【Daily Question 20090219】Briefly describe the steps for tuning PID parameters using the trial and error method

First adjust the gain, then integrate, and finally differentiate

In a closed-loop control system, depending on the characteristics of the controlled object, the controller parameters are first set within a common range. Then, a certain disturbance is introduced, and based on the effects of δ, TI, and TD on the process, these parameters are adjusted one by one until satisfactory results are achieved.

In my opinion, the values of PID parameters should, on the one hand, be determined based on the specific characteristics of the controlled system； On the other hand is experience. The empirical data for P.I.D. parameters are as follows: 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 F: P=40~100%, T=6~60s. Common mnemonic: 　　　　To determine the optimal parameter settings, check in ascending order. 　　Start with proportionality, then integration, and finally add differentiation. 　　If the curve oscillates frequently, increase the proportionality setting. 　　If the curve wanders around in large swings, reduce the proportionality setting. 　　If the curve takes time to return to its normal position, decrease the integration time. 　　If the curve’s fluctuations have a long cycle, extend the integration time further. 　　If the oscillation frequency is high, first reduce the differentiation setting. 　　Large errors lead to slow fluctuations. The differential time should be increased. The ideal curve consists of two waves, with the higher one at the front and the lower one at the back, in a 4:1 ratio. Observe, adjust, and analyze thoroughly – this way, the quality of the adjustment will remain high

1. Select a sufficiently short sampling period T. By sufficient shortness, it is meant that the sampling period is less than 1/10 of the pure lag time of the object. 2. Let the system operate in pure proportional control, and gradually reduce the proportionality gain ð (ð=1/Kp) to induce critical oscillations in the system. The gain and oscillation period at this point are the critical gain ðK and the critical oscillation period TK. 3. Select the degree of control. The so-called control degree is defined as the ratio of the system’s control performance to that of an analog regulator, with the analog regulator serving as a reference. Table 2: Parameter tuning table for the bit-expansion critical proportionality method. 500”) this. border=0. The images related to this theme are as follows: 500”) this. border=0. Thus, the problem of adjusting these four parameters is simplified to the problem of adjusting just one parameter, Kp. Change Kp and observe the control effect until it is satisfactory.

During tuning, it is also necessary to consider the actual conditions; for some cases, the proportionality of flow regulation can be below 10, with the integration time being in the range of a few seconds.

: ① First use P, then add I, and finally add D； ②During debugging, set the PID parameters to values that have the least impact, that is, P at its maximum value, I at its maximum value, and D at its minimum value ； ③The proportional gain is set according to the pure proportional control system in order to obtain a relatively ideal control process curve; thereafter, the proportional gain is increased by about 1.2 times, and the integral time is varied from large to small to achieve an even better control process curve ； ④Finally, under this integration time, change the scale factor again and check whether the regulation process curve improves ； ⑤If there is improvement, the originally set gain can be reduced and the integration time can be changed; by repeating this process several times, an appropriate gain and integration time can be obtained ； ⑥If the system stability is not sufficient due to external disturbances, the proportional gain and integration time can be increased appropriately to ensure sufficient stability of the system ； ⑦Appropriately reduce the set proportional gain and integral time, and add a differential action to achieve a control process with minimal overshoot and the shortest settling time.

Parameter tuning of the PID controller is a core aspect of control system design. It determines the values of the proportional gain, integral time, and derivative time of the PID controller based on the characteristics of the process under control. There are many methods for tuning PID controller parameters, which can be broadly divided into two categories: one is the theoretical calculation tuning method. It primarily determines the controller parameters through theoretical calculations based on the system’s mathematical model. The calculation data obtained using this method may not be directly usable; it must still be adjusted and modified based on actual engineering conditions. The second is the engineering tuning method, which relies primarily on engineering experience and is carried out directly during the testing of control systems. It is a simple method that is easy to master, and it is widely used in practical engineering applications. The engineering tuning methods for PID controller parameters mainly include the critical ratio method, the response curve method, and the attenuation method. The three methods each have their own characteristics, and what they all have in common is that experiments are conducted first, followed by the tuning of controller parameters using engineering experience formulas. However, the controller parameters obtained using either method require final adjustment and refinement during actual operation. The critical ratio method is generally used nowadays. The steps for tuning the PID controller parameters using this method are as follows: (1) First, pre-select a sufficiently short sampling period for the system to operate ； (2) Only a proportional control element is added, until the system exhibits critical oscillation in its step response to the input; at that point, the proportional gain and the critical oscillation period are recorded ； (3) The parameters of the PID controller are calculated using formulas under a certain degree of control. Setting of PID parameters: This is done based on experience and familiarity with the process, by referring to the measured values and the setpoint curve in order to adjust the values of P, I, and D. The ratio of I to D is 2; the specific value can be determined based on the instrument, after which the proportional band P can be adjusted. If P is set too high, it takes longer to reach stability; if P is too low, oscillations occur, and the set requirements can never be met. For the engineering tuning of PID controller parameters, the following are some empirical values for P.I.D parameters in various control systems: For 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.

(1) Use P first, then I, and finally D； (2) During debugging, set the PID parameters to values that have the least impact, that is, P at its maximum value, I at its maximum value, and D at its minimum value ； (3) Set the gain according to the pure proportional control system to obtain a relatively ideal control process curve; then increase the gain by about 1.2 times, and vary the integration time from large to small to achieve a better control process curve ； (4) Finally, under this integration time, change the proportionality again and check whether the regulation process curve improves ； (5) If there is improvement, the originally set gain can be reduced and the integration time can be changed; by repeating this process several times, an appropriate gain and integration time can be obtained ； (6) If the system stability is poor due to external disturbances, the proportional gain and integral time can be increased appropriately to ensure sufficient stability of the system ； (7) Slightly reduce the set proportional gain and integral time, and add a differential action to obtain a control process with minimal overshoot and the shortest settling time. This post was last edited by yinwolf on 2009-2-19 11:52]

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The order of proportion, integration, and differentiation. The mnemonic on the fourth floor is great, thank you!

