PID (Proportional Integral Derivative) control is one of the earliest developed control strategies. Because of its simple algorithm, good robustness and high reliability, it is widely used in industrial process control, especially for deterministic control systems that can establish accurate mathematical models.

In engineering practice, the most widely used regulator control laws are proportional, integral and differential control, referred to as PID control, also known as PID control, which is actually an algorithm. PID controller has been developed for nearly 70 years. It has become one of the main technologies of industrial control because of its simple structure, good stability, reliable operation and convenient adjustment. When the structure and parameters of the controlled object cannot be fully mastered, or the precise mathematical model cannot be obtained, and other technologies of control theory are difficult to adopt, the structure and parameters of the system controller must be determined by experience and on-site debugging, and then the application of PID control technology is the most convenient. That is, when we do not fully understand a system and the controlled object, or cannot obtain the system parameters through effective measurement methods, the PID control technology is most suitable. PID control, there are also PI and PD control in practice. PID controller is based on the system error, using proportion, integral and differential to calculate the control quantity for control.
PID temperature control instrument control schematic diagram

From the perspective of signal transformation, lead correction, lag correction, and lag lead correction can be summarized into three operations and their combinations: proportion, integral, and differential.

Scope of application of PID regulator: PID regulation control is a traditional control method, which is applicable to almost all sites such as temperature, pressure, flow, liquid level, etc. Different sites, only the PID parameters should be set differently. As long as the parameters are set properly, good results can be achieved. Both can reach 0.1% or even higher control requirements.

Deficiency of PID temperature control instrument control

1. In the actual industrial production process, there are often nonlinear and time-varying uncertainties, and it is difficult to establish an accurate mathematical model. The conventional PID controller cannot achieve the desired control effect;

2. In the actual production site, due to the trouble of parameter setting methods, the parameters of conventional PID controller are often set poorly, the effect is poor, and the adaptability to operating conditions is poor.

2、 Each correction link of PID controller

The primary task of any closed-loop control system is to respond to commands stably (stably), quickly (rapidly) and accurately (accurately). The main work of PID adjustment is how to achieve this task.

Increasing the proportion coefficient P will speed up the response of the system. Its effect on the output value is faster, but it cannot be well stabilized at an ideal value. The bad result is that although it can effectively overcome the influence of the disturbance, there are residual errors. Too large proportion coefficient will cause the system to have a relatively large overshoot, and produce oscillation, which will worsen the stability. The integration can eliminate the residual error on the basis of proportion. It can trim the error of the system with accumulated error after stabilization and reduce the steady-state error. Differential has the leading effect. For the control channel with capacity lag, the introduction of differential to participate in the control has a significant effect on improving the dynamic performance index of the system when the differential term is properly set. It can reduce the overshoot of the system, increase the stability, and reduce the dynamic error.

To sum up, P-the rapidity of response of the proportional control system, which acts on the output quickly, is like "now" (it works now, fast), I-the accuracy of the integral control system, which eliminates the accumulated error in the past, is like "past" (clearing the past grievances and returning to the accurate track), D-the stability of the differential control system, which has the leading control effect, It is like "future" (look ahead, take precautions, and develop only after stability). Of course, this conclusion can not be generalized, just to let beginners understand the role of PID more quickly.

When adjusting, your task is to balance and adjust the three parameters to achieve the best control effect and achieve stable, fast and accurate control characteristics when the system structure allows.

Proportional control can adjust the deviation quickly, timely and proportionally to improve the control sensitivity, but it has static error and low control accuracy. Integral control can eliminate deviation, improve control accuracy and steady-state performance, but it is easy to cause vibration and overshoot. Differential control is a kind of advanced control, which can adjust the system speed, reduce overshoot, and improve stability. However, if its time constant is too small, it will introduce interference, and the system impact will be large. If it is too small, the adjustment period will be long, and the effect will not be significant. Proportional, integral and differential control work together to reasonably select the parameters of PID regulator, namely, proportional coefficient KP and integral time constant τ I and differential time constant τ D. It can quickly, accurately and stably eliminate the deviation and achieve good control effect.

1. Proportional link

Reflect the deviation signal e (t) of the control system proportionally. Once the deviation is generated, the controller will immediately control to reduce the deviation. When there is only proportional control, the system output has steady-state error.

The smaller the P parameter, the stronger the proportional effect, the faster the dynamic response, and the stronger the ability to eliminate errors. However, the actual system has inertia. After the control output changes, the actual y (t) value will change slowly after a period of time. Because the actual system is inertial, the proportion effect should not be too strong, and too strong proportion effect will cause the system oscillation instability. Based on the above quantitative calculation, the size of P parameter shall be determined according to the system response and site commissioning. Generally, P parameter shall be adjusted from large to small to achieve the fastest response without overshoot (or large overshoot) as the best parameter.

Advantages: adjust the open-loop proportional coefficient of the system, improve the steady-state accuracy of the system, reduce the inertia of the system, and speed up the response speed.

Disadvantages: only using P controller, too large open-loop proportional coefficient will not only increase the overshoot of the system, but also make the system stability margin smaller, even unstable.

2. Integral link

The output of the controller is proportional to the integral of the input error signal. It is mainly used to eliminate static errors and improve the error-free degree of the system. The strength of the integral action depends on the integral time constant T. The larger the T, the weaker the integral action, and the stronger the inverse.

Why should we introduce integral function?

