The Primary Source of Disagreement in Process Control Tips

The primary reason why there are so many and so different schools of thought about control algorithms and tuning can be traced back to one parameter in the process response. What PID tuning and what PID structure is pronounced as best and even whether PID control should be used is based on an assumed range of values for this parameter. A simple tool can open the mind to relative merits of different solutions and provide the means to see the whole picture eliminating disagreement. 

I try not to let ego cause me to think my method is the only solution. I attempt to gather and use the knowledge from different views with a goal of achieving a more universal approach to improving process control.

Most of the control literature centers on a self-regulating process with a time constant to dead time ratio of 1.0 with a typical range of 0.5 to 2.0 for the ratio. For these ratios internal model control looks attractive and issues of oscillations are foremost. These ratios are prevalent in processes where there are not large liquid volumes. Processes with key unit operations that are inline volumes (e.g. pulp and paper) or gas volumes (hydrocarbon) fit this scenario. The lack of a large liquid volume or batch operations narrows the solution to either model based control or PID structure and tuning whose primary objective is to prevent oscillations in the process variable and even the controller output. Oscillations in controller output are disruptive by upsetting headers, recycle, and heat integration in these processes. A structure of proportional on process variable and integral on error (P on PV & I on Error) may be advocated to provide a smooth setpoint response with no overshoot or abrupt movement of the controller output. Derivative may not even be considered because the benefit of rate for these ratios is minimal and the movement of the controller output more abrupt.

Now consider my background of control loops in processes with large vessel volumes and batch operations. Here the more important loops (gas pressure, liquid temperature, and liquid concentration) have time constant to dead time ratios of 50:1 to 200:1 (two orders of magnitude larger than what is emphasized in the literature). Internal model control and pole zero cancellation approach cause incredibly poor disturbance rejection and slow approaches to setpoint. Lambda factors (ratio of closed loop to open loop time constant) ranging from 4 to 1 are two orders of magnitude too high (lambda factors of 0.04 to 0.01 are needed).  A structure P on PV and I on E and tuning for lower ratios causing the process to approach a setpoint with a closed loop time constant similar to the open loop time constant would result a time to reach setpoint a hundred times longer. 

Some tuning methods try to address large changes in time constant to dead time ratios by switching tuning rules and making the reset time a function of both dead time and time constant. A reset time that is proportional to the sum of both the dead time and time constant results in reset times that are too large for very small and very large time constant to dead time ratios. Thus, even if the objective is to minimize the error from load disturbances, the tuning cannot deliver what is needed.

There are a number of PID tuning methods that converge for the same objective of maximizing disturbance rejection and setpoint rise time. These methods inevitably make the reset time a function of only dead time. An exponential function of the dead time is used so that the reset time goes from 3 times the dead time for large ratios to about 1/3 of the dead time for small ratios. 

Lambda tuning can deal with a large range of ratios by not using a lambda factor but using lambda as a multiple of dead time and switching to integrating process tuning rules when the time constant to dead time ratio is greater than about 3. A lambda equal to the dead time and the use of integrating tuning rules result in a reset time of about 3 dead times. Integrator tuning rules also advocate the use of derivative action with the rate time set equal to the second largest time constant in the loop. Note that to deal with unknowns and nonlinearities, a lambda of 3 dead times is advocated.   

The lambda tuning for low ratios results in extremely small reset times and correspondingly low controller gains. The result is essentially integral-only control which has some benefits in terms of being immune to the noise more prevalent at these low ratios from the lack of a process time constant acting as a filter.

You have probably realized from the above the primary reason for disagreement is the size of the primary process time constant. A large primary process time constant associated with a liquid volume leads to a large time constant to dead time ratio. If you realize that there are few true integrators, the batch vessel temperature response can be effectively modeled as a self-regulating process with a large process time constant.  A continuous vessel temperature response can be modeled as a near integrating process. Thus, tuning methods and concerns are in play in terms of the filtering effect in the process whether the vessel has a near or true integrating process response.  For runaway processes, the primary process time constant associated with positive feedback must be large to be stable in closed loop control and tuning must be aggressive.  

Abrupt changes and oscillations in the controller output from structure or derivative action from a particular unit operation are often not important due to large utility system volumes associated with a large plant. Similarly the primary process time constants in large liquid storage volumes make the concern about oscillations from one production line unimportant. Even if the volume is not agitated, concentrations tend to equilibrate unless there is some laying (unlikely in product storage). 

So if your plant experience is limited to certain types of processes, how do you open your mind to other process requirements? For me a simple process simulation consisting of dead time, secondary time constant, and either a negative feedback primary time constant (self-regulating process), integrating process gain, or a positive feedback primary time constant (runaway) process with valve backlash and stiction, and measurement update time or analyzer cycle time provides the various scenarios I need to see a much more complete picture. Inverse response can be created by a lead-lag of opposite sign and the effect of a recycle stream can be introduced by tieback of the process output through an integrating response as a process input.

The bottom line is a recommendation to understand the size and importance of your primary process time constant and use simulation to expand your horizons.

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