Increasing the proportional coefficient P generally speeds up the system’s response and helps to reduce the steady-state error when such an error exists. However, an excessively large proportional coefficient leads to significant overshoot and oscillations, thereby deteriorating the stability of the system. Increasing the integration time I helps to reduce overshoot and oscillations, thereby enhancing the stability of the system, but it prolongs the time required for the system to reach steady state. Increasing the differential time D helps to speed up the system’s response time, reduces overshoot, and improves stability; however, it weakens the system’s ability to suppress disturbances. During trial adjustments, one can refer to the impact trends of the above parameters on the system control process, and follow a tuning procedure that starts with proportional control, followed by integral control, and then derivative control.

First method: first try to determine the proportionality, then add integration, and finally introduce differentiation. The second method: First, select the integration time and the differentiation time, with the differentiation time being one-fourth to one-third of the integration time; then adjust the scale by trial and error, repeating this process until the adjustment curve becomes satisfactory.

There are two methods for tuning using the trial-and-error approach: 1. First, use proportional action for trial tuning; once the transition process has stabilized to an acceptable level, add integral action to eliminate residual errors, and finally add derivative action to improve control quality. Observe the transition process curve in this order to carry out the tuning work. 2. First, set I according to the range specified in the empirical data table for PID parameters; if differential action is to be introduced, D can be taken as (1/3~1/4)I, and then P can be determined through trial and error. Repeat the trial and adjustment until the curve meets the requirements.

Steps for tuning PID parameters: ⑴ Set the integral coefficient S0 of the regulator to 0, and the actual derivative coefficient k to 0; then put the control system into closed-loop operation. Increase the proportional coefficient S1 gradually, apply step changes to the disturbance signal, and observe the control process until a satisfactory control performance is achieved. ⑵Take the proportionality coefficient S1 as the current value multiplied by 0.83, and increase the integration coefficient S0 from low to high; similarly, make the disturbance signal change in a stepwise manner until a satisfactory control process is obtained. ⑶The integration coefficient S0 remains unchanged; the proportionality coefficient S1 is adjusted to see if there is an improvement in the control process. If there is an improvement, further adjustments are made until satisfactory results are achieved. Otherwise, increase the original proportionality coefficient S1 slightly, and then adjust the integration coefficient S0 in an effort to improve the control process. This process of trial and error is repeated until satisfactory proportionality coefficient S1 and integration coefficient S0 are found. ⑷By introducing appropriate actual differential coefficients k and actual differential time TD, it is then possible to appropriately increase the proportional coefficient S1 and the integral coefficient S0. As with the previous steps, the setting of the differentiation time also requires repeated adjustments until the control process is satisfactory. Note: The PID regulator used in the simulation system differs from traditional industrial PID regulators; the various parameters are isolated from one another and do not affect each other, which makes it very convenient to observe the regulation patterns using it. The string 8 PID parameter is determined based on the inertia of the controlled object. For applications with high inertia, such as temperature control in large drying ovens, the value of P is generally above 10, I ranges from 3 to 10, and D is around 1. For systems with low inertia, such as a small motor driving a water pump for pressure closed-loop control, PI control is generally sufficient. P=1-10, I=0.1-1, D=0; these values need to be adjusted during on-site calibration.

Procedure of the empirical trial-and-error method: A commonly used approach is to first try to determine the proportionality factor, then apply integration, and finally introduce differentiation. The procedure is as follows: (1) First, set Ti to its maximum value, TD to zero, set the scale factor δ to a certain value according to the chart, and then put the system in automatic mode. If the transition time is too long, the proportionality should be reduced ； If the oscillation is too severe, the gain should be increased. (2) When integrating is introduced, the already adjusted gain must be increased by 10%∽20%, and then the integration time Ti should be adjusted step by step from large to small until a satisfactory transition process is achieved. (3) The differential action is added last; at this point, δ can be set to a smaller value than in the proportional action case, and the integration time TI can also be reduced accordingly. The differential time TD is taken as (1/3∽1/4) TI, but it is also necessary to keep adjusting it in order to minimize the transition time and the overshoot. :victory:

In my opinion, the values of PID parameters should, on the one hand, be determined based on the specific characteristics of the controlled system； On the other hand is experience. The empirical data for P.I.D. parameters are as follows: 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 F: P=40~100%, T=6~60s. Common mnemonic: 　　　　To determine the optimal parameter settings, check in ascending order. 　　Start with proportionality, then integration, and finally add differentiation. 　　If the curve oscillates frequently, increase the proportionality setting. 　　If the curve wanders around in large swings, reduce the proportionality setting. 　　If the curve takes time to return to its normal position, decrease the integration time. 　　If the curve’s fluctuations have a long cycle, extend the integration time further. 　　If the oscillation frequency is high, first reduce the differentiation setting. 　　Large errors lead to slow fluctuations. The differential time should be increased. The ideal curve consists of two waves, with the higher one at the front and the lower one at the back, in a 4:1 ratio. Observe, adjust, and analyze thoroughly – this way, the quality of the adjustment will remain high

Order of proportional, integral, and derivative