General method for PID controller parameter tuning - Database & Sql Blog Articles

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The following is a general method for parameter tuning of PID controllers:
The parameter tuning of the PID controller is the core content of the control system design. It determines the scale factor, integration time and derivative time of the PID controller according to the characteristics of the controlled process.
There are many methods for PID controller parameter tuning. There are two general categories: one is the theoretical calculation tuning method. It is mainly based on the mathematical model of the system, and the controller parameters are determined through theoretical calculations.
The calculation data obtained by this method may not be directly usable, and must be adjusted and modified through engineering practice. The second is the engineering setting method, which relies mainly on engineering experience and is directly carried out in the test of the control system. The method is simple and easy to grasp, and is widely used in engineering practice.
The engineering tuning method of PID controller parameters mainly includes critical ratio method, reaction curve method and attenuation method. Each of the three methods has its own characteristics, and the common point is to pass the test, and then adjust the controller parameters according to the engineering experience formula. However, no matter which method is used, the controller parameters need to be adjusted and improved in actual operation. The critical ratio method is generally used now. The tuning steps of the PID controller parameters using this method are as follows:
(1) First pre-select a sampling period that is short enough for the system to work;
(2) Add only the proportional control link until the system has a critical oscillation in the step response of the input, and record the proportional amplification factor and the critical oscillation period at this time;
(3) Calculate the parameters of the PID controller by a formula under a certain degree of control. PID parameter setting:
It is based on the familiarity of experience and technology, and the measurement value tracking and set value curve are referenced to adjust the size of P\I\D.
Proportion I / differential D = 2, the specific value can be determined according to the instrument, then adjust the proportional band P, P over the head, reach a stable time, P is too short, will oscillate, never hit the set requirements.
The engineering tuning of PID controller parameters, the empirical data of PID parameters in various adjustment systems can be referred to below:
Temperature T: P=20~60%, T=180~600s, D=3-180s;
Pressure P: P = 30 ~ 70%, T = 24 ~ 180s;
Liquid level L: P=20~80%, T=60~300s;
Flow rate L: P = 40 ~ 100%, T = 6 ~ 60s.
Commonly used on the book:
Parameter tuning to find the best, from small to large order;
First, the ratio is post-integrated, and finally the differential is added;
The curve oscillates frequently, and the proportional disk is enlarged;
The curve floats around the big bay, and the proportional disk is small;
The curve deviates from the recovery slowly, and the integration time decreases;
The curve has a long fluctuation period and the integration time is lengthened;
The curve oscillates at a fast frequency, first reducing the differential;
The momentum is large and the fluctuations are slow. The differential time should be lengthened;
Ideal curve two waves, front high and low
4 to 1;
When you look at the two-tone analysis, the quality of the adjustment will not be low.
The size of the PID parameter settings,
On the one hand, it depends on the specific circumstances of the controlled object;
The other is experience.
P is to solve the amplitude oscillation, P will have a large amplitude oscillation, but the oscillation frequency is small, and the system reaches a stable time;
I is to solve the speed of the action response, I is slower than the response speed, and vice versa;
D is to eliminate the static error, the general D setting is relatively small, and the impact on the system is relatively small.
For temperature control system P between 5-10%; I between 180-240s; D below 30. For pressure control system P between 30-60%; I between 30-90s; D below 30.
Here is a method of experience. This method is essentially a trial and error method. It is an effective method that has been summarized in production practice and has been widely used in the field.
The basic procedure of this method is to first determine a set of regulator parameters based on operating experience, and put the system into closed-loop operation, and then artificially add step disturbances (such as changing the set value of the regulator) to observe the adjusted or adjusted The step response curve of the output.
If the control quality is considered unsatisfactory, the regulator parameters are changed according to the influence of each tuning parameter on the control process. Repeat the test in this way until you are satisfied.
The empirical method is simple and reliable, but it requires a certain amount of on-site operation experience. The timing is easy to be subjective and one-sided. When the PID regulator is used, there are a plurality of tuning parameters, and the number of trial and error times is increased, and it is difficult to obtain an optimum tuning parameter. Take the PID regulator as an example to illustrate the tuning steps of the empirical method:
A. Let the regulator parameter integral coefficient S0=0, the actual differential coefficient k=0, the control system enters the closed-loop operation, change the proportional coefficient S1 from small to large, let the disturbance signal make a step change, observe the control process until it is satisfactory. Control process up to now.
B. Take the proportional coefficient S1 and multiply the current value by 0.83. Increase the integral coefficient S0 from small to large, and let the disturbance signal make a step change until a satisfactory control process is obtained.
