Physical Basics: Pumps

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PI Gains Tuning

In this topic the Manual Tuning method and the Ziegler-Nichols tuning method will be explained, since they are the most used and robust solutions to the tuning problem.

Manual Tuning

Starting from the standard PI parameters, the responsiveness of the system can be maximized by increasing the P gain. The P gain can be doubled until the system starts to oscillate, and only at this point cut by half.

Figure 1: Initial condition. The response is slow and overshoots.
Figure 2: Kp increased too much, the step response is too steep and unstable.
Figure 3: Kp moderately increased. The initial response is fast, but the end of the transient is too slow. Ki needs to be increased as well.

To reduce the duration of the transient, the I gain can be increased as well. Again, it can be doubled as many times as needed until the system becomes unstable, and then it can be halved.

Figure 4: Ki increased too much, the response overshoots and oscillates.
Figure 5: After proper tuning, the system is more responsive. There is no overshoot, and the transient is completed rapidly.

As a last step, minor adjustments can be done on the two gains to reduce the overshoot (in case it is critical for the process outcome).

Ziegler-Nichols Method

The Ziegler-Nichols method is based on the experiments and statistics performed by its inventors.

Based on their experience, a set of stable control loop parameters can be calculated knowing the system response to a marginally stable system.

This method is composed of different steps:

  1. Set Ki = 0 (P-only control loop)
  2. Increase Kp until the system has sustained oscillations (not converging to a stable response, but also not diverging to an uncontrolled response). This gain is called “Ultimate Gain – Ku”
  3. Measure the “Ultimate Oscillation Period – Tu” (the inverse of the oscillations frequency)
  4. The P and I gains according to the Ziegler-Nichols methods will then respectively be:
    • Kp = 0.45 Ku
    • Ki = 0.54 Ku/Tu

This tuning method usually provides a very aggressive response, with an overshoot. If the overshoot is not acceptable, the Kp should be reduced.

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