Contenido

Para el correcto funcionamiento de un controlador PID que regule un proceso o sistema se necesita, al menos:.

El sensor proporciona una señal analógica o digital al controlador, la cual representa el punto actual en el que se encuentra el proceso o sistema. La señal puede representar ese valor en tensión eléctrica, intensidad de corriente eléctrica o frecuencia. En este último caso la señal es de corriente alterna, a diferencia de los dos anteriores, que también pueden ser con corriente continua.

El controlador recibe una señal externa que representa el valor que se desea alcanzar. Esta señal recibe el nombre de punto de consigna (o punto de referencia, valor deseado o setpoint), la cual es de la misma naturaleza y tiene el mismo rango de valores que la señal que proporciona el sensor. Para hacer posible esta compatibilidad y que, a su vez, la señal pueda ser entendida por un humano, habrá que establecer algún tipo de interfaz (HMI-Human Machine Interface), son pantallas de gran valor visual y fácil manejo que se usan para hacer más intuitivo el control de un proceso.

El controlador resta la señal de punto actual a la señal de punto de consigna, obteniendo así la señal de error, que determina en cada instante la diferencia que hay entre el valor deseado (consigna) y el valor medido. La señal de error es utilizada por cada uno de los 3 componentes del controlador PID. Las 3 señales sumadas, componen la señal de salida que el controlador va a utilizar para gobernar al actuador. La señal resultante de la suma de estas tres se llama variable manipulada y no se aplica directamente sobre el actuador, sino que debe ser transformada para ser compatible con el actuador utilizado.

Las tres componentes de un controlador PID son: parte Proporcional, acción Integral y acción Derivativa. El peso de la influencia que cada una de estas partes tiene en la suma final viene dado por la constante proporcional, el tiempo integral y el tiempo derivativo, respectivamente.

Se pretenderá lograr que el bucle de control corrija eficazmente y en el mínimo tiempo posible los efectos de las perturbaciones.

Proportional

The proportional part consists of the product between the error signal and the proportional constant to make the steady-state error approach zero, but in most cases, these values ​​will only be optimal in a certain portion of the total control range, with the optimal values ​​being different for each portion of the range. However, there is also a limit value "in the proportional constant beyond which, in some cases, the system reaches values ​​higher than desired. This phenomenon is called overoscillation") and, for safety reasons, it should not exceed 30%, although it is advisable that the proportional part does not even produce overoscillation.

There is a continuous linear relationship between the value of the controlled variable and the position of the final control element (the valve moves to the same value per unit of deviation).

The proportional part does not consider time, therefore, the best way to solve the permanent error") and make the system contain some component that takes into account the variation with respect to time, is by including and configuring the integral and derivative actions.

The proportional formula is given by:.

Where:.

is the proportional gain, tuning value.

is the error (SP is the set point, and PV(t) is the process variable).

It is the time or instantaneous time (the current one).

The error, the proportional band and the initial position of the final control element are expressed as one. It will indicate the position that the final control element will occupy.

Example: Change the position of a valve (final control element) proportionally to the deviation of the temperature (variable) with respect to the set point (desired value).

Comprehensive

The purpose of the Integral control mode is to reduce and eliminate the error in steady state, caused by external disturbances and which cannot be corrected by proportional control.

Integral control acts when there is a deviation between the variable and the set point, integrating this deviation over time and adding it to the proportional action.

The error is integrated, which has the function of averaging or adding it for a given period; It is then multiplied by a constant Ki. Subsequently, the integral response is added to the Proportional mode to form the P + I control with the purpose of obtaining a stable response of the system without stationary error.

The integral mode presents a lag in the response of 90° which, added to the 180° of feedback (negative), brings the process closer to having a delay of 270°, then it will only be necessary for the dead time to contribute with 90° of delay to cause the oscillation of the process. <<< the total gain of the control loop must be less than 1, and thus induce an attenuation in the controller output to lead the process to stability. >>>

It is characterized by the integral action time in minutes per repetition. It is the time in which, in front of a step signal, the final control element repeats the same movement corresponding to the proportional action.

Integral control is used to avoid the drawback of the offset (permanent deviation of the variable with respect to the set point) of the proportional band.

The integral formula is given by:.

Where:.

is the integral gain, a tuning parameter.

is the integration variable (takes into account the value from instant 0 to the current instant).

Example: Move the valve (final control element) at a speed proportional to the deviation from the set point (desired variable).

