Question

14. The process engineer says that you are to move the PID controller from auto to manual if the PV analog signal (4-20 mA) is invalid in the low range (less than the minimum allowable value) for a CompactlogixA-B processor. Show with an example program how to accomplish this in ladder logic. Assume the analog is addressed as Analog_Value. Assume the PV signal is un-scaled and the minimum acceptable value is input 15. T/F Windup of the controller is possible in manual mode? T/F The controller performs exactly the same whether the controller is set for E = PV-SP or E-SP-PV. 16. In the chapter on safety, there was a chart comparing Categories (Cat) with SIL values. Show the comparisons between the two and show where fail-safe is required. chot 2.0 At what level is the power-supply incorporated into the safety hardware?

Answer 1

14) PID controller :

The control variable of the PID controller can be calculated using the formula

C= g_pe+ $\sum$ g_i e $\Delta$ t+g_d $\Delta$ E/ $\Delta$ t

Here the control variable c can be calculated using the above expression

e is the error

g_p is the proportional gain value

g_i denotes the integral gain value

g_d represents the derivative gain value

$\Delta$ E is the new error value

$\Delta$ t is the updated gime

For the given problem the controlled variable C can be written as

C=(G1000/p)*e+ $\sum$ [G1000/p)*G_i*Td* v_n]-[G1000/p)*Ts*(v_n-n_n-1)/Ts]+bias

In the above equation

G1000 represents the gain constant ranges from 1 to 1000 (allowable value)

p=proportional range from 1 to 1000

v_n= PV(process variable) at time n

v_n-1=PV(process variable) at time n-1

e=setpoint value-process variable=SP-PV at time n

Td= tuning constant

Ts= ouptut interval

bias=offset range

Example:

Ladder logic is like a ladder symbol we have five instruction sets:

Ts //solution interval for setting error

SR//starting register

ER//end register

LR//starting register for loop

WR//write register

Program:

s1: R1000 //stores the register content in s1

s2: R2000 //stores the register content in s2

A: R3000 // adds the offset R2000 and stores the content of analog input in A

Ts :R1001 // This stores the output difference between calculations

SR: R1010 //This instruction does the scaling of the PV, that is it sets the range of the process variable in two registers.

ER: R1015 // Scaled setpoint value, since we are using the feedback as the loop signal to the integral unit, the error is controlled. This sets the setpoint value SP.

LR: R1030 //The loop registers sets the range. If the acceptable range is 100 then the acceptable range is 1% to have the gain 100.

WR: R1040 // This is the register write operation mode. 0 indicates manual and 1 indicates the automatic mode.

s1: R1050 // shows the output of the PID instruction

s2: R2010 // reducing the offset value from the output and stores the analog input(A-B)

A: R2040 // if the value of the register R2040 in between 0 and 1000(permissible range) the value R2010 must be 0 and if the value of R2040 is above less than 0 or greater than 1000 then the value of R1050 is 8192(some memory value)

15) The wind up of the controller is possible in manual mode-True

Windup occurs when there is huge increase in the setpoint value which leads to the error larger than the regulated error value which in turn makes the system unstable. This can be avoided by

disabling the integral unit until the process variable comes to the controllable level.

setting up the integral term with in permissible limits

initializing the integral term each term with the error value as feedback (input) to the integral unit to obtain the regulated output.

The controller performs exactly the same when the controller is set for E=PV-SP or E=SP-PV -- False

The error value is calculated as E=SP-PV =Set point value-Process variable. The error is calculated to keep the integral term in control.