When to Use which Tuning Rule
There are more than 400 tuning rules for PI and PID controllers [1]. How can one possibly choose the best or most appropriate tuning rule from all of these? To simplify matters, the main differences between the tuning rules can be grouped into four categories:
- Type of process
- Tuning objective
- Process information required
- Type of controller
Most of the tuning rules apply to first-order plus dead time (self-regulating) and integrator plus dead time (integrating) process types. These two process types adequately cover the vast majority of control loops in process plants. Other tuning rules apply to higher-order, oscillating, or unstable processes. Most of the documented tuning rules apply only to processes with dominant time constants. This limits their practical application. The Cohen-Coon tuning rules are an exception.
Tuning objectives include quarter-amplitude damping, minimization of some error integral, a specific percentage overshoot, critically damped, robust tuning, and a specified closed-loop time constant. It is rare to find a tuning rule with an adjustable tuning factor that allows you to change the speed of response. The IMC / Lambda tuning rules are one exception.
The process information required for the tuning rules based on first-order plus dead time and integrator plus dead time process types can be obtained by doing process step tests. A few tuning rules are based on the ultimate cycling or relay tuning methods. Many of the academic tuning rules are based on high-order process models, but they never tell you how to obtain the process model; they just base the tuning on some fictitious model chosen by the author, which largely makes them useless for practical application.
Most tuning-rule authors developed tuning rules for both PI and PID controllers, but with no guidance when to use which one. Some PID tuning rules apply to the interactive algorithm, while most apply to the noninteractive algorithm. It is reasonably easy to convert from one type to the other.
To reduce all these complexities to something we can work with on most control loops, we can consider two process types (self-regulating and integrating), and two tuning objectives (fast and slow or very robust). And ideally we need an easy tuning factor to adjust the speed of response.
When to Use Which Tuning Rule
You could probably use any of the 400 tuning rules, as long as it applies to your situation. I have successfully tuned most (but not all) control loops using just a few tuning rules. Here is what I recommend for most loops:
For self-regulating processes, use the Cohen-Coon PI tuning rule with the following exceptions:
- Use a stability margin of two or more to improve robustness and adjust speed of response.
- If td > 4tau, use the tuning rule for dead-time-dominant processes.
- If you find it difficult to accurately measure the dead time, use the Lambda tuning rule.
- If you want the loop to have a specific speed of response, use the Lambda tuning rule.
- If you want the loop to absorb disturbances rather than pass them on to the next process, use the Lambda tuning rule with the closed loop time constant set three tomes the open loop time constant.
- Use the derivative control mode (PID tuning rule) only when you need every last bit of speed, and then only when the process lends itself well to the use of derivative.
For integrating processes, use the Ziegler-Nichols tuning rule, except for surge tanks and level averaging, where you should use the two tuning rules named after these control objectives.
Fast Response | Slow / Robust Response | |
Self-Regulating Process | Cohen-Coon (adjust the stability margin (SM) to change the speed of response) | Lambda (adjust the closed-loop time constant to change the speed of response) |
Integrating Process | Ziegler-Nichols (adjust the stability margin (SM) to change the speed of response) | Level-averaging (adjust the specification for maximum deviation from setpoint) |
If you use a PID tuning rule and an interactive controller algorithm, or a controller with the parallel algorithm, remember to convert the calculated tuning parameters to ones suitable for your controller algorithm. Also remember to measure your process characteristics in the same time-units your controller’s integral uses. And remember to integral time to integral gain – if that is what your controller uses. Finally, when tuning any control loop, watch out for control valve problems.
You can find much more information in my book Process Control for Practitioners.
Stay tuned!
Jacques Smuts
Principal Consultant – OptiControls
Reference
- O’Dwyer, A Summary of PI and PID Controller Tuning Rules for Processes with Time Delay. Part 1: PI Controller Tuning Rules, Proceedings of PID ’00: IFAC Workshop on Digital Control, Terrassa, Spain, April 4-7, 2000, pp. 175-180.
What’s a good tuning rule for self regulating processes where the setpoint is swept instead of constant? Using e.g. Cohen Coon gives me a very stable temperature at a specific setpoint, but when the setpoint is ramped the temperature starts to oscillate around the changing setpoint.
Marco, the “modified” Cohen Coon tuning rules should work well, i.e. they should not cause oscillations. Did you apply a stability margin of 2.0 or greater? Is your controller algorithm non-interactive? Is your final control element working properly, and its flow characteristic linear?