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For batch operation of loops with large process time constants, it is desirable to get to setpoint as fast as possible. The PID temperature controller is often entitled to a high controller gain by virtue of the extremely large process time constant or slow integrating process gain compared to the dead time. To reduce batch cycle time, it is extremely important that the closed-loop time constant be much faster than the process time constant. It is not uncommon to have a Lambda factor (ratio of closed-loop time constant to process time constant) that is less than 0.02. For a process-time constant of 200 minutes, a dead time of two minutes, and a small setpoint change where the controller output does not hit an output limit, the closed-loop time constant can be less than four minutes approaching the process dead time. The savings in batch cycle time is 196 minutes compared to a lambda of 1.0 or a combination of feedback or feed-forward action that puts the controller output immediately at its final resting value.
However, noise may prevent the use of a high controller gain and low Lambda factor. A threshold sensitivity limit can be set just larger than the noise so proportional and derivative action does not amplify noise. When used in conjunction with the enhanced PID for wireless, the threshold sensitivity limit prevents integral action from chasing noise.
For the fastest possible rise time (time to get within a control band of setpoint), a smart bang-bang logic can be used where the controller output is positioned immediately to a limit. When the PV value one dead time into the future is predicted to be close to setpoint, the controller output is set and held at the final resting value for one dead time, and then released for feedback correction. While this logic applies best to integrating process responses as encountered in batch temperature, it is also applicable to self-regulating processes with large time constants that behave as "near-integrating" processes as seen in continuous temperature control on large well-mixed vessels. For more information on setpoint feed forward and smart bang-bang control check out Deminar #7 (http://tinyurl.com/6xzbrhv).