How to set pid parameters

The control parameters of digital PID controller can be selected according to the continuous-time PID parameter tuning method.

Before selecting digital PID parameters, the controller structure should be determined first. For the system that allows static error (or steady-state error), P or PD controller can be selected appropriately to make the steady-state error within the allowable range. For systems that must eliminate steady-state errors, PI or PID controllers with integral control should be selected. Generally speaking, PI, PID and P controllers are widely used. For objects with time delay, differential control is often added.

Selection parameter

After the controller structure is determined, parameters can be selected. The selection of parameters should be based on the specific characteristics of the controlled object and the performance requirements of the control system. In engineering, it is generally required that the whole closed-loop system is stable, can respond quickly and track smoothly to the given changes, and has a small overshoot; Under different disturbances, the controlled quantity can be guaranteed at a given value; When the environmental parameters change, the whole system can remain stable, and so on. Some of these requirements contradict the performance of the control system itself. We must meet the requirements of the main aspects, give consideration to other aspects and compromise appropriately. Here is an empirical method. This method is essentially a trial and error method, which is an effective method summed up in production practice and has been widely used in the field.

The basic procedure of this method is to determine a set of regulator parameters according to the operation experience, put the system into closed-loop operation, and then artificially add step disturbance (such as changing the given value of the regulator) to observe the step response curve of the regulated quantity or regulator output. If the control quality is not satisfactory, the regulator parameters are changed according to the influence of each set parameter on the control process. Repeat this experiment until you are satisfied.

The empirical method is simple and reliable, but it needs some field operation experience, and the timing is easy to be subjective and one-sided. When using PID regulator, there are many tuning parameters and the number of trial and error increases, so it is difficult to get the best tuning parameters.

Here, taking PID regulator as an example, the setting steps of empirical method are introduced in detail:

(1) If the regulator parameter integral coefficient S0=0 and the actual differential coefficient k=0, the control system will be put into closed-loop operation, and the proportional coefficient S 1 will change from small to large, so that the disturbance signal will change step by step, and the control process will be observed until a satisfactory control process is obtained.

⑵ Multiply the proportional coefficient S 1 as the current value by 0.83, and change the integral coefficient S0 from small to large, which also makes the disturbance signal change step by step until a satisfactory control process is obtained.

(3) Keep the integral coefficient S0 unchanged and change the proportional coefficient S 1 to see if the control process is improved. If there is improvement, continue to adjust until it is satisfactory. Otherwise, increase the original proportional coefficient S 1, and then adjust the integral coefficient S0 to improve the control process. This trial and error is repeated until satisfactory proportional coefficient S 1 and integral coefficient S0 are found.

⑷ By introducing appropriate actual differential coefficient k and actual differential time TD, the proportional coefficient S 1 and the integral coefficient S0 can be appropriately increased. Like the previous steps, it is necessary to adjust the setting of differential time repeatedly until the control process is satisfactory.

Note: The PID regulator used in the simulation system is different from the traditional industrial PID regulator, and the parameters are isolated from each other and do not affect each other, so it is very convenient to observe the regulation law with it.

PID parameters are determined according to the inertia of the controlled object. Inertia is large, such as the temperature control of large drying room. Generally, P can be above 10, I = 3- 10, and D = 1. Small inertia, such as small motor belt

A water pump carries out closed-loop pressure control, and generally only PI control is used. P = 1- 10, I = 0. 1- 1, D = 0, which should be corrected during field debugging.

I provide an incremental PID for your reference.

△U(k)= Ae(k)-Be(k- 1)+Ce(k-2)

A=Kp( 1+T/Ti+Td/T)

B=Kp( 1+2Td/T)

C=KpTd/T

T sampling period Td differential time ti integration time

You can use the above algorithm to construct your own PID algorithm.

U(K)=U(K- 1)+△U(K)

The parameter tuning of PID controller can be independent of the mathematical model of the controlled object. In engineering, the parameters of PID controller are often determined by experiment, trial and error method or experimental empirical formula.

Keywords common methods, sampling period selection,

Experimental trial and error method

The experimental trial-and-error method is to observe the response curve of the system through closed-loop operation or simulation, and then try the parameters repeatedly according to the influence of each parameter on the system until a satisfactory response appears, thus determining the PID control parameters.

Setup steps

The setting steps of experimental trial and error method are "proportion first, then integration, and finally differentiation".

(1) Setting proportional control

Change the proportional control function from small to large, and observe each response until a response curve with fast response and small overshoot is obtained.

(2) the overall link

If the steady-state error cannot meet the requirements under proportional control, integral control should be added.

First, reduce the proportional coefficient selected in step (1) to 50 ~ 80% of the original value, and then set the integration time to a larger value to observe the response curve. Then reduce the integration time, increase the integration effect, and adjust the proportional coefficient accordingly, and try again and again to get satisfactory response, and determine the parameters of proportion and integration.

(3) setting differential link

If after step (2), PI control can only eliminate the steady-state error, and the dynamic process is not satisfactory, then differential control should be added to form PID control.

First set the differential time TD=0, gradually increase TD, and change the proportional coefficient and integration time accordingly, and try again and again until satisfactory control effect and PID control parameters are obtained.

Experimental experience method

Extended critical proportional band method

The extended critical proportional band method is a commonly used experimental empirical method to adjust PID parameters. Its biggest advantage is that the parameter tuning does not depend on the mathematical model of the controlled object, and it is simple and easy to do, and it can be directly set on site.

The extended proportional band method is suitable for the controlled object with self-balancing characteristics, and it is an extension of the critical proportional band method for parameter tuning of continuous-time PID controller.

Setup steps

The steps of tuning the parameters of digital PID controller with extended proportional band method are as follows:

(1) preselect a sufficiently short sampling period TS. Generally speaking, TS should be less than one tenth of the pure delay time of the controlled object.

(2) Use the selected TS to make the system work. At this time, the integral function and differential function are removed, and the control is selected as a pure proportional controller to form a closed-loop operation. Gradually reduce the proportional band, that is, increase the proportional amplification factor KP until the system appears critical oscillation (stable edge) in response to the input step signal, and then record the proportional amplification factor as Kr and the critical oscillation period as Tr.

(3) Select the degree of control.

The control degree is to compare the control effects of digital PID controller and continuous-time PID controller.

Error square integration is usually used.

As an evaluation function of control effect.

Define the degree of control

(3-25)

The length of the sampling period TS will affect the quality of the sampling data control system, which is also the best setting. The control quality of sampled data control system is lower than that of continuous time control system. Therefore, the degree of control is always greater than 1, and the greater the degree of control, the worse the quality of the corresponding sampling-data control system. The selection of control degree should be based on the control quality requirements of the designed system.

(4) Look-up table to determine parameters. According to the selected control degree, look up Table 3-2 and get the corresponding parameters TS, KP, TI and TD in digital PID.

(5) Operation and correction. Add the obtained parameters into PID controller, run in closed loop, observe the control effect, make appropriate adjustments and get satisfactory results.