Don't use a low pass filter in feedback control
It is generally accepted that a low pass filter can improve the performance and stability of a controller, as well as reduce the risk of oscillations or other undesired behavior. This is particularly true when the third derivative term of the PID algorithm is used.
The third derivative D-term is worthy of further examination.
Headache
The author of Control Engineering wrote:
"The third factor in PID is the least understood. Derivative action can do good things, but when used improperly, it causes headaches.”
From the literature and from reports of control engineering experts, the third derivative term appears to cause problems indeed. It causes problems in the configuration and problems during commissioning of the PID controller and in the process or system itself.
The author continues with the following.
“About 90% of the loops out there are probably PI control. It’s going to get you good enough control for most of your applications, and it’s simpler. A well tuned PI controller is going to beat a moderately tuned PID controller every time.”
Why disable the third term?
How can adding extra information make a feedback check worse? From the point of view of physics and mathematics, the derivative signal is additional information that a feedback control cannot possibly degrade. On the contrary, this information should improve the feedback control performance of each process and system.
Crazy idea
"Could it be possible that the PID formula contains an inconsistency?" (Tezzit)
Given the hundred-year success, this seems like a crazy idea. At present, 30,000 aircrafts are controlled by the formula, as well as 60,000 power plants, 1 billion cars and 2 billion room thermostats. At this moment of day, over 50 billion PID formulas are being recalculated every 100 ms.
But in fact it's not a crazy idea at all because it's an empirical formula. It was developed through experimentation and observation rather than theoretical derivation. There is currently no phenomenological explanation of the interactive behavior between the controller and the process/system in terms of physics. The presence of three dimensionless coefficients without a good physical justification supports the characterization of PID as an empirical formula.
The same support goes for questions like why does PID control become unstable so often when the third term is active?
That PID could contain an inconsistency is perhaps even probable. Otherwise, how could it be possible that today's high-performing machine learning algorithms are unable to find the global optimum of the values of three PID coefficients?
“It must be made clear that a sufficiently skilled human with sufficient process knowledge, data and time available can outperform any autotuner in any situation.”
This is a quote from a publication of the International Federation of Automatic Control (IFAC)
In view of the statement (quote) one may wonder whether the so-called sufficiently skilled human has found the global optimum, or just a local optimum.
Similar seemingly unsolvable questions can be asked about the second-order derivative. It is known that this information can improve feedback control by more than 20%.
Heat exchanger feedforward control
Over the years, our deeptech company, Tezzit, has conducted research and development on a feedforward control algorithm for heat exchanger control. By combining high performance feedforward control with feedback control, we were able to shift control corrections from the traditional PID towards the fast-acting feedforward control algorithm. We were able to develop a correct feedforward heat exchanger control algorithm by addressing mathematical inconsistencies in the LMTD and NTU formulas from thermodynamics.
Inconsistencies?
In the process of combining feedforward and feedback control, we stumbled upon several mathematical and physics inconsistencies in the PID algorithm. Inconsistencies which affect its interactive behavior with the process/system it controls.
As a result, we developed a new feedback control algorithm called S-control, which replaces dimensionless coefficients with measurable physical properties. It is one on one exchangeable with the existing PID algorithm.
To give the reader a little more guidance with this special claim, one component within the S-control technology is explained in more detail; the signal filter.
Signal filter
One key component of the S-control technology is the signal filter. Generally a 1st/2nd order low pass filter is used. By applying a low pass filter to the feedback signal, the controller can remove high frequency noise and improve its performance, particularly when the third derivative term of the PID algorithm is active. Our research has not only mathematically and physically confirmed the predictive effect of the derivative term, but also provided insights in how to correct and improve it, as well as how to replace the dimensionless D-term coefficient with a measurable quantity.
Additionally, we have found that traditional signal filters, such as low pass and moving average filters, can introduce significant time delays that negate the predictive power of feedback control.
Instead, research results show to use a signal smoothing filter with the smallest possible delay, such as the Savitzky-Golay filter, to achieve better control performance. References are listed below.
Previous
The previous LinkedIn article explored the oscillating behavior of the PID control.
Previous post Why should PID oscillate?
LinkedIn groups
In the past few weeks we have posted some substantive posts in various LinkedIn groups of control engineering experts. Based on more than 200,000 reads, more than a 1.200 likes and over 150 comments, it can be assumed that control engineering experts consider it not impossible that the PID algorithm contains an inconsistency.
The configuration problems, the dimensionless coefficients and the questionable control performance (oscillations) of the PID algorithm are decisive here. In none of the responses of the control engineering experts are the stated two problems of PID control contradicted. On the contrary.
This article was published in two subsequent posts in the following groups:
References
Types of Filters - Control systems generally provide first-order lag and/or moving-average filters. A few control systems provide higher-order filters.
A major drawback of using wavelet approximation or the low pass filter is that it causes time shifts between the original and filtered signals. Such time disparity can cause difficulties in matching and aligning among signals for analysis.?
By tuning the parameters (N and M) of a Savitzky-Golay filter, the smoothness of its output waveform can be controlled without causing any time delay.
A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares.?
The Savitzky-Golay smoothing and differentiation filter can be used to reduce high frequency noise in a signal due to its smoothing properties and reduce low frequency signal using differentiation. These properties are the reason the “savgol” filter is one of the most popular signal processing tools in spectroscopy and chemometrics.?
Am I certain that I am only removing noise and not distorting the signal??Savitzky and Golay found out that this sliding window approach can be interpreted as a so-called linear time invariant system. (9:23)
YouTube presentation by Cees Taal (TOON/PyData)
The Importance of Smoothing - It is often said that "differentiation increases the noise". That is true, but it is not the main problem.
Interestingly, neglecting to smooth a derivative was ultimately responsible for the failure of the first spacecraft of NASA's Mariner program on July 22.
The Savitzky-Golay method is ideal for computing smoothed derivatives because it combines differentiation with the right kind of smoothing.
Algorithm Design and Development supervisor
2 年I would sincerely and honestly recommend to reach for some professional "Control Engineering" literature by say, Normam S. Nise or Katsuhiko Ogata
Working on Advanved Refrigeration Cycle Optimization
2 年Hidden in the most diverse applications, PID controllers are present in every step of our lives. Its hundred year old algorithm controls over 50 billion processes and systems. Despite the unprecedented success, PID has two problems: 1: How to configure the algorithm? 2: Questionable control performance. Both problems are causally related.? Several discussions in the mentioned LinkedIn discussion groups of control experts revolve around the mathematics of feedback control. More specifically, it involves mathematical models of processes and systems that need to be controlled and, of course, the mathematics of the PID algorithm itself. In one the discussions I contributed to a discussion as follows: You are right about the math and physics regarding a right angle step change. In addition, almost all processes and systems are governed by relatively simple physics and mathematical equations.? It seems that PID control is not straight forward math and physics. Only the mathematical formula of the PID is.? To be continued in the next comment.