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Simple PID code

One method of handling the integration and bumpless transfer to automatic mode is an algorithm that calculates the change in output from one pass to the next using the derivative of the PID algorithm, or:

dOut/dt  = gain  x  (dError/dt + ResetRate x Error + Derivative x d2Error/dt2

derivative of output = gain x (derivative of error +  reset rate  x error + second derivative of error)

This program is run every second. If the control loop is in manual, the output is adjusted by the operator through the operator interface software. If the control loop is in Automatic, the output is computed by the PID algorithm.

Each pass the output is changed by adding the change in output to the previous pass output. That change is the sum of:

• the change in error (Err-ErrLast)
• the error multiplied by the reset rate, and
• the second derivative of the error (Err-2*ErrLast+ErrLastLast) times the derivative.

The total is then multiplied by the gain.

This simple version of the PID controller work well in most cases, and can be tuned by the standard PID tuning methods (some of which are discussed later). It has “Parallel” rather than “Series” reset and derivative, and derivative is applied to the error rather than the input only.

Variables:

Input         Process input
InputLast     Process input from last pass, used in deriv. calc.
Err            Error, Difference between input and set point
ErrLast       Error from last pass                
ErrLastLast   Error from next to last pass
OutP          Output of PID algorithm
Mode          value is ‘AUTO’ if loop is in automatic
Action        value is ‘DIRECT’ if loop is direct acting
Derivative        Derivative value in minutes
Reset           reset rate in repeats per minute
SetP                     Set Point, set by operator
Mode                   String, set to "AUTO" or "Manual" by operator
Action                  String, set to "REVERSE" or "DIRECT" during configuration

The PID emulation code:

 1.           IF Mode = ‘AUTO’ THEN

2.             Err=SetP- Input           Error based on reverse action

3.             IF Action = ‘DIRECT’ THEN

4.                   Err=0 – Err           Change sign of error for direct action

5.             ENDIF

6.            OutP=OutP+Gain*(Err-ErrLast+Reset*Err+Deriv*(Err-ErrLast*2+ErrLastLast))
Calculate the change in output using the derivative of the PID algorithm, then add to the previous output.

7.             ErrLastLast=ErrLast

8.         ErrLast=Err

9.       ELSE

11.         ErrLastLast=Err

12.         ErrLast=Err

13.       ENDIF

14.       IF OutP > 100 THEN OutP=100  Limit output to between

15.       IF OutP < 0 THEN OutP=0      0 and 100 percent

The only serious problem with this form of the algorithm occurs when the output has reached an upper or lower limit. When it does, a change in the measurement can unexpectantly pull the output away from the limit.

Next: A Better Implementation