PID Values from Process Gain, Dead Time, and Time Constant

The Ziegler-Nichols method uses a group of formulas to determine the P, I, and D values for a P-only controller, a PI controller, and for the three-mode PID controller. Keep in mind that PID values for gain, reset, and rate would be put into a controller in order to get a QAD response. Since this is a new system and the values to use are unclear, we will use the values of process gain, dead time, and time constant that were determined when the system was tested in manual mode to help us determine the values the controller will use when it's in automatic mode. Table 1 shows these formulas.

Table 1: Formulas for determining the values for gain (P), reset (I), and rate (D). These formulas will produce the PID values to make the system response quarter-amplitude decay (QAD).

Table 2 shows the formulas from Table 1 with the values from the graph filled in. This time, the calculations are solved and the actual values for proportional (P), integral (I), and derivative (D) are shown. The proportional value is determined to be 0.22 if a gain-only controller is used. If the controller is to use gain and reset, the proportional value should be set at 0.20 and the integral value would be set to 15. If the controller is to be a three-mode controller, the gain should be set to 0.27, the integral should be set to 10, and the derivative should be set to 2.5. One would enter these values into the controller via the keypad and the system response should be a quarter-amplitude decay (QAD). If the response needs to be changed, so that there is less overshoot, one could increase the integral value or decrease the gain value from the keypad.

Table 2: Formulas with the values for PID calculated for a quarter-amplitude decay response.

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