Chap. 21 The PID Instruction and application of FB-PLC

Chap. 21 The PID Instruction and application of FB-PLC
Chapter 21
21.1
General purpose PID control
Introduction of PID control
As the general application of process control, the open loop methodology may be good enough for most situations,
because the key control elements or components are more sophisticated, and the performances of which are getting
better, there is no doubt, the stability and reliability may meet the desired requirement. It is the way to get not bad C/P
value with great economic consideration. But the characteristics of the elements or components may change following the
time eclipse and the controlling process may be affected by the change of loading or external disturbances, the
performance of open loop becomes looser; it is the weakness of such solution. Thus, closed loop (with the sensors to
feedback the real conditions of controlling process for loop calculation) PID control is one of the best choices for
manufacturing process to make perfect quantity and best products.
FB-PLC provides digitized PID mathematical algorithm for general purpose application, it is enough for most of
applications, but the response time of loop calculation will have the limitation by the scan time of PLC, thus it must be
taken into consideration while in very fast closed loop control.
For an introduction to key parts of a control loop, refer to the block diagram shown below. The closed path around
the diagram is the "loop" referred to in "closed loop control".
Control Variable
Process Variable
Manufacturing Process
Mn
Error
Loop calculation
PV
+
Loop controller
SP
Set Point
Figure21-1. Typical Analog Loop Control System
21-1
21.2 How to select the controller
Depends on the requirement, the users may apply the suitable controller for different applications; it is much better
of the thinking that the control algorithm is so simple and easy to operate and the final result will be good enough, that's
all. Therefore comes the answers, there are three types of controller could be activated from the PID mathematical
expression, these are so called "Proportional Controller”, "Proportional + Integral Controller" and "Proportional + Integral +
Derivative Controller". The digitized mathematical expression of each controller shown bellows.
21.2.1 Proportional Controller
The digitized mathematical expression as follows:
Mn = (1000/Pb) × (En) + Bias
Where,
Mn :Output at time “n”.
Pb :Proportional band
- the expression stating the percent change in error required to change the output full scale.
〔Range:2〜5000,unit in 0.1%;Kc(gain)=1000/Pb〕
En :The difference between the set point (SP) and the process variable (PV) at time "n";
En = SP - PVn
Ts
:Solution interval between calculations(Range:1〜3000, unit in 0.01S)
Bias :Offset to the output(Range:0〜4095)
The algorithm of "Proportional Controller" is very simple and easy to implement, and it takes less time for loop
calculation. Most of the general applications, this kind of controller is good enough, but it needs to adjust the offset
(Bias)to the output to eliminate the steady state error due to the change of set point.
21.2.2 Proportional + Integral Controller
The digitized mathematical expression as follows:
n
Mn =(1000/Pb) × (En) +
∑ [(1000/Pb)×Ti×Ts×En] + Bias
0
Where,
Mn
: Output at time “n”.
Pb
: Proportional band 〔Range:2〜5000,unit in 0.1%;Kc(gain)=1000/Pb〕
En
: The difference between the set point (SP) and the process variable (PV) at time "n";
En = SP - PVn
Ti
: Integral tuning constant(Range:0〜9999,it means 0.00〜99.99 Repeats/Minute)
Ts
: Solution interval between calculations(Range:1〜3000, unit in 0.01S)
Bias : Offset to the output(Range:0〜4095)
The most benefit of the controller with integral item is to overcome the shortage of the "Proportional Controller"
mentioned above; via the integral contribution, the steady state error may disappear, thus it is not necessary to
adjust the offset manually while changing the set point. Almost, the offset(Bias)to the output will be 0.
21-2
21.2.3 Proportional + Integral + Derivative Controller
The digitized mathematical expression as follows:
n
Mn = (1000/Pb) × (En) +
∑ [(1000/Pb)×Ti×Ts×En] − [(1000/Pb)×Td×(PVn−PVn-1)/Ts] + Bias
0
Where,
Mn
:Output at time “n”.