C. The integral coefficient S0 remains unchanged, change the proportional coefficient S1, observe whether the control process is improved, and if there is improvement, continue to adjust until it is satisfied. Otherwise, the original proportional coefficient S1 is increased a little, and then the integral coefficient S0 is adjusted to improve the control process. Try again and again until you find a satisfactory scale factor S1 and integral coefficient S0.
D. Introduce the appropriate actual differential coefficient k and the actual differential time TD, at which point the proportional coefficient S1 and the integral coefficient S0 can be appropriately increased. As with the previous steps, the tuning time adjustment needs to be adjusted repeatedly until the control process is satisfactory.
The PID parameters are determined based on the inertia of the control object. Large inertia such as:
The temperature control of the large drying room can generally be above 10, I=3-10, D=1. Small inertia such as: a small motor with a water pump for pressure closed-loop control, generally only with PI control. P = 1-10, I = 0.1-1, D = 0, these are to be corrected when debugging in the field. Yes, look at occasion applications, PID is composed of three parts: proportional, differential, and integral. In practice, only one or two of them are used, such as P, PI, PD, and PID. You can reach the control requirements... There will be PID function command in the plc programming command... As for the determination of the P, I, D values, it is necessary to make multiple adjustments in the field to determine...
Proportional control (P): Proportional control is one of the most commonly used control methods. For example, we control a heater to maintain a constant temperature of 100 degrees. When starting heating, the temperature difference is far from the target temperature. At this time, we usually increase the heating. Let the temperature rise quickly. When the temperature exceeds 100 degrees, we turn off the output. Usually we will use such a function.
e(t) = SP – y(t);
u(t) = e(t)*P
SP - set value
e(t) - error value
y(t) - feedback value
u(t) - output value
P——The proportionality coefficient hysteresis is not very large. The control object can satisfy the control requirements by using the proportional control method, but many of the controlled objects have hysteresis. That is, if the set temperature is 200 degrees, when the proportional control is used, if the P selection is relatively large, there will be an upward climb when the temperature reaches 200 degrees and the output is 0, and the temperature will still be unstoppable, for example, rise to 230 degrees, when the temperature exceeds 200 degrees too much, it starts to fall back. Even though the output starts to heat up, the temperature will still fall to a certain temperature to fall back, for example, to 170 degrees, and finally the whole system will Stabilization oscillates within a certain range.
If the amplitude of this oscillation is allowed, for example, the control of the household appliance, then the proportional control can be used.
Proportional integral control (PI): The existence of integral is an improvement proposed for proportional control or whether it has a difference or an oscillation. It is often controlled with a proportional, that is, PI control.
There are many formulas, but most of them are not much different. The standard formula is as follows:
u(t) = Kp*e(t) + Ki∑e(t) +u0
u(t) - output
Kp - proportional amplification factor
Ki——Integral amplification factor
e(t) - error
U0——control quantity reference value (basic deviation)
You can see that the integral term is a cumulative value of historical error. If the light is controlled by proportionality, we know if it is not the set value or the oscillation. After using the integral term, we can solve the problem. Fixed value static error problem, for example, after using PI control in a control, if there is static error, the output will not reach the set value. At this time, the accumulated error value of the integral term will become larger and larger. After Ki, it will occupy more of the output weight, making the output u(t) larger and larger, and finally achieve the purpose of eliminating static error.
In the case of two combinations of PI, our adjustment method is as follows:
1. Set the I value to 0 first, and put the P value to be relatively large. When a stable oscillation occurs, we reduce the P value until the P value does not oscillate or the oscillation is small (the term is called the critical oscillation state). In the case, we can also add a little more on the basis of some P values.
2. Increase the I value until the output reaches the set value.
3. After the system is cooled, re-power it to see if the system's overshoot is too large and the heating speed is too slow.
Through the above debugging process, we can see that the P value can be used to adjust the response speed of the system, but too large will increase the overshoot and settling time; while the I value is mainly used to reduce the static error.
PID control:
Because the existence of I in the PI system will affect the response speed of the entire control system, in order to solve this problem, we have added D differential term in the control, and the differential term is mainly used to solve the system's response speed problem, and its complete formula as follows:
u(t) = Kp*e(t) + Ki∑e(t) + Kd[e(t) – e(t-1)]+u0
In the process of PID debugging, we should pay attention to the following steps:
1. Turn off I and D, that is, set to 0. Increase P to make it oscillate;
2. Reduce P and find the critical oscillation point;
3. Increase I to reach the target value; re-power on to see if the overshoot, oscillation and stabilization time meet the requirements;
4. Appropriately add some differential terms for overshoot and oscillation;
5. Note that all commissioning should be debugged under the maximum competition, so as to ensure that the results of the commissioning can be valid within the full working range;