T HE C ONTROL V ARIABLE

T HE C ONTROL V ARIABLE

During the control of a process, the controller calculates the error value and adjusts the control variable accordingly to bring the error to zero. Like the error, the value of the control variable can also be expressed as a percentage of range; however, the control variable is expressed in terms of the full range of the controller’s output (i.e., the control field device). This range of the controller output is defined as:

CV actual − CV CV % min =

CV max − CV min

where:

CV % = the control variable value as a percentage of its range CV actual = the actual value of the controller output CV max = the maximum value of the controllable signal CV min = the minimum value of the controllable signal

The order and the sign of the nominator and denominator terms in this equation result in a control variable percentage value that is always positive, since the value of CV actual cannot be less than its minimum possible value.

Industrial Text & Video Company 1-800-752-8398

www.industrialtext.com

S ECTION PLC Process Process Responses C HAPTER 4 Applications

and Transfer Functions 14

E X AM PLE 1 4 -2

The PLC system shown in Figure 14-12 has an analog output module that sends a 0–10 VDC signal to an electric-to-pneumatic (I/P) con- verter. The I/P converter controls a steam valve that regulates the process to a set point of 140 °

C. The range of the controller output is from 0 to 4095 counts, which provides a range of 20 to 220 °

C in steam temperature control. The process variable has a value of 130 °

C. Find the percentage of controller output as a function of voltage.

I/P Converter

To Reactor

Output Module

Figure 14-12. Process regulated by an I/P converter.

S OLU T I ON

Figure 14-13 illustrates the relationship between the control variable output and the controllable range of temperature. Since the relation- ship between the controller output and the temperature is linear, the equation of the control variable as a function of voltage is repre- sented by:

 Temp max − Temp min   10 V − 0 V 

CV volt =

where T is the given value of the temperature and CV volt is the output of the controller in voltage. Note that this equation takes the form of the equation of a line, Y = mX + b (see Appendix E). At a temperature

of 140 °

C, then, the controller output in voltage would be:

Industrial Text & Video Company 1-800-752-8398

www.industrialtext.com

S ECTION PLC Process Process Responses C HAPTER 4 Applications

and Transfer Functions 14

CV 4095 counts 10 V

CV actual

6V

0 counts 0 V

Temp

220 ° C Figure 14-13. Relationship between control variable output and temperature range.

20 ° C SP = 140 °

CV volt =

 20  = 6 volts

So, the control variable in voltage as a percentage of total output would be:

CV actual − CV CV % min = CV max − CV min

6V0V − = 10 V 0 V −

If the minimum temperature output of 20 °

C corresponded to a con- troller output of 1 volt instead of 0 volts, the percentage output would be different because the value of the control variable ( CV actual ) would change, thus changing the percentage result (see Figure 14-14). A

temperature of 140 °

C would require a 6.4 volt output, which as a

percentage of the range would become: CV

4095 counts 10 V

6.4 V

1V 0 counts 0 V

Temp 20 ° C SP = 140 ° C 220 ° C

Figure 14-14. Minimum temperature output of 20 °

C corresponding to a 1 V

control variable output.

Industrial Text & Video Company 1-800-752-8398

www.industrialtext.com

S ECTION PLC Process Process Responses C HAPTER 4 Applications

and Transfer Functions 14

CV % =

64 . V–0V

10 V – 0 V 64 = . 10 = . 0 64 = 64 %

Having a minimum control output value that is greater than zero is common in many process control systems, because most systems require that the control element be constantly on to regulate the process variable. Note, however, that the range of the control variable is still from 0 to 10 V.