • • • • • • • • • • • • • • • • • • • • • • • • • • •
(S)
C
F2
M
*(j )
+ jn
•
G
• • • • • • • • • • • • • • • • • • • • • •
M
•
(S) to be the phase
G
G
)
M
• • • • • • • • • • • • • •
*(j )) taking the
F2
C
(j )
where the
•
G
C
(j )
M
C
F1
(10)
(11)
(12)
(j )
(j )
(9)
(8)
to
M
•
Where:
That is, extra phase delay of 2
account.
That is, if the angular frequency satisfying | G
is assumed to be
When this determines
function with
This formula (14) must be satisfied in the control system using the
frequency of the tacho-generator regardless of the control system
and indicates that the upper limit value of the control gain with
is inevitably determined when the motor and tacho-generator are
determined.
Improvement of the control precision in the rotating speed requires
| Gc(j
fore established.
6. Conclusion
According to the theoretical consideration above, the design of
speed control system making the best use of the characteristics of
the motor is described as follows:
If
is desirable to be set around minimum
As C
peak-to-peak value of the output pin waveform becomes larger and
the drive waveform becomes closer to pulse shape.
In most of design cases, both sides are therefore desirable to be
equal.
(3) Selection of gain constant
Keeping the relation satisfying formulae (16) and (17) above,
obtain a value for stable control by changing the K
value.
If the motor set speed is divided into several stages, stage of lower
speed is less stable. In this case, experiment must be made at
lower speeds.
G
: Set value of tacho-generator frequency
M
F1
sharply changes with motor load changed, a circuit constant
G
| G
M
0.357
(1)
(2)
is smaller, influence by
)
> 4
C
•
(j
G
MITSUBISHI <CONTROL / DRIVER IC>
•
F1
F2
M
•
M
M
(j
od
)
can be obtained.
G
M
•
M
B
R
G
R
od
) | >> 1. The following formula must be there-
F •
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
M
>> 1
F •
C
B
(j
1
F1
C
, the following relation must be established.
C
G
F2
F1 •
+ C
M
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
, the possible gain of open-loop transfer
) | < 0.357 x
MOTOR SPEED CONTROL
F2
C
F2
M
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
/
4
1
F2
M51971L/FP
G
(radian) must be taken into
becomes smaller, but the
M
G
.
G
M
• • • • • • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • •
C
*(j )
CP
•
G
M
or C
*(j ) | = 1
F1
+C
(14)
(17)
(15)
(16)
(13)
F2
M