PID regulation

Many people who work in automation are confused about how to adjust PID parameters. This is actually not difficult at all. Anyone who has attended junior high school can become a good parameter adjuster as long as they have received rigorous training. What? Do junior high school students understand the principles of integration and differentiation? Well, junior high school students have not learned calculus, but once you explain the physical meaning of calculus to them, and then carefully train them to have the habit and ability to judge curves, they can completely master the PID parameter adjustment.

What is PID

Before we figure out how to quantify, we must first understand a basic concept: the regulator. What does a regulator do? The regulator is the human brain, the core of a regulation system. Any control system, as long as it has a brain or control method with PID, is an automatic regulation system. What if there is no control method with PID? It is not necessarily not an automatic regulation system, because various control ideas have emerged later. For example, fuzzy control, which is the most popular research nowadays, and neuron control, etc.; later, a regulation system with self-organizing ability was produced, which means the ability to automatically adjust parameters; there is also a comprehensive control that combines fuzzy control or neuron control with PID, etc. We will introduce it later. In this article, unless otherwise specified, it refers to traditional PID control. It can be said that any system with control ideas and regulation methods is called an automatic regulation system. And the thing that places the most core regulation method is called a regulator.

The basic regulator has two input quantities: the controlled quantity and the set value. The controlled quantity is the value that reflects the actual fluctuation of the controlled object. For example, water level, temperature, pressure, etc.; the set value, as the name implies, is the value set by people, that is, the value that people expect the controlled quantity to reach. The controlled quantity must change frequently. The set value can be fixed or frequently changing. For example, in the AGC system of a power plant, the set value of the unit load is a frequently changing quantity.

The basic regulator has at least one analog output. After the brain calculates the situation, it issues a command. It issues a precise command to let the actuator act according to its requirements. There are other links between the brain and the actuator (hand), such as limiters, servo amplifiers, etc. Some limiters are built in the brain, and some servo amplifiers are built in the actuator.

The three input and output quantities mentioned above are the most important quantities of the regulator, and there are many other auxiliary quantities. For example, in order to achieve manual-automatic switching, automatic instructions are required; for safety, deviation alarms are required, etc. These can be ignored for the time being. For the convenience of thinking, we only need to remember these three quantities: set value, controlled quantity, and output instruction.

In fact, for the convenience of description, people usually simplify it into two quantities: input deviation and output command. Input deviation is the difference between the controlled quantity and the set value. There is no need to elaborate on this, right?

Back to the question just now: What is PID?

P is the proportion, which is the input deviation multiplied by a coefficient;

I is the integral, which is the integration operation of the input deviation;

D stands for differentiation, which performs differentiation operation on the input deviation.

It's that simple. Many years later, I still think: this theory is so beautiful!

The inventor of this method seems to be Nichols. I don't have more information, so I can't be sure whether it was invented by Nichols. But the PID parameter tuning method was indeed invented by him.

In fact, this method has been adopted by many system maintainers. To put it simply, it is to first adjust the system to pure proportional action, then enhance the proportional action to make the system oscillate, record the proportional action and oscillation period, then multiply the proportional action by 0.6, and extend the integral action appropriately. Although the original intention of this article is to avoid cumbersome calculation formulas and describe engineering problems in a language that even laymen can understand, the most basic formula still involves the following, and this formula is also very simple. Those who are interested can take a look, and those who are not interested can ignore it. The formula is expressed as follows:

Kｐ＝０．６*Kｍ

Ｋｄ＝Ｋｐ*π／4*oh

Ｋ＝Ｋｐ*ω／p

Kp is the proportional control parameter

Kd is the differential control parameter

Ki is the integral control parameter

Km is the proportional value when the system starts to oscillate;

ω is the frequency of oscillation in polar coordinates

This method only provides a general idea, and the specific situation is much more complicated. For example, in a water level regulation system, the differential effect can be canceled and the integral effect can be adjusted according to the situation; some systems are beyond the understanding of ordinary people, and some parameters can be set very large or very small. We will introduce the specific adjustment method later. The impact of differential and integral on the system will also be analyzed later.

A few basic concepts

Single loop: means there is a PID regulation system.

Cascade: What if one PID is not enough? Connect two PIDs in series to form a cascade control system. It is also called a dual-loop control system. In Chapter 3, we will explain the cascade control system in more detail. I will not introduce it too much here.

Positive action: For example, a pool has an inlet and an outlet. The inlet is fixed and the water level is adjusted by adjusting the water volume at the outlet. If the water level is high, the water volume needs to be adjusted to increase. For the PID regulator, the output increases with the increase of the regulated volume and decreases with the decrease of the regulated volume. This is called positive action.

Negative effect: For this pool, we keep the water output fixed and adjust the water level by adjusting the water inlet. If the water level in the pool increases, we need to reduce the water inlet. For the PID regulator, the effect of the output decreasing as the regulated amount increases is called negative effect.

Dynamic deviation: During the adjustment process, the deviation between the adjusted value and the set value changes at any time. The deviation between the two at any time is called dynamic deviation. It is referred to as dynamic difference.

Static deviation: After the adjustment becomes stable, the deviation between the adjusted quantity and the set value is called static deviation. It is also called static error for short.

Callback: The regulating effect of the regulator appears, causing the regulated quantity to start changing from rising to falling, or from falling to rising.

P in PID tuning

The so-called P is the proportional action, which is to multiply the input deviation of the regulator by a coefficient as the output of the regulator.

Review: The input deviation of the regulator is the difference between the regulated value and the set value.

Generally speaking, the set value does not change often, that is to say: when the set value remains unchanged, the output of the regulator is only related to the fluctuation of the regulated quantity. Then we can basically derive the following conceptual formula:

Output fluctuation = controlled variable fluctuation * proportional gain

Note that this is just a conceptual formula, not a real calculation formula. The purpose of making a conceptual formula is that smart people like you and me don't bother to spend energy on verifying those tedious formulas. What do we care about? We care about the deep meaning inside the formula. Haha. Let's work hard to explore its deep meaning.

Through the conceptual formula, we can get the following conclusions, for a single-loop control system, under pure proportional action:

The output waveform is completely similar to the waveform of the controlled variable.

There is actually only one standard for judging the curve of pure proportional action. In a nutshell: the output multiplied by the proportional coefficient changes as much as the controlled variable changes. In other words: the waveform of the controlled variable and the output are completely similar.

In order to help you understand this standard more deeply, let's make some inferences about the output curve and the controlled quantity curve:

1. For a positive-acting regulatory system, the peak and trough occur at the same time.

2. For a negative-action regulation system, the peak of the regulated quantity is the bottom of the output, and the bottom is the peak of the output.

3. For a positive-acting regulating system, when the regulated quantity curve rises, the output curve rises; when the regulated quantity curve falls, the output curve falls. The trends of the two are exactly the same.

4. For the negative-action regulation system, the regulated variable curve and the output curve are relative.

5. The fluctuation cycles are exactly the same.

5. As long as the controlled variable changes, the output will change; if the controlled variable does not change, no matter how large the static deviation is, the output will not change.

The above five inferences are very important, please remember them firmly. It doesn't matter whether you remember them or not, as long as you can melt them into your mind.

Is it melted? Then let me ask you a question:

1. When the controlled quantity is called back, will the output also be called back?