How can one truly understand PID?
Category: Technical Classroom
2024-09-09
To truly understand and apply anything, we need to start from the most fundamental aspects, usually the most basic definitions and concepts. We can basically understand, familiarize ourselves with, and apply them. PID: Proportional Integral Derivative Controller. To become familiar with and understand it, we need to combine it with the entire control diagram. The general conventional system control diagram is shown in the following figure, where C represents the controller, P represents the controlled object, r represents the expected data, d represents external disturbances, and n represents external noise. We are replacing C with a PID controller here.
PID controller
There are three main forms of PID controllers: parallel, series, and ideal. Parallel connection means that the three parameters are independent of each other, and the parallel formula is as follows:
The serial formula is as follows:
The ideal formula is as follows:
So before dealing with the PID control algorithm of the controller, it is necessary to first determine the form of implementing the PID control function, and then proceed with parameter tuning.
Parameter meaning
After selecting the form of PID controller, we need to understand the meanings of the three parameters of PID, as well as the roles played by each parameter and their impact on the system. P: Proportional parameter, representing Present (now), amplifies the error proportionally, reduces rise time, reduces system error, but increases overshoot; I: The integral parameter, representing Past, accumulates past error values and can eliminate overshoot and error, but it increases adjustment time. D: Differential parameters, representing Future, can determine the trend of error changes and reduce overshoot.
Engineering Applications of Algorithms
How to apply theoretical algorithms to practical engineering applications, and how to adjust algorithms for problems that arise in engineering, requires some simple summaries.
The application of PID control algorithm mainly considers the following points:
Noise Filtering and high frequency roll-off
Filtering mainly involves adding a low-pass filter to the differential term D. Why is it a differential term? Let's analyze it briefly
If the input signal is:
The noise signal is a sine signal with a frequency of wn. After differentiating the signal,
When the wn ratio is large, the amplitude of the differentiated signal will be very large, which will generate significant interference, so filtering processing is needed.
Set point weight and 2 DOF
Wind up
Windproof strategy is to consider integral saturation or controller output saturation, which requires limiting the output to ensure that the data is within a reasonable output range.
Tuning
Parameter tuning requires different methods, mainly including empirical value method, Lambda tuning method, trial and error method, zero pole placement method, etc.
Computuer implementation
The improvement of program code mainly involves discretizing the program code and performing programming operations.
The above are some simple summaries and generalizations. If there are any errors, please criticize and advise.
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