The tuning of the pH controller can be approximated from three key parameters: the open-loop gain (Ko), the largest time constant of the loop (t1), and the total dead time (t^) in the loop. The total loop time delay is the most important of these terms. It is the sum of the dead times from valve dead band, reagent dissolution time, reagent piping transportation delay, the mixing equipment turnover time, mixing equipment transportation delay, sample transportation delay, electrode lag, transmitter damping (normally negligible), and digital filters and digital system scan update time. It is the time required for a disturbance to be recognized by the controller and the corrective reaction by the controller arrive at the entry point of that disturbance. Regardless of where the disturbance enters, the total loop time delay is the time it takes the disturbance effect to traverse the loop in Figure 7.40.16. The controller integral time and derivative time settings depend upon the loop dead time as shown in Equations 7.40(18), (19), and (21). The largest time constant slows down the excursion and gives the controller time to compensate for the upset. The largest time constant in a well-designed installation which is in excellent working condition and is provided with substantial back-mixed volumes is the process time constant (r1). The controller gain is proportional to the ratio of this time constant to the loop dead time (t) multiplied by the open-loop gain (Ko) per Equation 7.40(17), if the dead time (tJ is less than the time constant (r1). Kc is proportional to the open-loop gain (Ko) per Equation 7.40(20) for systems where the dead time is greater than the time constant.
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