Pb
:Proportional band 〔Range:2〜5000,unit in 0.1%;Kc(gain)=1000/Pb〕
En
: The difference between the set point (SP) and the process variable (PV) at time "n";
En = SP - PVn
Ti
: Integral tuning constant(Range:0〜9999,it means 0.00〜99.99 Repeats/Minute)
Td
:Derivative tuning constant (Range:0〜9999,it means 0.00〜99.99 Minute)
PVn
: Process variable at time “n”
PVn-1 : Process variable when loop was last solved
Ts
:Solution interval between calculations(Range:1〜3000, unit in 0.01S)
Bias
:Offset to the output(Range:0〜4095)
Derivative item of the controller may have the contribution to make the response of controlling process smoother
and not too over shoot. But because it is very sensitive of the derivative contribution to the process reaction, most
of applications, it is not necessary of this item and let the tuning constant (Td) be equal to 0.
21.3 Explanation of the PID instruction and example program follows
The followings are the instruction explanation and program example for PID (F U N 3 0 ) loop control of FB-PLC.
21-3
Mathematics instructions
FUN 30
PID
Convenient instruction of PID loop operation
FUN 30
PID
Ts :Solution interval between calculations
30.PID
Auto/Manual A/M
(1〜3000 ; unit in 0.01S)
ERR Invalid setting
Ts :
SR :
SR :Starting register of loop settings ;
Bumpless Transfer BUM OR :
HA
High Alarm
LA
Low Alarm
it takes 8 registers in total.
PR :
Direct/Reverse D/R
WR :
OR :Output register of PID loop operation.
PR :Starting register of loop parameters;
it takes 7registers.
Range
Operand
Ts
SR
OR
PR
WR
HR
ROR
DR
WR :Staring register of working registers
K
R0 R5000 D0
∣
∣
∣
R3839 R8071 D3071
○
○
○
○
○
○
○*
○*
○*
○*
○
○
○
○
○
for this instruction ;
it takes 5 registers and can't be
1〜3000
repeated in using.
●
The FB-PLC software algorithym uses mathematical functions to simulate a three-mode (PID) analog
controlling technique to provide direct digital control. The control technique responds to an error with an
output signal. The output is proportional to the error, the error's integral and the rate of change of the process
variable. Control algorithyms include, P, PI, PD and PID which all include the features of auto/manual
operation, bumpless/balanceless transfers, reset wind-up protection, and adaptive tuning of gain, integral,
and derivative terms.
●
The digitized mathematical expression of FB-PLC PID instruction as bellows:
n
Mn = (1000/Pb) × (En) +
∑ [(1000/Pb)×Ti×Ts×En] − [(1000/Pb)×Td×(PVn−PVn-1)/Ts] + Bias
0
Where,
Mn
: Output at time “n”
Pb
: Proportional band
- the expression stating the percent change in error required to change the output full scale.
〔Range:2〜5000,unit in 0.1%;Kc(gain)=1000/Pb〕
Ti
: Integral tuning constant (Range:0〜9999,it means 0.00〜99.99 Repeats/Minute
Td
: Derivative tuning constant (Range:0〜9999,it means 0.00〜99.99 Minute)
PVn
: Process variable at time “n”
PVn-1 : Process variable when loop was last solved
En
: The difference between the set point (SP) and the process variable (PV) at time "n";
En = SP - PVn
Ts
: Solution interval between calculations(Range:1〜3000, unit in 0.01S)
Bias
: Offset to the output(Range:0〜4095)
21-4
Mathematics instructions
FUN30
PID
Convenient instruction of PID loop operation
FUN30
PID
Principle of PID parameter adjustment
As the proportional band (Pb) adjustment getting smaller, the larger the proportional contribution to the
output. This can obtain a sensitive and rapid control reaction. However, when the proportional band is
too small, it may cause oscillation. Do the best to adjust “Pb” smaller (but not to the extent of making
oscillation), which could increase the process reaction and reduce the steady state error.
Integral item may be used to eliminate the steady state error. The larger the number (Ti, integral tuning
constant), the larger the integral contribution to the output.
