Question: Answer the following questions regarding the computer implementation of the digital PID controller.

(a) Can the controller tuning constants be changed while the controller is functioning without disturbing the manipulated variable? (Consider the velocity and full-positional forms separately.)

(b) For the velocity form of the PID, what is the value for MWN-1 for the first execution of the controller?

(c) For the full-position form of the PID, the sum of the error term might become very large and overflow the word length. Is this a problem likely to occur?

(d) Discuss how the calculations could be programmed to introduce limits on the change of the manipulated variable (?MVN), the set point (SPw), and the manipulated variable (MV#).

(e) Can you anticipate any performance difficulties when the limitations in (d) are implemented? If yes, suggest modifications to the algorithm.