The output of the proportional action is proportional to the size of the error. The larger the error, the larger the output. The smaller the error, the smaller the output. The error is zero, and the output is zero. Since the output is zero when there is no error, it is impossible for proportional adjustment to completely eliminate the error and make the controlled PV value reach the given value. There must be a stable error to maintain a stable output in order to keep the PV value of the system stable. This is usually said that the proportion function is differential adjustment, which has static error. Strengthening the proportion function can only reduce the static error, but can not eliminate the static error (static error: static error, also known as steady-state error).

In order to eliminate the static error, an integral action must be introduced, which can eliminate the static error, so that the controlled y (t) value is finally consistent with the given value. The purpose of introducing the function of integration is to eliminate the static error and make the value of y (t) reach the given value and keep consistent.

The principle of integrating to eliminate static error is to integrate the error as long as there is an error, so that the output will continue to increase or decrease until the error is zero, the integration will stop, the output will not change, the PV value of the system will remain stable, and the y (t) value is equal to the u (t) value, achieving the effect of error-free adjustment.

However, because the actual system has inertia, the value of y (t) will not change immediately after the output changes, and it must wait for a period of time to change slowly. Therefore, the speed of integration must match the inertia of the actual system. If the inertia is large, the integration effect should be weak, and the integration time I should be larger, and vice versa. If the integration effect is too strong and the integration output changes too fast, the phenomenon of over-integration will be caused, resulting in over-harmonic oscillation of integration. In general, I parameter is also adjusted from large to small, that is, the integral effect is adjusted from small to large, and the system response is observed so that the error can be eliminated quickly and the given value can be reached without causing oscillation.

For an automatic control system, if there is steady-state error after entering the steady-state state, the control system is said to have steady-state error or simply referred to as the system with steady-state error. In order to eliminate steady-state error, "integral term" must be introduced into the controller. The error of the integral term pair depends on the integration of time. With the increase of time, the integral term will increase. In this way, even if the error is small, the integral term will increase with the increase of time. It will drive the output of the controller to increase and further reduce the steady-state error until it is equal to zero. Therefore, the proportional+integral (PI) controller can make the system have no steady-state error after entering the steady-state. PI controller not only maintains the "memory function" of integral controller to eliminate steady-state error, but also overcomes the disadvantage of insensitive response when using integral control alone to eliminate error.

Advantages: eliminate steady-state error.

Disadvantages: the addition of integral controller will affect the stability of the system and reduce the stability margin of the system.

3. Differential link

Reflect the change trend of the deviation signal, and introduce an effective early correction signal into the system before the deviation signal becomes too large, so as to speed up the action speed of the system and reduce the adjustment time. In differential control, the output of the controller is proportional to the differential of the input error signal (that is, the rate of error change).

Why introduce differential action?

As previously analyzed, both proportional regulation and integral regulation are based on the generation of errors before they are adjusted to eliminate errors, which are post adjustment. Therefore, this kind of regulation is not bad for the steady state, but it is bad for the dynamic state, because the disturbance caused by load changes or set value changes must wait for the generation of errors before slowly adjusting to eliminate them.

However, the general control system has requirements not only for stability control, but also for dynamic indexes. Usually, it requires that the speed of recovering to the steady state after the disturbance caused by load change or given adjustment should be faster. Therefore, only the proportional and integral adjustment can not fully meet the requirements, and the differential action must be introduced. Proportional action and integral action are post adjustment (i.e. adjustment after error), while differential action is pre prevention control, that is, as soon as y (t) is found to have a trend of becoming larger or smaller, a control signal to prevent its change is immediately output to prevent overshoot or overshoot.

The greater D is, the stronger the differential action is. The smaller D is, the weaker the differential action is. D is usually adjusted from small to large during system commissioning, and the specific parameters are determined by the test.

For example, due to the change of y (t) caused by the adjustment of the given value or load disturbance, the proportional and differential actions must not be adjusted until the change of y (t) value, and when the error is small, the resulting proportional and integral adjustment actions are also small, and the ability to correct the error is also small. When the error is large, the resulting proportional and integral actions will increase. Because it is not ideal to adjust dynamic indicators afterwards. The differential action can be adjusted as soon as the trend of error is found before the error is generated. It is controlled in advance, so the timeliness is better. It can minimize the dynamic error and make the overall effect better. However, the differential action can only be used as a supplement to proportional and integral control, and cannot play a leading role. The differential action cannot be too strong. Too strong will also cause system instability and oscillation. The differential action can only be adjusted from small to large after P and I are adjusted, and try to add it bit by bit.

The automatic control system may oscillate or even lose stability in the adjustment process of overcoming errors. The reason is that there are large inertia components (links) or delay components, which have the effect of restraining errors, and their changes always lag behind the changes of errors. The solution is to make the change of the effect of restraining error "advance", that is, when the error is close to zero, the effect of restraining error should be zero. That is to say, it is often not enough to introduce only the "proportion" term in the controller. The role of the proportion term is only to amplify the amplitude of the error. At present, what needs to be added is the "differential term", which can predict the trend of error change. In this way, the controller with proportion+differential can make the control effect of restraining error equal to zero or even negative in advance, thus avoiding serious overshoot of the controlled quantity. Therefore, for the controlled object with large inertia or delay, the proportional+differential (PD) controller can improve the dynamic characteristics of the system in the process of regulation. PD control only works in the dynamic process and blocks the steady state. Therefore, differential control cannot be used alone under any circumstances.

Advantages: make the response speed of the system faster, reduce overshoot, reduce oscillation, and have a "prediction" effect on the dynamic process.

In the low frequency band, it is mainly the PI control law that acts to improve the system type and eliminate or reduce the steady-state error; In the middle and high frequency band, PD law plays a role, increasing the cut-off frequency and phase margin, and improving the response speed. Therefore, the controller can comprehensively improve the control performance of the system.

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