How Do I Choose the Best PID Controller?

PID controller (proportional-integral-derivative controller) is composed of proportional unit (P), integral unit (I) and differential unit (D). Through the setting of Kp, Ki and Kd three parameters. PID controller is mainly suitable for systems that are basically linear and whose dynamic characteristics do not change with time.

A PID controller (Proportion Integration Differentiation) consists of a proportional unit P, an integral unit I, and a differential unit D. Through the setting of three parameters Kp, Ki and Kd. PID controller is mainly suitable for systems whose basic linear and dynamic characteristics do not change with time.

PID controller is a common in industrial control applications

A control loop consists of three parts:

The measurement result obtained by the sensor of the system controller makes a response through an output device. The controller obtains the measurement result from the sensor, and then subtracts the measurement result from the demand result to obtain the error. Then use the error to calculate a correction value to the system as the input result, so the system can eliminate the error from its output result.

In a PID loop, there are three algorithms for this correction value, eliminating current errors, averaging past errors, and predicting future errors by changing the error.

For example, if a water tank is supplying water to a plant, the water in the water tank needs to be maintained at a certain height. A sensor will be used to check the height of the water in the tank, and the measurement result will be obtained. The controller will have a fixed user input value to indicate the water surface height required by the water tank, assuming that this value is to maintain 65% of the water volume. The output device of the controller is connected to a water valve controlled by a motor. Open the valve to fill the water tank, and close the valve to reduce the amount of water in the tank. The control signal of this valve is the variable we control, and it is also the input of this system to keep the water volume of this tank fixed.

The PID controller can be used to control any variable that can be measured and can be controlled. For example, it can be used to control temperature,

PID is named after its three correction algorithms. All three algorithms use addition to adjust the value being controlled. In fact, most of these addition operations become subtraction operations because

Although different types of controllers have different structures and principles, there are only three basic control laws: proportional (P) control, integral (I) control, and derivative (D) control. These kinds of control laws can be used independently, but more occasions are used in combination. Such as proportional (P) control, proportional-integral (PI) control, proportional-integral-derivative (PID) control, etc.

Proportional (P) control

Separate proportional control is also called "difference control". The change in output is proportional to the deviation of the input controller. The larger the deviation, the larger the output. In practical applications, the size of the proportionality should be determined according to the specific situation. The proportionality is too large and the control effect is too weak, which is not conducive to the system to overcome the disturbance. The remaining margin is too large and the control quality is poor. If the control effect is too strong, it will easily lead to the deterioration of the stability of the system and cause oscillation.

For controlled objects with sensitive response and strong amplification ability, in order to improve the stability of the system, the proportionality should be made slightly larger; for controlled objects with slow response and weak amplification ability, the proportionality can be selected to be smaller. Increasing the sensitivity of the entire system can also reduce the residuals accordingly.

Simple proportional control is suitable for occasions with small disturbances, small lags, small load changes, and low requirements, which allow a certain margin to exist. The use of proportional control law in industrial production is more common.

Proportional integral (PI) control

Proportional control law is the most basic and most commonly used one among the basic control laws. Its biggest advantage is that the control is timely and rapid. As long as there is a deviation, the controller immediately produces a control effect. However, the disadvantage of not being able to finally eliminate the residual limits its use alone. The way to overcome the residual is to add integral control to the proportional control.

The output of the integral controller is proportional to the integral of the input deviation over time. "Integral" here means "accumulation". The output of the integral controller is not only related to the magnitude of the input deviation, but also to the time that the deviation exists. As long as the deviation exists, the output will continue to accumulate (the output value will become larger or smaller), and the accumulation will stop until the deviation is zero. Therefore, integral control can eliminate the residual. The integral control law is also called the differenceless control law.

The integration time characterizes the strength of the integral control effect. The smaller the integration time, the stronger the control effect; otherwise, the weaker the control effect.

