Kp: proportional coefficient—– proportional band (proportional degree) P: expressed as a percentage of the ratio of the relative value of the input deviation signal change to the relative value of the output signal change (the reciprocal of the proportional coefficient)
T: sampling time
Ti: integration time
Td: differential time
Temperature T: P=20~60%, Ti=180~600s, Td=3-180s
Pressure P: P=30~70%, Ti=24~180s,
Level L: P=20~80%, Ti= 60~300s,
flow L: P=40~100%, Ti=6~60s.
(1) Generally speaking, during the tuning, it is observed that the curve oscillates very frequently, and the proportional band needs to be increased to reduce the oscillation; when the maximum deviation of the curve is large and tends to be a non-periodic process, the proportional band needs to be reduced.
(2) When the curve fluctuates greatly, the integration time should be increased; after the curve deviates from the given value and cannot come back for a long time, the integration time should be reduced to speed up the elimination of residuals.
(3) If the curve oscillates violently, the differential action needs to be minimized, or the differential action is not added temporarily; the maximum deviation of the curve is large and the decay is slow, and the differential time needs to be extended to increase the action
(4) If the proportional band is too small, the integral time is too small or the differential time is too large, periodic violent oscillations will occur. If the integral time is too small, the oscillation period will be longer; if the proportional band is too small, the oscillation period will be shorter; if the differential time is too large, the oscillation period will be the shortest
(5) If the proportional band is too large or the integration time is too long, the transition process will change slowly. If the proportional band is too large, the curve such as irregular waves deviates from the given value. If the integration time is too long, the curve will slowly return to the given value through a non-periodic abnormal path.
Note: When the integral time is too long or the derivative time is too large and exceeds the allowable range, no matter if the proportional band is changed, it cannot be remedied.
1. PID debugging steps There is
no control algorithm that is more effective and convenient than the PID adjustment law. Some of the more fashionable regulators these days are basically derived from PID. It can even be said: Is the PID regulator some other control tuning algorithm?
Why is PID so widely used and so enduring?
Because PID solves the most basic problems to be solved by automatic control theory , namely the stability, rapidity and accuracy of the system. Adjusting the parameters of the PID can realize the system's stability, taking into account the system's load capacity and anti-disturbance ability. At the same time, the integral term is introduced into the PID regulator, and a zero integral point is added to the system, making it a first-order or A system of more than one order, such that the steady-state error of the system's step response is zero.
Because the controlled objects of the automatic control system vary widely, the parameters of the PID must also change to meet the performance requirements of the system. This brings considerable trouble to users, especially for beginners. The following briefly introduces the general steps for debugging PID parameters:
1. Negative Feedback
Automatic control theory is also known as negative feedback control theory. First check the system wiring to make sure the feedback of the system is negative feedback. For example, in a motor speed control system, the input signal is positive, and when the motor is required to rotate forward, the feedback signal is also positive (in PID algorithm, error = input - feedback), and the higher the motor speed, the larger the feedback signal. The rest of the systems are the same way.
2. PID debugging general principles
a. When the output does not oscillate, increase the proportional gain P.
b. When the output does not oscillate, reduce the integral time constant Ti.
c. When the output does not oscillate, increase the differential time constant Td.
3. General Steps
a. Determine Proportional Gain P
When determining the proportional gain P, first remove the integral term and differential term of the PID, generally set Ti=0, Td=0 (see the PID parameter setting description for details), so that the PID is purely proportional. The input is set to 60%~70% of the maximum allowable value of the system, and the proportional gain P is gradually increased from 0 until the system oscillates; in turn, the proportional gain P is gradually reduced from this time until the system oscillation disappears, and record For the proportional gain P at this time, set the proportional gain P of the PID to 60%~70% of the current value. Proportional gain P debugging is completed.
b. Determine the integral time constant Ti
After the proportional gain P is determined, set a larger initial value of the integral time constant Ti, then gradually decrease Ti until the system oscillates, and then in turn, gradually increase Ti until the system The oscillations disappear. Record the Ti at this time, and set the integral time constant Ti of the PID to be 150%~180% of the current value. The integration time constant Ti debugging is completed.
c. Determine the differential time constant Td The
integral time constant Td generally does not need to be set, it can be set to 0. To set, it is the same as the method for determining P and Ti, taking 30% of the non-oscillation.
d. No-load and on-load joint debugging of the system, and then fine-tune the PID parameters until the requirements are met.