When there is steady state error, adjust the
“Ti” larger to decrease the error.
When the “Ti” = 0, the integral item makes no contribution to the output.
For ex, if the reset time is 6 minutes, Ti=100/6=17;if the integral time is 5 minutes, Ti=100/5=20.
Derivative item may be used to make the process smoother and not too over shoot. The larger the
number (Td, derivative tuning constant), the larger the derivative contribution to the output. When there
is too over shoot, adjust the “Td” larger to decrease the amount of over shoot.
When the “Td” = 0, the derivative item makes no contribution to the output.
For ex, if the rate time is 1 minute, then the Td = 100; if the rate time is 2 minute, then the Td = 200.
Properly adjust the PID parameters can obtain an excellent result for loop control.
Instruction description
When control input "A/M"=0, it performs manual control and will not execute the PID calculation. Directly fill
the output value into the output register (OR) to control the loop operation.
When control input "A/M"=1, it defines the auto mode of loop control; the output of the loop operation is
loaded by the PID instruction every time it is solved. It is equal to Mn (control loop output) in the digital
approximation equation.
When control input "BUM"=1, it defines bumpless transfer while the loop operation changing from manual
into auto mode.
When control input "A/M"=1, and direction input "D/R"=1, it defines the direct control for loop operation;
it means the output increases as error increases
When control input "A/M"=1, and direction input "D/R"=0, it defines the reverse control for loop operation;
it means the output decreases as error increases
When comes the error setting of loop setting points or loop parameters, the PID operation will not be
performed and the output indication "ERR" will be ON
While the engineering value of the controlling process is greater than or equal to the user set High Limit,
the output indication "HA" will be ON regardless of "A/M" state.
While the engineering value of the controlling process is less than or equal to the user set Low Limit, the
output indication "LA" will be ON regardless of "A/M" state.
21-5
Mathematics instructions
FUN30
PID
●
Convenient instruction of PID loop operation
FUN30
PID
Description of operand Ts:
Ts:It defines the solution interval between PID calculations, the unit is in 0.01 sec; this term may be
constant or variable data.
●
Description of operand SR (Loop setting registers):
SR+0 = Scaled Process Variable:This register is loaded by the PID instruction every time it gets solved. A
linear scaling is done on SR+6 using the high and low engineering range found in SR+4 and
SR+5.
SR+1 = Setpoint (SP) :The user must load this register with the desired setpoint the loop should control
at. The setpoint is entered in engineering units, it must be the range:LER ≦ SP ≦ HER
SR+2 = High Alarm Limit (HAL): The user must load this register with the value at which the process
variable should be alarmed as a high alarm (above the setpoint). This value is entered as the
actual alarm point in engineering units and it must be the range:LER ≦ LAL < HAL ≦ HER
SR+3 = Low Alarm Limit (LAL): The user must load this register with the value at which the process
variable should be alarmed as a low alarm (below the setpoint). This value is entered as the
actual alarm point in engineering units and it must be the range:LER ≦ LAL < HAL ≦ HER
SR+4 = High Engineering Range (HER): The user must load this register with the highest value for
which the measurement device is spanned. (For example a thermocouple might be spanned for 0
to 500 degrees centigrade, resulting in a 0 to 10V analog input to the FB-PLC (0V=0℃, 10V=500
℃); the high engineering range is 500, this is the value entered into SR+4.)
The high engineering range must be:−9999 < HER ≦ 9999
SR+5 = Low Engineering Range (LER):The user must load this register with the lowest value for which
the measurement device is spanned.
The low engineering range must be:−9999 ≦ LER ≦ LAL < HAL ≦ HER
SR+6 =
Raw Analog Measurement (RAM):The USER'S PROGRAM must load this register with the
process variable (measurement). It is the value that the content of analog input register(R3840
〜R3903)is added by the offset of 2048. It must be the range:0 ≦ RAM ≦ 4095
SR+7 = Offset of Process Variable (OPV):The user must load this register with the value as described
follows: OPV must be 0 if the raw analog signal and the measurement span of the analog input
module are all 0〜20mA, there is no loss of the measurement resolution; OPV must be 819 if the
raw analog signal is 4〜20mA but the measurement span of the analog input module is 0 〜
20mA, there will have few loss of the measurement resolution(4095 × 4 / 20 = 819).
