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What is the concept of automatic control?

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Author : wang
Update time : 2023-02-24 11:22:17

Let's use a metaphor, trying to control the water level in a pool.


If the water out is greater than the water in, the water level of the pool will continue to drop; On the contrary, if the water output is less than the water intake, the water level of the pool will continue to rise until overflow. Obviously, we should control the amount of water in according to the amount of water out. This control method can of course be controlled by hand. We stand at the edge of the pool, according to the rise or fall of the water level, to adjust the inlet valve, so that the water level is controlled at a certain level. We can also use automatic control so that the system automatically maintains the water level near a fixed level.

How to maintain the water level at a fixed level? We first need to install the sensor on the fixed water level, when the liquid level rises to the fixed water level, turn off the inlet water valve; When the liquid level drops away from the fixed water level, open the inlet valve. This control is called all-on, all-off bit control.

 

We can see that the water level in Figure 3 stabilizes around the control line over time, and the overshoot becomes smaller and smaller.

 

In order to realize the control in Figure 3, we should not only set the supporting sensor to collect the liquid level height, but also set the supporting sensor to collect the flow rate of water in and out. At the same time, the control of valve opening must also be continuously controlled.
 

Now, let's move away from water level control and talk about the general situation.

 

The deviation between the controlled quantity and the control point is represented by e to control the output quantity:
design formula.1
In 1, the larger the deviation e, the larger the control output; the smaller the deviation, the smaller the control output. Kp here is the scale factor.1 is called proportional control.
When the deviation e is small, the control output is small to zero. Therefore, we integrate the deviation e, whose control output is: design formula.2
Ki in 2 is called integral coefficient, and Equation 2 is called proportional integral PI control mode.
If deviation e mutates, the amount of control must be increased, that is:
design formula.3
Kd in 3 is called differential coefficient, and Equation 3 is called proportional integral differential PID control mode.

PID control mode, widely used in automatic control, whether liquid level, flow, position, speed, temperature, pressure, and so on can use PID control.

 

Because the temperature has hysteresis, the automatic control of temperature generally adopts PI mode. For the speed and flow rate, the change is large, so PD mode is used more.

 

The following is the curve timing diagram of PID control mode:

 

However, PID is univariable, if it is multi-variable control is complicated, often with the help of computers or PLC to implement multi-variable control.

 

Having said that, we can already give the concept of automatic control, in production practice, for the object subject to automatic control, we must first analyze its working characteristics, and then write out its working characteristics differential equation. Such equations are often very complex and difficult to solve. We use the function transformation of complex variable function to transform the differential equation in the domain of real numbers into the domain of complex numbers, which becomes an algebraic equation. After solving the problem, we reverse transform it into the domain of real numbers and continue to solve to get the result. In this case, the most typical function transformation is the Laplace transform.

More often than not, we don't transform back, we solve and perform control directly in the complex domain. It can be seen that automatic control and mathematical complex functions have formed an indissoluble bond.
Although automatic control is so complicated, its application is closely related to our daily life. For example, rice cooker control, refrigerator, and air conditioning control, all belong to the category of automatic control.
Interestingly, in the PLC programming interface, PID module can be directly adjusted, and I or D can be closed, three coefficients Kp, Kd and Ki can be set.

Most of our custom instruments are controlled by PLC in order to provide our customers with the required equipment within the specified delivery date.