2. Introduction to PID control
At present, the level of industrial automation has become an important symbol to measure the modernization level of all walks of life. At the same time, the development of control theory has also experienced three stages: classical control theory, modern control theory and intelligent control theory. A typical example of intelligent control is a fuzzy fully automatic washing machine, etc. Automatic control systems can be divided into open-loop control systems and closed-loop control systems. A control system includes a controller, a sensor, a transmitter, an actuator, and an input and output interface. The output of the controller is added to the controlled system through the output interface and the actuator; the controlled quantity of the control system is sent to the controller through the input interface through the sensor and transmitter. Different control systems have different sensors, transmitters, and actuators. For example, the pressure control system uses a pressure sensor. The sensor of the electric heating control system is the temperature sensor. At present, there are many PID control and its controllers or intelligent PID controllers (instruments), and the products have been widely used in engineering practice. There are various PID controller products, and major companies have developed PID controllers. The intelligent regulator with parameter self-tuning function, in which the automatic adjustment of PID controller parameters is realized by intelligent adjustment or self-correction and self-adaptive algorithm. There are pressure, temperature, flow, liquid level controllers realized by PID control, programmable logic controllers (PLC) that can realize PID control functions, and PC systems that can realize PID control. The programmable logic controller (PLC) uses its closed-loop control module to realize PID control, and the programmable logic controller (PLC) can be directly connected with ControlNet, such as Rockwell's PLC-5. There are also controllers that can realize PID control functions, such as Rockwell's Logix product series, which can be directly connected to ControlNet and use the network to realize its remote control functions. 1.
Open-loop control system Open-loop control system means that the output of the controlled object (controlled quantity) has no effect on the output of the controller.
In this control system, there is no reliance on sending the controlled variable back to form any closed loop.
2. Closed-loop control system
The characteristic of closed-loop control system is that the output (controlled quantity) of the controlled object of the system will be sent back to affect the output of the controller, forming one or more closed loops. The closed-loop control system has positive feedback and negative feedback. If the feedback signal is opposite to the system given value signal, it is called negative feedback. If the polarity is the same, it is called positive feedback. Generally, the closed-loop control system adopts negative feedback. , also known as negative feedback control system. There are many examples of closed loop control systems. For example, human is a closed-loop control system with negative feedback, and eyes are sensors, acting as feedback, and the human body system can finally make various correct actions through continuous correction. Without eyes, there is no feedback loop, and it becomes an open-loop control system. For another example, when a real fully automatic washing machine has the ability to continuously check whether the clothes are washed, and automatically cut off the power after washing, it is a closed-loop control system.
3. Step response
Step response refers to the output of the system when a step input (step function) is added to the system. Steady-state error refers to the difference between the expected output of the system and the actual output after the response of the system enters the steady state. The performance of the control system can be described by three words: stable, accurate and fast. Stability refers to the stability of the system. For a system to work normally, it must first be stable. From the point of view of the step response, it should be convergent. Accuracy refers to the accuracy and precision of the control system. It is described by Steady-state error, which represents the difference between the steady-state value of the system output and the expected value; fastness refers to the rapidity of the response of the control system, which is usually quantitatively described by the rise time.
4. The principle and characteristics of PID control
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 regulation. The PID controller has a history of nearly 70 years since its inception. 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 grasped, or an accurate mathematical model cannot be obtained, and other techniques of control theory are difficult to use, the structure and parameters of the system controller must be determined by experience and on-site debugging. PID control technology is the most convenient. That is, when we do not fully understand a system and the controlled object, or cannot obtain system parameters through effective measurement methods, PID control technology is most suitable. PID control, there are also PI and PD control in practice. The PID controller is based on the error of the system, using proportional, integral and differential to calculate the control amount for control.