It must be the range:0 ≦ OPV < 4095
When the setting mentioned above comes error, it will not perform PID operation and the output indication
"ERR" will be ON.
●
Description of operand OR:
OR:Output register, this register is loaded directly by the user while the loop in manual operation mode.
While the loop in auto operation mode, this register is loaded by the PID instruction every time it is
solved. It is equal to Mn (control loop output) in the digital approximation equation. It must be the
range:0 ≦ OR ≦ 4095
21-6
Mathematics instructions
FUN 30
PID
●
Convenient instruction of PID loop operation
FUN 30
PID
Description of operand PR (Loop parameters):
PR+0 =
Proportional Band (Pb):The user must load this register with the desired proportional
constant. The proportion constant is entered as a value between 0002 and 5000 where the
smaller the number, the larger the proportional contribution.
(This is because the equation uses 1000 divided by Pb.)
It must be the range:2 ≦ Pb ≦5000, unit is in 0.1%
Kc(gain)=1000/ Pb
PR+1 =
Reset Time Constant (Ti):The user may load this register to add INTEGRAL action to the
calculation. The value entered is "Repeats/Minute" and is entered as a number between 0000
and 9999. (The actual range is 00.00 to 99.99 Repeats/Minute.) The larger the number,
the
larger the integral contribution to the output.
It must be the range:0 ≦ Ti ≦ 9999 (0.00〜99.99 Repeats/Minute)
PR+2 =
Rate Time Constant (Td):The user may load this register to add DERIVATIVE action to the
calculation. The value is entered as minutes and ia entered as a number between 0000 and
9999. (The actual range is 00.00 to 99.99 minutes.) The larger the number, the larger the
derivative contribution to the output.
It must be the range:0 ≦ Td ≦ 9999 (0.00〜99.99 Minutes)
PR+3 =
Bias:The user may load this register if a bias is desired to be added to
the output when
using PI or PID control. A bias must be used when running PROPORTIONAL only control. The
bias is entered as a value between 0 and 4095 and is added directly to the calculated output.
Bias is not required for most applications and may be left at 0.
It must be the range:0 ≦ Bias ≦ 4095
PR+4 =
High Integral Wind_up Limit (HIWL):The user must load this register with the output value,
(0 to 4095), at which the loop shoud go into "anti-reset wind-up" mode. Anti-reset wind-up
consists of solving the digital approximation for the integral value. For most applications this
should be set to 4095.
It must be the range:0 ≦ HIWL ≦ 4095
PR+5 =
Low Integral Wind_up Limit (LIWL):The user must load this register with the output value, (0
to 4095), at which the loop shoud go into "anti-reset wind-up" mode. It functions in the same
manner as PR+4. For most applications this should be set to 0.
It must be the range:0 ≦ LIWL ≦ 4095
PR+6 =
PID Method:
=0 , Standard PID method;
=1 , Minimum Overshoot Method;
Method 0 is prefer because most applications using PI control (Td=0).
The user may try method 1 when using PID control and the result is not stable.
When the setting mentioned above comes error, it will not perform PID operation and the output indication
"ERR" will be ON.
21-7
Mathematics instructions
FUN 30
PID
●
FUN 30
PID
Convenient instruction of PID loop operation
Description of operand WR (Working registers):
WR+0 = Loop status register:
Bit0 =0 , Manual operation mode
=1 , Auto mode
Bit1 : This bit will be a 1 during the scan the solution is being solved,
and it is ON for a scan time.
