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 Limit cycle method
• In the limit cycle method, the two-position ON/OFF operation is performed three times for output of the manipulated amount
for the real system. From the vibration waveform data of the measured values, the vibration amplitude (Xc) and the
vibration cycle (Tc) are measured. Based on the measured values, each constant is determined.
• In the limit cycle method, less influence of the noise of the measured values is given as compared in the step response
method, and a stable tuning result can be obtained.
Example: Measured value ≤ set point (reverse action)
Set point[%]
Manipulated amount[%]
Limit cycle output upper limit
(Pr.1215-1000)
Limit cycle output lower limit
(Pr.1216-1000)
PID gain tuning start
STF
PID
PGT
*1
Details of the two-position ON/OFF operation
PID control operation
Reverse action
Forward action
• The manipulated amount is output at the limit cycle output upper limit (Pr.1215 - 1000). (When the measured value is higher
than the set point, the manipulated amount is once output at the limit cycle lower limit (Pr.1216 - 1000), and then after the
set point exceeds the measured value, the manipulated amount is output at the limit cycle output upper limit (Pr.1215 -
1000).)
• The two-position ON/OFF operation is repeated three times. From the waveform data of the values measured for output
of the second and third two-position operation, the vibration amplitude (Xc) and the vibration cycle (Tc) are measured.
• From the vibration amplitude (Xc) and the vibration cycle (Tc), the threshold sensitivity (Ku) and the threshold cycle (Tu)
are calculated.
• Each constant is calculated using a formula depending on the Pr.1218 setting, and PID gain tuning is finished.
• After the integral term is cleared, PID control is performed with the constant to which the change has been applied (the
constant used before PID gain tuning when a fault occurs).
Measured value[%]
2d
(two-position
output)
During
PID
control
Initial output of the manipulated amount
When measured value ≤ set point
Manipulated amount = Upper limit of the output
(Pr.1215 - 1000)
When measured value > set point
Manipulated amount = Lower limit of the output
(Pr.1216 - 1000)
When measured value ≤ set point
Manipulated amount = Lower limit of the output
(Pr.1216 - 1000)
When measured value > set point
Manipulated amount = Upper limit of the output
(Pr.1215 - 1000)
Vibration
period Tc
Vibration
amplitude Xc
(1)
(2)
(3)
During
During PID gain tuning
control
Two-position ON/OFF operation
Using measured value ≥ set point + hysteresis (Pr.1217)
Manipulated amount = Lower limit of the output (Pr.1216
- 1000)
Using measured value ≤ set point - hysteresis (Pr.1217)
Manipulated amount = Upper limit of the output (Pr.1215
- 1000)
Using measured value ≥ set point + hysteresis (Pr.1217)
Manipulated amount = Upper limit of the output (Pr.1215
- 1000)
Using measured value ≤ set point - hysteresis (Pr.1217)
Manipulated amount = Lower limit of the output (Pr.1216
- 1000)
PID gain tuning end
Limit cycle hysteresis
(Pr.1217)
Limit cycle hysteresis
Vibration
amplitude Xc
(Pr.1217)
Time
Two-position
ON/OFF operation
(1) First time
(2) Second time
(3) Third time
Time
PID
5. PARAMETERS
5.11 (A) Application parameters
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