Although integral control can eliminate the residual, it has the disadvantage of untimely control. Because the accumulation of the integral output is gradual, the control effect produced by it always lags behind the change of the deviation. It cannot overcome the influence of interference in time and effectively, and it is difficult to stabilize the control system. Therefore, in practice, integral control is generally not used alone, but is combined with proportional control to form proportional integral control. Taking the advantages of the two in this way, they make up for each other. It not only has the speedy and timely function of proportional control, but also has the ability of integral control to eliminate the residual. Therefore, proportional integral control can achieve a more ideal process control.

The parameter tuning of the PID controller is

First figure out what is adaptive control

In order to improve product quality, increase production, and save raw materials in the production process, production management and production processes are always required to be in an optimal working state. Therefore, an optimal control method has been produced, which is called

Problems in PID control

Some literature points out that 60% of controllers in the actual industry have performance problems. In the industrial process, the cause of poor control loop performance can be attributed to one or more of the following situations:

1) The controller is poorly tuned and lacks maintenance. The reasons for this situation include: the controller has never been tuned or tuned based on the mismatch model, or it may be the use of an inappropriate type of controller. In industrial process automatic control systems, more than 90% of the controllers are PID-type controllers, even if other controllers may be used to obtain better performance in some cases. In fact, the most common cause of poor control loop performance is a lack of controller maintenance. After years of operation, the dynamic characteristics of the actuator and the controlled object may change due to wear and other reasons. Only a few engineers maintain the control loop, and operators and engineers often lack awareness of the reasons for poor control loop performance.

2) Equipment failure or structural design is unreasonable. Poor control loop performance can be caused by sensor or actuator failures, such as excessive friction. If the industrial plant or the components of the plant are not designed properly, the problem may be more serious. These problems cannot be effectively solved by re-tuning the controller.

3) Missing or insufficient feedforward compensation. If not handled properly, external disturbances will degrade the performance of the circuit. Therefore, when the disturbance is measurable, it is recommended to use feedforward control (FFC) to compensate for the disturbance.

4) The control structure design is unreasonable. Improper input / output pairing, neglecting the mutual coupling between system variables, Competing Controllers, insufficient degrees of freedom, the existence of strong non-linearity, and lack of compensation for large delays can all lead to control structure problems.

PID control performance evaluation

Existing literature points out that it is feasible to estimate the minimum variance that PID control can achieve from conventional operating data in a known process; for PID control, using the minimum variance performance that PID can achieve as an evaluation benchmark, the evaluation results are more reasonable; by fitting the model The PID controller parameters estimated afterwards can significantly reduce the process output variance. ^[1]

At present, control performance monitoring / assessment (CPM / CPA) for control systems is one of the most researched directions in the process control world today. The performance monitoring and evaluation of the controller can be traced back to the work of Astrom (1967), DeVrieWu (1978) and others in the 1960s and 1970s; by 1970, the minimum variance control by Box, Jenkins (1976), and Astro , MVC); 1989 Harris (1989) used the minimum variance control to evaluate the variance performance of the SISO system, making this field have pioneering results and new goals in random performance monitoring and evaluation. Since then, CPM / CPA technology has attracted the attention and research of a large number of control theory scholars and has achieved rapid development. After the efforts of previous people, this technology has developed into an interdisciplinary comprehensive technology involving control theory, system identification, signal processing, and probability statistics. It is often referred to as the performance monitoring and evaluation of control loops, and the performance monitoring and control of controllers. Evaluation, performance evaluation, etc. ^[2]

In order to solve the problem of the decrease of the performance of the controller's loop caused by the time-varying PID controller in industrial systems, Liu Xiaoyan of Zhejiang University proposed a PID controller based on the PID reachability evaluation benchmark proposed by Edgar. Performance evaluation, optimization and monitoring methods, namely: PID loop evaluation optimization algorithm. The algorithm uses the system's closed-loop input and output data for online identification of sliding windows. The PID minimum variance reachability criterion based on MVC (MinimumVariance Control) is used to evaluate the performance of the PID controller, and the optimal PID controller parameters in the sense of minimum variance are calculated. ; Compare the theoretical minimum variance with the output variance as the start-stop threshold for online optimization of the PID system. Simulation has proven its effectiveness. ^[3]