Bit2=1 , Bumpless transfer
Bit4 : The status of "ERR" indication
Bit5 : The status of "HA" indication
Bit6 : The status of "LA" indication
WR+1 = Loop timer register:This register stores the cyclic timer reading from the system's 1ms cyclic
timer each time the loop is solved. The elapsed time is calculated by calculating the difference between
the current reading of the system's 1ms cyclic timer and the value stored in this register. This difference is
compared to 10 × the solution interval. If the difference is greater than or equal to the solution interval,
the loop should be solved this scan.
WR+2 = Low order integral summation:This register stores the low order 16 bits of the 32 bit sum created
by the integral term.
WR+3 = High order integral summation:This register stores the high order 16 bits of the 32 bit sum
created by the integral term.
WR+4 = Process variable - previous solution:The raw analog input (Register SR+6) at the time the loop
was last sovled. This is used for the derivative control mode.
Program example
11.( + )
Sa : R3840
Adding the content of analog input register with the offset
2048 and stores it into R1006 being as the raw analog
input of PID instruction.
X0
X0=0,Manual operation
=1,Auto operation
A/M
BUM
D/R
Sb : 2084
D : R1006
30.PID
Ts : R 999
SR : R1000
OR : R1010
PR : R1020
WR : R1030
12.( )
Sa : R1010
R1010 is the output of PID instruction.
Sb : 2048
Deducting the offset 2048 from the output value and stores
it into the analog output register to output.
D : R3904
21-8
ERR
HA
LA
Y0
Y1
Y2
Mathematics instructions
FUN 30
PID
Convenient instruction of PID loop operation
FUN 30
PID
R999 :The setting of solution interval between
calculations; for example the content of R999 is
200, it means it will perform this PID operation
every 2 seconds.
R1020 :The setting of proportional band; for
example the content of R1020 is 20,
it means the proportional band is 2.0%
and the gain is 50.
R1000 :Scaled process variable, which is the engineering
unit loaded by the PID instruction every time it
gets solved. A linear scaling is done on R1006
using the high and low engineering range found
in R1004 and R1005.
R1021 :The setting of integral tuning constant;
for example the content of R1021 is 17,
it means thereset time is 6 minutes
(100/6≒17).
R1001 :Setpoint, it is the desired value the loop should
control at; which is entered in engineering unit.
For example the span of controlling process is
0°C〜500°C, the setting of R1001 is equal to
100, it means the desired result is at 100°C.
R1002 :The setting of high alarm limit; which is entered in
engineering unit.
The example mentioned above, if the setting of
R1002 is equal to 105, it means there will have
the high alarm while the loop is greater than or
equal to 105°C.
R1003 :The setting of low alarm limit; which is entered in
engineering unit. The example mentioned, if the
setting of R1003 is equal to 95, it means there
will have the low alarm while the loop is less than
or equal to 95°C.
R1004 : The setting of high engineering range. The
example mentioned, if the setting of R1004 is
equal to 500, it means the highest value of this
loop is 500°C.
R1005 : The setting of low engineering range. The
example mentioned, if the setting of R1005 is
equal to 0, it means the lowest value of this loop
is 0°C.
R1006 :Raw analog measurement; it is the value that the
content of analog input register (R3840〜R3903)
is added by the offset of 2048.
R1007 :Offset of process variable; let it be 0 if the raw
analog signal and the span of the analog input
module are all 0〜10V.
21-9
R1022 :The setting of derivative tuning constant;
for example the content of R1022 is 0, it
means PI control.
R1023 :The setting of the bias to the output;
most applications let it be 0.
R1024 :The setting of high integral wind-up;
most applications let it be 4095.
R1025 :The setting of low integral wind-up;
most applications let it be 0.
R1026 :The setting of PID method;
most applications let it be 0.
R1030 = Loop status register
Bit0 =0, Manual operation mode
=1, Auto operation mode
Bit1 : This bit will be a 1 during the scan the
solution is being solved, and it is ON for
a scan time.
Bit2=1 , Bumpless transfer
Bit4 : The status of "ERR" indication
Bit5 : The status of "HA" indication
Bit6 : The status of "LA" indication
R1031〜R1034: They are the working registers,
please refer to the description of
operand WR.
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