Proportional (P) Control
Proportional control is the simplest control method. The output of its controller is proportional to the input error signal. When there is only proportional control, the system output has a steady-state error (Steady-state error).
Integral (I) Control
In integral control, the output of the controller is proportional to the integral of the input error signal. For an automatic control system, if there is a steady-state error after entering the steady state, the control system is called a system with a steady-state error or a system with Steady-state Error for short. In order to eliminate steady-state errors, an "integral term" must be introduced in the controller. The integral term integrates the error over time, and as time increases, the integral term increases. In this way, even if the error is small, the integral term will increase with time, which pushes the output of the controller to increase to further reduce the steady-state error until it equals zero. Therefore, the proportional + integral (PI) controller can make the system free from steady-state error after entering the steady state.
Differential (D) Control
In differential control, the output of the controller is proportional to the differential of the input error signal (ie, the rate of change of the error). The automatic control system may oscillate or even become unstable during the adjustment process to overcome the error. The reason is that there is a large inertial component (link) or a lag (delay) component, which has the effect of suppressing the error, and its change always lags behind the change of the error. The solution is to "lead" the change in the effect of suppressing the error, that is, when the error is close to zero, the effect of suppressing the error should be zero. That is to say, it is often not enough to introduce only the "proportional" term in the controller. The function of the proportional term is only to amplify the amplitude of the error, and what needs to be added at present is the "differential term", which can predict the trend of the error change, In this way, the controller with proportional + derivative can make the control effect of suppressing error equal to zero or even negative in advance, thereby avoiding serious overshoot of the controlled variable. Therefore, for the controlled object with large inertia or lag, the proportional + derivative (PD) controller can improve the dynamic characteristics of the system during the adjustment process.
5. Parameter setting of PID controller
The parameter tuning of the PID controller is the core content of the control system design. It determines the proportional coefficient, integral time and differential time of the PID controller according to the characteristics of the controlled process. There are many methods for PID controller parameter tuning, which can be summarized into two categories: one is the theoretical calculation tuning method. It is mainly based on the mathematical model of the system to determine the controller parameters through theoretical calculation. The calculated data obtained by this method may not be used directly, and must be adjusted and modified through engineering practice. The second is the engineering tuning method, which mainly relies on engineering experience and is carried out directly in the test of the control system. The method is simple and easy to master, and is widely used in engineering practice. The engineering tuning methods of PID controller parameters mainly include critical proportional method, response curve method and decay method. The three methods have their own characteristics, and the common point is to pass the test, and then adjust the controller parameters according to the engineering experience formula. But no matter which method is adopted, the controller parameters obtained need to be finally adjusted and perfected in actual operation. Now generally used is the critical ratio method. The steps of using this method to tune the parameters of the PID controller are as follows: (1) First select a sufficiently short sampling period to allow the system to work; (2) Only add the proportional control link until the system has a critical oscillation in the step response to the input. Write down the proportional amplification factor and the critical oscillation period at this time; (3) The parameters of the PID controller are obtained by formula calculation under a certain degree of control.
3. Engineering tuning of PID controller parameters, the empirical data of PID parameters in various adjustment systems can be referred to 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 L: P=40~100%, T=6~60s.
4. Common formulas of PID:
find the best parameter setting, check in order from small to large.
First , proportional, then integrate, and finally add differential. The curve
oscillates very frequently, and the proportional dial should be enlarged.
The curve deviates and recovers slowly, and the integral time decreases. The fluctuation period of the
curve is long, and the integral time is longer. The
oscillation frequency of the curve is fast. First reduce
the differential. The differentiation time should be lengthened. The
ideal curve has two waves. The front is high and the back is low. 4 to 1.
Look at the second adjustment and analyze it, and the adjustment quality will not be low.
