PID M ODULES
PID M ODULES
Proportional-integral-derivative (PID) interfaces are used in process applications that require continuous closed-loop control employing the PID algorithm. These modules provide proportional, integral, and derivative
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control actions according to sensed parameters, such as pressure and tempera- ture, which are the input variables to the system. PID control is often referred to as three-mode, closed-loop feedback control. Figures 8-13 and 8-14 illustrate PID control in block diagram form and process form, respectively.
Output
Block
Field Device
Transfer of Information
(e.g., valve)
(PID Control)
Input
Sensor
(e.g., set point, limits,
alarms, etc.)
Input Field Device
Figure 8-13. Block diagram of PID control.
Temperature Sensor
Set
PID
Analog Output
(PID Control)
Analog Steam Input
TC
Tank must
Temperature
be at a set point
temperature Figure 8-14. Illustration of a PID control process.
Transmitter
The basic function of closed-loop process control is to maintain certain process characteristics at desired set points. Process characteristics often deviate from their desired set point references as a result of load material changes, disturbances, and interactions with other processes (see Figure 8- 15). During control, the actual process characteristics (liquid level, flow rate, temperature, etc.) are measured as the process variable (PV) and compared with the target set point (SP). If the process variable (actual value) deviates from the set point (desired value) an error (E) occurs (E = SP – PV). Once the module detects an error, the control loop modifies the control variable (CV) output to force the error to zero.
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PID Module
Disturbances Output Output
set point
SP
Error ( E)
PID
Variable Module Control
from PLC +
E = SP – PV Control
(e.g., temp.
target ˚ C)
PV
(e.g., steam valve)
Process Variable
Input To Module
Sensor (e.g., temp.)
Input Device
Figure 8-15. Closed-loop process control.
The following equation defines one of the control algorithms implemented by
a PID module:
dE
V out = KE P + K I Edt + K ∫ D
dt where:
K P = the proportional gain
I = T I , which is integral gain ( T I = reset time ) K D = KT P D , which is derivative gain ( T D = rate time )
E = SP − PV , which is error V out = the control variable output
The PID module receives the process variable in analog form and computes the error difference between the actual value and the set point value. It then uses this error difference in the algorithm computation to initiate a three- step, simultaneous, corrective action through a control variable output. First, the module formulates a proportional control action based on an output control variable that is proportional to the instantaneous error value
(K P E ). Then, it initiates an integral control action (reset action) to provide additional compensation to the output control variable. This causes a change in the process variable in proportion to the value of the error over a period
of time (K I or K P /T I ). Finally, the module initiates a derivative control action (rate action) adding even more compensation to the control output (K D = K P T D ). This action causes a change in the output control variable proportional to the rate of change of error. These three steps provide the desired control action in proportional (P), proportional-integral (PI), and proportional-integral- derivative (PID) control fashion, respectively.
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A PID module receives primarily control parameter and set point informa- tion from the main processor. The module can also receive other parameters, such as maximum error and maximum/minimum control variable outputs for high and low alarms, if these signals are provided. During operation, the PID interface maintains status communication with the main CPU, exchang- ing module and process information. Figure 8-16 illustrates a block diagram of the PID algorithm and a typical PID module connection arrangement.
Feedforward Input
Lag Controlled
Variable
BIAS Variable
Digital PV –
I Output
(a)
PC Processor
auto/manual station
Manual Request Man/Auto Tracking
Block Transfer
Manual Request
Tieback Input
PR
Analog Input ( PV)
+5 VDC 1.2 A Optional Supply
(b)
Figure 8-16. (a) Block diagram of the PID algorithm and (b) a connection diagram for
Allen-Bradley’s 1771-PID module.
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Depending on the module used, PID interfaces can also receive data about the update time and the error deadband. The update time is the rate or period in which the output variable is updated. The error deadband is the quantity that is compared to the error signal (see Figure 8-17); if the error deadband is less than or equal to the signal error, no update takes place. Moreover, some modules also provide square root calculations of the process variable. To provide this calculation, the module performs a square root extraction of the process variable to obtain a linearized scaled output, which is then used by the PID loop. The control of flow by a PID is an example of an application using
a square root extractor. Chapter 15, which describes process controller responses, explains more about PID.
PV Update
PV
Error > + DB
+ DB
SP
Deadband ( DB)
– DB Error < – DB
Update
Time
Figure 8-17. Error deadband.