Evolving PID tuning rules
Note that the so-called model-free tuning just discussed is in fact partial or indirect model-based tuning. This is because the ultimate gain directly relates to the inverse of the process gain and ultimate period relates to the process dead time and lag. Significant progress in process model identification with commonly available identification tools makes it possible and easy to develop a process model and apply process-model parameters directly for model-based tuning. The first-order-lag-plus-dead-time model is the most common approximation for self-regulating processes (see Figure 3), and linear-integrator-with-gain-and-dead-time is used for integrating processes (see Figure 4).
[Figure 3. First Order Plus Dead Time Self-Regulating Process Response]
[Figure 4. Integrating Process Response]
There are many model-based tuning techniques; the most popular are Internal Model Control (IMC), Lambda tuning, and recently developed SIMple Control (SIMC) rules.
The most important feature of model-based tuning is its ability to shape control loop performance and robustness by using a tuning parameter. The tuning parameter relating to the speed of response is used to vary the trade-off between performance and robustness, coordinate response among loops, and achieve process control objectives (averaging level, tight control, etc.). In principle for self-regulating processes, the methods adjust the PID controller reset (or reset and rate) to match process dynamics and then adjust the controller gain to achieve the desired closed loop response. IMC and Lambda tuning have become popular because oscillation and overshoot are avoided, controllers are less sensitive to noise, and control performance can be specified in an intuitive way through the closed-loop time constant. However, load disturbance rejection is typically worse than in quarter-amplitude decay tuning. The SIMC rules were developed to improve model-based tuning performance, primarily for disturbance rejection when desired. SIMC rules provide a higher integral gain (smaller reset time) for the processes with a small dead time than Lambda or IMC tuning rules, by applying this formula:
As it follows from the formula, for the processes with a small dead time and large time constant with a properly selected λ to satisfy the condition τ > 4 (τd + λ), reset time is set as Ti = 4(τd + λ) , instead of Ti = τ, as in Lambda or IMC tuning.
Controller proportional gain Kp is calculated in the same way as for the Lambda or IMC tuning:
For the integrating process controller, parameters are:
It is interesting to notice that optimum tuning rules geared toward minimum integrated absolute error (IAE) advanced by F. Greg Shinskey are only a particular case of SIMC tuning rules for the integrating process:
In fact, such formulas are very close to what is obtained when using λ= 0. This results in the following gain and reset time:
Formulas which do not apply filter λ are therefore for a maximum performance with no designed robustness margin and no possibility of setting a desired loop performance. Therefore, using such formulas is particularly undesirable when process parameters may change causing loop instability. Instead, simple formulas provide the ability to design loop performance and robustness in a required way.
Which brings us back to…
Historically, PID controller tuning started from observing a loop with proportional action on the verge of stability, and then decreasing proportional gain to get stable operation and calculating integral and derivative terms from the loop oscillation period. In fact, all above indicators are related in some way to the process model parameters. Therefore, if all process model parameters are explicitly known, it is possible to satisfy tuning requirements in the best way. There are several model-based tuning rules which give a simple and intuitively understandable method to set a desired loop performance and robustness for a given process.
Willy K. Wojsznis is a senior technologist, and Terry Blevins is principal technologist, future architecture, for Emerson Process Management.
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- PID controllers are virtually everywhere, yet effective tuning remains a challenge
- Conceptually, there is more similarity among various methods than one might expect
- Ultimately, a strategy needs to reflect the needs of the process, and selection depends on understanding those needs
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Read more on control strategy:
• Fixing PID, Nov. 2012
• Feedback controllers do their best, Oct. 2012
• Disturbance-rejection vs. setpoint-tracking controllers, Sept. 2011
• Understanding derivative in PID control, Feb. 2010
• Three faces of PID, Mar. 2007