Kp: proportional coefficient—– proportional band (proportional degree) P: expressed as a percentage of the ratio of the relative value of the input deviation signal change to the relative value of the output signal change (the reciprocal of the proportional coefficient)
T: sampling time
Ti: integration time
Td: differential time
Temperature T: P=20~60%, Ti=180~600s, Td=3-180s
Pressure P: P=30~70%, Ti=24~180s,
Level L: P=20~80%, Ti= 60~300s,
flow L: P=40~100%, Ti=6~60s.
(1) Generally speaking, during the tuning, it is observed that the curve oscillates very frequently, and the proportional band needs to be increased to reduce the oscillation; when the maximum deviation of the curve is large and tends to be a non-periodic process, the proportional band needs to be reduced.
(2) When the curve fluctuates greatly, the integration time should be increased; after the curve deviates from the given value and cannot come back for a long time, the integration time should be reduced to speed up the elimination of residuals.
(3) If the curve oscillates violently, the differential action needs to be minimized, or the differential action is not added temporarily; the maximum deviation of the curve is large and the decay is slow, and the differential time needs to be extended to increase the action
(4) If the proportional band is too small, the integral time is too small or the differential time is too large, periodic violent oscillations will occur. If the integral time is too small, the oscillation period will be longer; if the proportional band is too small, the oscillation period will be shorter; if the differential time is too large, the oscillation period will be the shortest
(5) If the proportional band is too large or the integration time is too long, the transition process will change slowly. If the proportional band is too large, the curve such as irregular waves deviates from the given value. If the integration time is too long, the curve will slowly return to the given value through a non-periodic abnormal path.
Note: When the integral time is too long or the derivative time is too large and exceeds the allowable range, no matter if the proportional band is changed, it cannot be remedied.
1. PID debugging steps There is
no control algorithm that is more effective and convenient than the PID adjustment law. Some of the more fashionable regulators these days are basically derived from PID. It can even be said: Is the PID regulator some other control tuning algorithm?
Why is PID so widely used and so enduring?
Because PID solves the most basic problems to be solved by automatic control theory , namely the stability, rapidity and accuracy of the system. Adjusting the parameters of the PID can realize the system's stability, taking into account the system's load capacity and anti-disturbance ability. At the same time, the integral term is introduced into the PID regulator, and a zero integral point is added to the system, making it a first-order or A system of more than one order, such that the steady-state error of the system's step response is zero.
Because the controlled objects of the automatic control system vary widely, the parameters of the PID must also change to meet the performance requirements of the system. This brings considerable trouble to users, especially for beginners. The following briefly introduces the general steps for debugging PID parameters:
1. Negative Feedback
Automatic control theory is also known as negative feedback control theory. First check the system wiring to make sure the feedback of the system is negative feedback. For example, in a motor speed control system, the input signal is positive, and when the motor is required to rotate forward, the feedback signal is also positive (in PID algorithm, error = input - feedback), and the higher the motor speed, the larger the feedback signal. The rest of the systems are the same way.
2. PID debugging general principles
a. When the output does not oscillate, increase the proportional gain P.
b. When the output does not oscillate, reduce the integral time constant Ti.
c. When the output does not oscillate, increase the differential time constant Td.
3. General Steps
a. Determine Proportional Gain P
When determining the proportional gain P, first remove the integral term and differential term of the PID, generally set Ti=0, Td=0 (see the PID parameter setting description for details), so that the PID is purely proportional. The input is set to 60%~70% of the maximum allowable value of the system, and the proportional gain P is gradually increased from 0 until the system oscillates; in turn, the proportional gain P is gradually reduced from this time until the system oscillation disappears, and record For the proportional gain P at this time, set the proportional gain P of the PID to 60%~70% of the current value. Proportional gain P debugging is completed.
b. Determine the integral time constant Ti
After the proportional gain P is determined, set a larger initial value of the integral time constant Ti, then gradually decrease Ti until the system oscillates, and then in turn, gradually increase Ti until the system The oscillations disappear. Record the Ti at this time, and set the integral time constant Ti of the PID to be 150%~180% of the current value. The integration time constant Ti debugging is completed.
c. Determine the differential time constant Td The
integral time constant Td generally does not need to be set, it can be set to 0. To set, it is the same as the method for determining P and Ti, taking 30% of the non-oscillation.
d. No-load and on-load joint debugging of the system, and then fine-tune the PID parameters until the requirements are met.
