Monday, May 28, 2018

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Heuristic PID Tuning Procedures

In contrast to quantitative tuning procedures where definite numerical values for P, I, and D controller settings are obtained through data collection and analysis, a heuristic tuning procedure is one where general rules are followed to obtain approximate or qualitative results. The majority of PID loops in the world have been tuned with such methods, for better or for worse. My goal in this section is to optimize the effectiveness of such tuning methods.

When I was first educated on the subject of PID tuning, the only procedure presented for loop tuning was a crude step-by-step procedure:

  1. Configure the controller for proportional action only (integral and derivative control actions set to minimum effect), setting the gain near or at 1.

  2. Increase controller gain until self-sustaining oscillations are achieved, “bumping” the setpoint value up or down as necessary to provoke oscillations.

  3. When the ultimate gain is determined, set the controller gain for half that value.

  4. Repeat steps 2 and 3, this time adjusting integral action instead of proportional.

  5. Repeat steps 2 and 3, this time adjusting derivative action instead of proportional.

The first three steps of this procedure are identical to the steps recommended by Ziegler and Nichols for closed-loop tuning. The last two steps are someone else’s contribution. While this particular procedure may be peculiar to my own personal path of education, it showcases the general spirit of most heuristic tuning methods: adjust each controller parameter to be more and more aggressive until some compromise is reached between fast action and instability.

Much improvement may be made to any “trial-and-terror” PID tuning procedure if one is aware of the process characteristics and recognizes the applicability of P, I, and D actions to particular characteristics. Simply experimenting with P, I, and D parameter values is tedious at best and dangerous at worst if one has no understanding of what each type of control action if useful for, and the limitations of each control action.


Features of P, I, and D actions

Purpose of each action

  • Proportional action is the “universal” control action, capable of providing at least marginal control quality for any process.

  • Integral action is useful for eliminating offset caused by load variations and process self-regulation.

  • Derivative action is useful for canceling lags.


Limitations of each action

  • Proportional action will cause oscillations if sufficiently aggressive, in the presence of lags and/or dead time. The more lags (higher-order), the worse the problem. It also directly amplifies process noise.

  • Integral action will cause oscillation if sufficiently aggressive, in the presence of lags and/or dead time. Any amount of integral action will guarantee setpoint overshoot in purely integrating processes.

  • Derivative action dramatically amplifies process noise, and will cause oscillations in fast-acting processes.


Special applicability of each action

  • Proportional action works exceptionally well when aggressively applied to self-regulating processes dominated by first-order lag, and to purely integrating processes.

  • Integral action works exceptionally well when aggressively applied to fast-acting, self-regulating processes. Has the unique ability to ignore process noise.

  • Derivative action works exceptionally well to speed up the response of processes dominated by large lag times, and to help stabilize runaway processes.


Gain and phase shift of each action

  • Proportional action acts on the present, adding no phase shift to a sinusoidal signal. Its gain is constant for any signal frequency.

  • Integral action acts on the past, adding a 90o phase shift to a sinusoidal signal. Its gain decreases with increasing frequency.

  • Derivative action acts on the future, adding a +90o phase shift to a sinusoidal signal. Its gain increases with increasing frequency.


Tuning recommendations based on process dynamics

Knowing which control actions to focus on first is a matter of characterizing the process (identifying whether it is self-regulating, integrating, runaway, noisy, has lag or dead time, or any combination of these traits based on an open-loop response test1) and then selecting the best actions to fit those characteristics. The following table shows some general recommendations for fitting PID tuning to different process characteristics



General rules:

  • Use no derivative action if the process signal is “noisy”

  • Use proportional action sparingly if the process signal is “noisy”

  • The slower the time lag(s), the less integral action to use

  • The higher-order the time lag(s), the less proportional action (gain) to use

  • Self-regulating processes need integral action

  • Integrating processes need proportional action

  • Dead time requires a reduction of all PID constants below what would normally work


Once you have determined the basic character of the process, and understand from that characterization what the needs of the process will be regarding P, I, and/or D control actions, you may “experiment” with different tuning values of P, I, and D until you find a combination yielding robust control.


1Recall that an open-loop response test consists of placing the loop controller in manual mode, introducing a step-change to the controller output (manipulated variable), and analyzing the time-domain response of the process variable as it reacts to that perturbation.

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