Dead Time Dominance Does Not Have to Be Deadly

Severely dead-time-dominant loops are particularly challenging because a control loop cannot see and start to correct for an unmeasured disturbance until after one dead time. Complete correction takes at least two dead times. Also, such loops are more susceptible to noise, since there is not a major process time constant acting as a filter. Many tuning methods break down and model-based methods are prone to failure. Here is the lowdown and some workable solutions.

Since you may not be into conceptual revelations and technical jibber-jabber, here is a summary of what does and doesn't work so well for severely deadtime dominant loops. 

  1. Feedforward of  measured disturbances is robust and exceptionally beneficial
  2. Feedforward of setpoint changes helps reduce the time to reach setpoint
  3. A head start logic can provide the greatest improvement in setpoint response
  4. Derivative mode should not be used (rate time should be zero)
  5. Traditional PI best gain is about ¼ the inverse of the open gain
  6. Near integrator tuning gives PI best gain if deadtime block used in identification
  7. Traditional PI best reset time is about half of the total loop deadtime
  8. Enhanced PID developed for wireless gives extraordinary performance and simplifies tuning when wireless or an analyzer is the largest source of deadtime
  9. Contrary to popular opinion, deadtime compensation has marginal value
  10. Contrary to popular opinion, model predictive control has marginal value

Since the peak error is essentially the open loop error for deadtime dominant systems per Equation C-2 in Appendix C of the January/February 2012 InTech article “PID Tuning Rules Appendices”, feedback control can do nothing to attenuate the maximum excursion for step disturbances. If the disturbance can be measured, feedforward control can provide a dramatic improvement provided the feedforward correction is not too late. Dynamic compensation is quite easy since just a delay is needed if the feedforward arrives too soon. A lead-lag is not needed for dynamic compensation since time constants are by definition negligible. Also, the feedforward timing window is quite large since the deadtime is large.

Setpoint feedforward can provide an improvement in the rise time (time to reach a new setpoint). The more the controller is detuned, the greater the improvement. In general a 2:1 or more reduction in rise time is possible for severely deadtime dominant loops.

The biggest improvement in setpoint response comes from a head start as discussed in the output tracking strategies in the ISA Automation Week 2012 paper "Effective Use of PID Features." The strategy simplifies for severely deadtime dominant systems to simply putting the PID output at the final resting value for one deadtime.

The rate time should be zero since the lack of a significant process time constant means the process variable response is nearly a step and oscillations appear as square waves. While the derivative mode has a built in filter, whenever the PV does respond, there will be a bump from the derivative action. Also, severely deadtime dominant systems tend to be noisy since attenuation in the process is nearly nonexistent because the process time constant is negligible.

The reset time can be decreased. The reset time low limit is about ½ the total loop deadtime allowing for some error in the deadtime.  The Equation C-13 in Appendix C of the January/February 2012 InTech article "PID Tuning Rules Appendices" provides a way of estimating the change in the reset time factor as a function of the relative amount of total loop deadtime to open loop time constant.

Severely deadtime dominant systems have a total loop deadtime much greater than the open loop time constant. If we look at the equations from last week for controller tuning, we see that controller gain nearly goes to zero. However if we use the near-integrator method of tuning discussed last week and the deadtime block to compute the rate of change of the process variable as mentioned in Future PV Values are the Future, we end up with a controller gain that is the "a" coefficient times the inverse of the open loop gain. The derivation of this surprising finding is shown in Universal-Method-of-Computing-PID-Gain.pdf . Here the detuning factor Kx is the "a" coefficient from last week. The near-integrator was thought to be only applicable to self-regulating responses with large process time constants. If you use the deadtime block in the identification, the method can be used for all known types of dynamics including runaway and integrating besides self-regulating. The method can even handle inverse response, if the response in the wrong direction is recognized.

If most of the deadtime comes from a wireless measurement or analyzer, an enhanced PID developed for wireless can simplify the whole control application. The controller does not need to be detuned for the additional deadtime. In fact, the PID gain can be set equal to the inverse of open loop gain providing a full and immediate correction for a setpoint change or a recognized disturbance (a = 1.0). The July/August 2010 InTech article "Wireless – Overcoming challenges of PID control & analyzer applications." This PID even handles the extremely variable and large update time from an offline analyzer.

Deadtime compensation can quite easily be done by simple insertion of a deadtime block in the back calculate path for the positive feedback implementation of the integral mode. While it is natural to believe that a system dominated by deadtime would benefit from deadtime compensation, the reality is quite different. When the deadtime becomes much greater than the time constant, two things happen that make improvement tenuous. First, the compensator becomes much more sensitive to an underestimate or overestimate of the deadtime. A slight overestimate can cause high frequency oscillations. Second, the tuning cannot be made much faster. For sheet thickness control by manipulation of die bolt actuators, the deadtime is known well enough from sheet speed to use a deadtime compensator. However, most other industrial processes have sources of deadtime with unknown variability making deadtime estimates difficult at best.

Strangely enough, loops with a process time constant much greater than the deadtime benefit the most from deadtime compensation. Slides 107-110 in ISA-Edmonton-2012-Effective-Use-of-Measurements-Valves-PID-Controllers-Rev1.pdf debunk many of the myths on deadtime compensators and gives the real scoop on what benefits exists. Model Predictive Control (MPC) suffers a similar fate as noted in the ISA book Models Unleashed.