Reference: How To Obtain Three Constants In Pid Control (Limit Cycle Method - Mitsubishi Electric MELSEC-FX3S Series Manual

FX /FX /FX /FX /FX
3S 3G 3GC 3U
PID Instruction (FNC 88)
4.1.3

Reference: How to obtain three constants in PID control (limit cycle method)

For acquiring satisfactory control results in PID control, it is necessary to obtain the optimal value of each
constant (parameter) suitable to the control target.
This paragraph explains the limit cycle method to obtain the amplitude (a) and vibration cycle (
input value, and then calculate the proportional gain (K
the expressions shown in the table below.
What is the limit cycle method
Changes in the input value in two-position control (in which the output Upper Limit Value (ULV) and output
Lower Limit Value (LLV) are switched according to the deviation) are measured, and then three constants in
the PID control are obtained.
Operation characteristics (in an example of backward operation)
τ
During the " w" period after the tuning cycle is finished, the output value is held at the output Lower Limit
Value (LLV), and then normal PID control is started.
τ
The value " w" can be obtained by the expression "
parameter "Kw" can be set in the parameter
(Setting range: Kw = −50 to +32717[%])
(When the abnormal range is specified, "
Output value
ULV
(Output upper
limit value)
LLV
(Output lower
limit value)
Input value
SV+SH
PV
SV(target value)
SV-SH
PV
Operation characteristics and three constants
Control type
Only proportional
control (P operation)
PI control
(PI operation)
PID control
(PID operation)
M-20
PLC User's Manual - Analog Control Edition
3UC
Proportional gain (K
1
(
ULV - LLV
a
0.9
(
ULV - LLV
a
1.2
(
ULV - LLV
a
), integral time (T
P
τ
w = (50 + Kw)/100 × (
+28.
S
3
τ
w" is handled as "0")
τ
τ τ
0 1
) [%] Integral time (T
P
)
⎯
×100
)
× 100 τ
33 ×
on
)
× 100 τ
20 ×
on
4.1 Limit Cycle Method
) and differential time (T
I
τ τ
- on)", and the wait setting
τ
τ
on
w
τ
2
SH : PV input threshold (hysteresis)
PV
) [×100ms] Differential time (T
I
τ
on
1 -
τ
τ
on
τ
50 ×
1 -
τ
4 Auto-Tuning
τ τ
, on) of the
) based on
D
Time
a
Time(s)
) [×10ms]
D
⎯
⎯
τ
on
1 -
on
τ