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.