2. Introduction to PID control
At present, the level of industrial automation has become an important symbol to measure the modernization level of all walks of life. At the same time, the development of control theory has also experienced three stages: classical control theory, modern control theory and intelligent control theory. A typical example of intelligent control is a fuzzy fully automatic washing machine, etc. Automatic control systems can be divided into open-loop control systems and closed-loop control systems. A control system includes a controller, a sensor, a transmitter, an actuator, and an input and output interface. The output of the controller is added to the controlled system through the output interface and the actuator; the controlled quantity of the control system is sent to the controller through the input interface through the sensor and transmitter. Different control systems have different sensors, transmitters, and actuators. For example, the pressure control system uses a pressure sensor. The sensor of the electric heating control system is the temperature sensor. At present, there are many PID control and its controllers or intelligent PID controllers (instruments), and the products have been widely used in engineering practice. There are various PID controller products, and major companies have developed PID controllers. The intelligent regulator with parameter self-tuning function, in which the automatic adjustment of PID controller parameters is realized by intelligent adjustment or self-correction and self-adaptive algorithm. There are pressure, temperature, flow, liquid level controllers realized by PID control, programmable logic controllers (PLC) that can realize PID control functions, and PC systems that can realize PID control. The programmable logic controller (PLC) uses its closed-loop control module to realize PID control, and the programmable logic controller (PLC) can be directly connected with ControlNet, such as Rockwell's PLC-5. There are also controllers that can realize PID control functions, such as Rockwell's Logix product series, which can be directly connected to ControlNet and use the network to realize its remote control functions. 1.
Open-loop control system Open-loop control system means that the output of the controlled object (controlled quantity) has no effect on the output of the controller.
In this control system, there is no reliance on sending the controlled variable back to form any closed loop.
2. Closed-loop control system
The characteristic of closed-loop control system is that the output (controlled quantity) of the controlled object of the system will be sent back to affect the output of the controller, forming one or more closed loops. The closed-loop control system has positive feedback and negative feedback. If the feedback signal is opposite to the system given value signal, it is called negative feedback. If the polarity is the same, it is called positive feedback. Generally, the closed-loop control system adopts negative feedback. , also known as negative feedback control system. There are many examples of closed loop control systems. For example, human is a closed-loop control system with negative feedback, and eyes are sensors, acting as feedback, and the human body system can finally make various correct actions through continuous correction. Without eyes, there is no feedback loop, and it becomes an open-loop control system. For another example, when a real fully automatic washing machine has the ability to continuously check whether the clothes are washed, and automatically cut off the power after washing, it is a closed-loop control system.
3. Step response
Step response refers to the output of the system when a step input (step function) is added to the system. Steady-state error refers to the difference between the expected output of the system and the actual output after the response of the system enters the steady state. The performance of the control system can be described by three words: stable, accurate and fast. Stability refers to the stability of the system. For a system to work normally, it must first be stable. From the point of view of the step response, it should be convergent. Accuracy refers to the accuracy and precision of the control system. It is described by Steady-state error, which represents the difference between the steady-state value of the system output and the expected value; fastness refers to the rapidity of the response of the control system, which is usually quantitatively described by the rise time.
4. The principle and characteristics of PID control
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 regulation. The PID controller has a history of nearly 70 years since its inception. 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 grasped, or an accurate mathematical model cannot be obtained, and other techniques of control theory are difficult to use, the structure and parameters of the system controller must be determined by experience and on-site debugging. PID control technology is the most convenient. That is, when we do not fully understand a system and the controlled object, or cannot obtain system parameters through effective measurement methods, PID control technology is most suitable. PID control, there are also PI and PD control in practice. The PID controller is based on the error of the system, using proportional, integral and differential to calculate the control amount for control.
