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Model-based optimization methods for PID controllers
The way you measure a process variable responds over time to changes the controller output signal is essential for the design and tuning of a PID controller. The best way to learn about the behavior a dynamic process is to perform experiments, commonly known as "bump tests." Critical to success is to process data generated by the bump test be descriptive of the actual behavior of the process. Discussed are the qualities required for the "good" Dynamic Data and methods for modeling the dynamic data for controller design. The dynamic model parameters are not only used in correlations to calculate the adjustment values, but also provide insight into the parameters of the controller design, such as circular time of the sample and if time Dead presents a performance challenge. It is increasingly common for dynamic studies were performed with the controller in automatic (closed loop). To cycle studies Closed, dynamic data is generated by striking the set point. The method for using closed loop data is illustrated. The concepts in this paper illustrated using a simulation of the control level.
FORM OF AUDITOR
The methods described here apply to the entire family PID algorithm. The examples explore the most popular driver of the PID family, the Proportional-Integral (PI) controller:
In this driver, u (t) is the controller output and is the controller bias. The fitting parameters are controller gain and reset time. Because it is in the denominator, more small values of reset time to provide greater weight to (increase the influence of) the integral term.
CONTROLLER DESIGN PROCEDURE
The design of any controller of the family of PID algorithms entails the following steps:
specifying the design level of operation,
dynamic data collection process as close as possible to this level of design
a propitious time for first order plus dead (FOPDT) data model process, and
using the model parameters resulting in a correlation to obtain initial values of the controller tuning.
The form FOPDT of the dynamic model is:
[2]
where y (t) is the measured process variable and u (t) is the controller output signal. When the equation. 2 meets the test data, important parameters that describe the dynamic behavior of the outcome of the process:
Gain constant process of state
Overall process time constant,
Apparent Dead Time,
These three parameters of the model are important because they are used in correlations to calculate the baseline adjustment for a variety of drivers [1]. The model parameters are also important because:
the sign indicates the direction driver (+ invest in quality - direct action)
indicates the size of the maximum desirable loop sample (make sure the time sample)
the ratio indicates whether a Smith predictor showed benefit (useful if)
dynamics model itself can be used within the architecture of feed forward, Smith predictor, decoupling and other control strategies based on models.
DEFINITION OF TEST DATA PROCESSING OF GOOD
As discussed above, the collection and analysis of dynamic process are critical steps in controller design and implementation ready. A "good" set of data contains controller messages to measure the process variable data that is descriptive of the dynamic nature of the process. For that data set, the answer to all these questions about your data should be "yes" [1]. Ultimately it is your responsibility to consider these steps to ensure success.
Was the process at steady state before data collection started?
Suppose that a change in controller output requires a dynamic response of a process, but the data file only shows the last part of the answer without showing the change in real output driver that caused the dynamics in the first place. Popular modeling tools in fact conforms to a model of these data, but will bias the adjustment in an attempt to account for an invisible "force invisible ". This model is not descriptive of actual process and therefore of little value for control. To avoid this problem, it is important that the collection will start only after the process has settled out. The modeling tool can then properly account for all variations in the installation process of the model.
"The dynamics of the test clearly dominate the process noise?
When generating dynamic process data, it is important that the change in controller output cause
response in the process that clearly dominates the measurement noise. A general rule is to define a
noise band of ± 3 standard deviations of error randomly around the constant process variable
operation. Then, when the data collection during the change of output driver will force the process variable move at least ten times this noise band (the signal to noise ratio must be greater than ten). If you meet or exceed this requirement, the data would result in the joint process rich dynamic information needed to design the controller.
Riots were quiet during the dynamic test?
It is essential that the test data contain process variable dynamics that have been clearly (and in the ideal world exclusively) forced by changes in the output of the controller and explained in step 2. Dynamics caused by unmeasured disturbances can seriously degrade the accuracy of analysis, as the modeling tool such behavior model as if they were the result of changes in the output signal of the controller. In fact, a fit of the model may look perfect, however, an alteration that occurred during the data collection can make the model fit is nonsense. If you suspect a disturbance event has damaged the test data, is conservative to rerun testing.
Does the model fit appear to the visual approach the data frame?
It is important that the modeling tool display a plot which shows the model fit at the top of the data. If the two lines do not look similar, then the model fit is suspect. Of course, as explained in step 3, if the data has been corrupted by unmeasured disturbances, the model fit may look great but the usefulness of the analysis may be compromised.
Y band noise signal to noise
When generating dynamic process data, it is important that the change in controller output signal causes a response in the process variable as clearly dominates the measurement noise. One way to quantify the amount of noise in the measurement process variable is with a noise band. As illustrated in Fig. 1, a band of noise is based on the standard deviation of random error in the measurement signal when the controller output is constant and the process is steady state. Here, the band noise is defined as ± 3 standard deviations of the measurement of noise around the steady state as the process variable (99.7% tracking signal is contained within the noise band). While other definitions of the noise band have been proposed, this definition is conservative when used for controller design.
When generating dynamic process data, the change in controller output should cause the measured process variable to move at least ten times the size of the noise band. Stated concisely, the signal to noise ratio must be greater than ten. In Fig. 1, the noise band is 0.25 ° C. Therefore, the output of the controller must move fast enough during a test to make the measured exit temperature to move at least 2.5 ° C. This is a specification minimal. In practice it is conservative to exceed this.
Figure 1 - Noise Band covers ± 3 Standard Deviations from the noise measurement
Tuning Control from correlations
Correlations recommended setting for family controllers are PID Internal Model Control the (IMC) relations [1]. This is an extension of the popular lambda tuning correlations and include the added sophistication direct downtime the optimization calculations.
The first step in using the IMC (lambda) correlation adjustment is to calculate the closed-loop time constant. All time constants describe the speed or the speed of response. The closed-loop time constant describes the desired speed or speed of a driver in response to a change point adjustment. Therefore, a small (a short response time) involves a driver or fast aggressive response. The time constants of closed loop is calculated as:
Aggressive Tuning: (See the online version to see the photo of the formula)
Moderate Tuning: ("")
Conservative Pitch: ("")
Final adjustments can be verified online and may require adjustments. If the process is responding slowly to shocks and changes in the setpoint, the controller gain is too small and / or the reset time is too large. On the contrary, if the process is responding quickly and is oscillating to a degree that makes you uncomfortable, the controller gain is too large and / or the reset time is too small.
Examples: In an online copy
PI Controller Tuning Map
Figure 6 - How PI controller parameters adjustment impact set point tracking performance
CONCLUSIONS
Understanding the dynamic behavior of a process is essential for the proper design and tuning of a PID controller. The design and tuning methodology is recommended: step, pulse or disrupt the controller output near the design level operation, to record the controller output and measured data of process variables as the process responds, as a first order plus dead time (FOPDT) model dynamic data processing, using the dynamic model parameters in a correlation to compute P-Only, PI, PID and PID with filter test your driver to ensure satisfactory performance.
LITERATURE CITED
1. Cooper, Douglas, "Practical Process Control Station using Control, "published by the control station,
Inc, Storrs, CT (2004).
For more information on optimization techniques based models and technologies, see the other resources below:
PID Control - Practical Process Control (2 day workshop)
http://www.bin95.com/process_control_atlanta_training.htm
Full list of authors:
Jeffrey Arbogast - Department of Chemical Engineering
Douglas J. Cooper, PhD - Control Station, Inc.
Robert C. Rice, PhD - Control Station, Inc.
To view the online version complete with photos, please http://www.bin95.com/PID_Controller_Design.htm visit
About the Author
More from these authors and much more. please see ”More PID TRaining resources”...
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