Top Ten Limitations – Tuning

Money spent to reduce deadtime (e.g. greater agitation, faster valves, faster measurements) will be wasted if the controller is not tuned faster. You may have wonderful process dynamics but loop performance will be lousy if the PID is not tuned to be commensurate with the opportunity. A loop with excessively slow tuning and low deadtime will have similar peak and integrated errors for disturbances to a loop with high deadtime but with tuning as fast as allowed. The rise time for set point changes will also suffer. Whereas deadtime sets the ultimate limit to performance as noted in Top Ten Limitations – Deadtime, tuning sets the practical limit. The difference between the practical and ultimate limits can be resolved by an implied deadtime from the slow tuning. If the tuning is set for maximum disturbance rejection, the implied deadtime reduces to the actual deadtime as detailed in the August 2008 Application Note: Effect of Sample Delay on Standard PID Tuning and Loop Performance.

Why is PID Tuning so Sluggish?

(1) The process disturbance time constant is so slow the PID has no trouble catching up even with very slow tuning. The extreme example is bioreactor temperature control, where changes in heat evolution have a time constant of days. Step disturbances mostly occur in text books and only in a process by an automatic or manual discrete action such as the opening and closing of an on-off valve. As processes use more loops than sequences or manual control, process disturbances are slowed down, particularly by slow tuning. Slow tuning breeds slow tuning.

(2) Most tuning is done based on making setpoint changes and achieving a smooth response with no overshoot, resulting in slower tuning than used for maximum disturbance rejection. Users can mimic load disturbances by momentarily putting the controller in manual and making an output change and then returning to auto. However, this is rarely done. Most text books focus on setpoint response. If a disturbance is introduced, it is a step on the process output an even rarer case that is convenient for showing the advantage of Internal Model Control as detailed in the May 2011 Control article Meditating on Disturbance Dynamics. For more info checkout Disturbance Location and Speed. 

(3) Most loops are nonlinear. Controllers are tuned to provide a smooth setpoint response for the worst case dynamics.

(4) There are no online performance metrics of peak and integrated error for unmeasured disturbances even though the load disturbance is recognizable and measureable in terms of the shift in PID output and the equations are simple and provide recognition of fundamental relationships. The equations are derived from the PID algorithm and a first order plus deadtime response in ISA books (Chapter 2 of Advanced Control Unleashed and Appendix C of New Directions in Bioprocess Modeling and Control). These equations are detailed and discussed in the 2012 Springer book chapter on Industrial-Applications-of-PID-Control.

(5) Interaction problems from fast tuning are a favorite topic in text books even though in my experience these are rare and could be solved by feedforward to provide decoupling or by analog output velocity limiting with PID dynamic reset limiting.

(6) There are hundreds of tuning rules, each implied to be the only solution by the author. Often Ziegler Nichols rules are discounted as terrible even though simply cutting the controller gain in half would have provided the smoother response.

(7) Vessel level, pressure, and temperature loops have a permissible PID gain way above the comfort zone.

(8) Trial and error tuning for vessels uses too small of a gain and too small of reset time resulting in slow oscillations that become more persistent with a greater amplitude by a further reduction in the PID gain. The effect is counter intuitive as users get further below the low gain limit. Integrating processes have a window of allowable gains. Too high of a gain causes rapid oscillations whose amplitude grows as the gain is increased. Too low of a gain when coupled with reset action causes slow oscillations whose damping decreases as the PID gain is decreased. The response for too low of a gain is always stable but the oscillations become incredibly slow and nearly equal in amplitude for a very low PID gain. The cycling may not be recognizable because the period is so slow disturbances will come and go altering the pattern.

Many well published tuning rules reduce to about the same controller gain for maximum disturbance rejection including the Ziegler Nichols rules if you cut the gain in half. You don’t see this unification in the literature because each person wants to believe their tuning rule is the best. For more see What Have I Learned? – Einstein.

The implications of an increase in peak error from a low PID gain can be rather severe in terms of SIS activation, equipment damage, environmental violations, side reactions, runaway reactions, and relief valves opening or rupture discs blowing as noted in Exceptional Opportunities in Process Control – Peak and Integrated Errors – Part 2.

The situation with reset time is not so clear. Some tuning methods set the reset time equal to the process time constant and focus on setpoint response. This works well for many systems encountered in pulp and paper or wherever interaction is significant and the ratio of loop deadtime to process time constant ratio is not extremely small (sort of go hand-in-hand) or extremely large. For very large process time constants, a reset time equal to the process time constant is much larger than useful for max disturbance rejection. For very small process time constant to deadtime ratios, the reset time can be set less than half of the deadtime, the limit for how low you can go for deadtime dominant systems. Setting the reset time equal to the time constant plus the deadtime solves this latter problem but not the former problem. The best reset time for minimum integrated error from unmeasured load disturbances is about 40 times the deadtime for runaway loops and 4 times the deadtime for self-regulating loops with a small deadtime to time constant ratio. As the loop deadtime becomes progressively larger than the process time constant, the reset time can be decreased towards a low limit of 0.5 times the deadtime for a pure deadtime loop. For integrating loops, the reset time could be set 4 times the deadtime if the controller gain is set nearly as high as permitted. Since so many PID have a controller gain on integrating processes that are way below the maximum permitted. The reset time must be increased to keep the product of the controller gain and reset time above a limit to prevent the onset of slow oscillations. Consequently, I have a rule of thumb that the reset time is 40 times the deadtime for integrating processes, to keep users out of trouble. Thus for non-self-regulating processes (integrating and runaway), I increase the reset time by a factor of ten. While these estimates of reset time are not as good as a more exact solution knowing all of the process dynamics, the rules of thumb provide a practical check of reset time since deadtime is the fastest and easiest parameter to identify.