Proportional (P) Control
Proportional control is the simplest control method. The output of its controller is proportional to the input error signal. When there is only proportional control, the system output has a steady-state error (Steady-state error).
Integral (I) Control
In integral control, the output of the controller is proportional to the integral of the input error signal. For an automatic control system, if there is a steady-state error after entering the steady state, the control system is called a system with a steady-state error or a system with Steady-state Error for short. In order to eliminate steady-state errors, an "integral term" must be introduced in the controller. The integral term integrates the error over time, and as time increases, the integral term increases. In this way, even if the error is small, the integral term will increase with time, which pushes the output of the controller to increase to further reduce the steady-state error until it equals zero. Therefore, the proportional + integral (PI) controller can make the system free from steady-state error after entering the steady state.
Differential (D) Control
In differential control, the output of the controller is proportional to the differential of the input error signal (ie, the rate of change of the error). The automatic control system may oscillate or even become unstable during the adjustment process to overcome the error. The reason is that there is a large inertial component (link) or a lag (delay) component, which has the effect of suppressing the error, and its change always lags behind the change of the error. The solution is to "lead" the change in the effect of suppressing the error, that is, when the error is close to zero, the effect of suppressing the error should be zero. That is to say, it is often not enough to introduce only the "proportional" term in the controller. The function of the proportional term is only to amplify the amplitude of the error, and what needs to be added at present is the "differential term", which can predict the trend of the error change, In this way, the controller with proportional + derivative can make the control effect of suppressing error equal to zero or even negative in advance, thereby avoiding serious overshoot of the controlled variable. Therefore, for the controlled object with large inertia or lag, the proportional + derivative (PD) controller can improve the dynamic characteristics of the system during the adjustment process.
5. Parameter setting of PID controller
The parameter tuning of the PID controller is the core content of the control system design. It determines the proportional coefficient, integral time and differential time of the PID controller according to the characteristics of the controlled process. There are many methods for PID controller parameter tuning, which can be summarized into two categories: one is the theoretical calculation tuning method. It is mainly based on the mathematical model of the system to determine the controller parameters through theoretical calculation. The calculated data obtained by this method may not be used directly, and must be adjusted and modified through engineering practice. The second is the engineering tuning method, which mainly relies on engineering experience and is carried out directly in the test of the control system. The method is simple and easy to master, and is widely used in engineering practice. The engineering tuning methods of PID controller parameters mainly include critical proportional method, response curve method and decay method. The three methods have their own characteristics, and the common point is to pass the test, and then adjust the controller parameters according to the engineering experience formula. But no matter which method is adopted, the controller parameters obtained need to be finally adjusted and perfected in actual operation. Now generally used is the critical ratio method. The steps of using this method to tune the parameters of the PID controller are as follows: (1) First select a sufficiently short sampling period to allow the system to work; (2) Only add the proportional control link until the system has a critical oscillation in the step response to the input. Write down the proportional amplification factor and the critical oscillation period at this time; (3) The parameters of the PID controller are obtained by formula calculation under a certain degree of control.
3. Engineering tuning of PID controller parameters, the empirical data of PID parameters in various adjustment systems can be referred to 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 L: P=40~100%, T=6~60s.
4. Common formulas of PID:
find the best parameter setting, check in order from small to large.
First , proportional, then integrate, and finally add differential. The curve
oscillates very frequently, and the proportional dial should be enlarged.
The curve deviates and recovers slowly, and the integral time decreases. The fluctuation period of the
curve is long, and the integral time is longer. The
oscillation frequency of the curve is fast. First reduce
the differential. The differentiation time should be lengthened. The
ideal curve has two waves. The front is high and the back is low. 4 to 1.
Look at the second adjustment and analyze it, and the adjustment quality will not be low.