Derivative

The derivative action is proportional to the speed of change of the error, that is, it takes into account the inertia of the measured variable. This gives the derivative action a forward-looking nature, allowing the error to oscillate and providing the controller with the ability to adapt to unforeseen changes in the characteristics of the system (for example, changes in ambient temperature or the material worked on in a temperature controller).

Derivative action manifests itself when there is a change in the absolute value of the error; (if the error is constant, only the proportional and integral modes act).

The error is derived with respect to time and multiplied by a constant Kd and then added to the previous signals (P+I).

The derivative formula is given by:.

Where:.

is the derivative gain, a tuning parameter.

It is time or instantaneous time (the present).

Derivative control is characterized by the derivative action time in minutes of advance.

Derivative action is appropriate when there is a delay between the moment of the corrective action and its impact on the controlled variable.

When the derivative action time is large, there is instability in the process.

When the derivative action time is small, the variable oscillates too much in relation to the set point.

It is usually rarely used due to its sensitivity to noise and the complications that this entails.

The optimal time of derivative action is the one that returns the variable to the set point with the minimum oscillations.

Example: Corrects the position of the valve (final control element) proportionally to the speed of change of the controlled variable.

The derived action can help reduce the overshoot of the variable during the start of the process. It can be used in systems with considerable delay times, because it allows a rapid impact of the variable after a disturbance occurs in the process.

Kp proportionality constant: can be set as the controller gain value or proportional band percentage.

Example: Changes the position of the valve proportionally to the deviation of the variable with respect to the set point. The P signal moves the valve faithfully following the temperature changes multiplied by the gain.

Integration constant Ki: indicates the speed with which the proportional action is repeated.

Kd derivation constant: makes the response of the proportional action present by doubling it, without waiting for the error to double. The value indicated by the derivation constant is the period during which the proportional action corresponding to 2 times the error will manifest and then disappear.

Example: Moves the valve at a speed proportional to the deviation from the set point. The I signal adds the different areas between the variable and the set point, repeating the proportional signal according to the derived action time (minutes/repetition).

Both the Integral action and the Derivative action affect the dynamic gain of the process. The integral action serves to reduce the stationary error, which would always exist if the constant Ki were zero.

Example: Corrects the valve position proportionally to the speed of change of the controlled variable. The signal d is the slope (tangent) along the curve described by the variable.

The output of these three terms, the proportional, the integral, and the derivative are added to calculate the output of the PID controller. Defining y (t) as the output of the controller, the final form of the PID algorithm is:.

El objetivo de los ajustes de los parámetros PID es lograr que el bucle de control corrija eficazmente y en el mínimo tiempo los efectos de las perturbaciones; se tiene que lograr la mínima integral de error.

Si los parámetros del controlador PID (la ganancia del proporcional, integral y derivativo) se eligen incorrectamente, el proceso a controlar puede ser inestable, por ejemplo, que la salida de este varíe, con o sin oscilación, y está limitada solo por saturación o rotura mecánica. Ajustar un lazo de control") significa ajustar los parámetros del sistema de control a los valores óptimos para la respuesta del sistema de control deseada.

El comportamiento óptimo ante un cambio del proceso o cambio del "setpoint" varía dependiendo de la aplicación. Generalmente, se requiere estabilidad ante la respuesta dada por el controlador, y este no debe oscilar ante ninguna combinación de las condiciones del proceso y cambio de "setpoints". Algunos procesos tienen un grado de no linealidad y algunos parámetros que funcionan bien en condiciones de carga máxima no funcionan cuando el proceso está en estado de "sin carga".

Hay varios métodos para ajustar un lazo de PID. El método más efectivo generalmente requiere del desarrollo de alguna forma del modelo del proceso, luego elegir P, I y D basándose en los parámetros del modelo dinámico. Los métodos de ajuste manual pueden ser muy ineficientes.

La elección de un método dependerá de si el lazo puede ser "desconectado" para ajustarlo, y del tiempo de respuesta del sistema. Si el sistema puede desconectarse, el mejor método de ajuste a menudo es el de ajustar la entrada, midiendo la salida en función del tiempo, y usando esta respuesta para determinar los parámetros de control.

Ahora describimos como realizar un ajuste manual.

manual adjustment

If the system must be kept online, one tuning method is to first set the I and D values ​​to zero. Next, increase P until the loop output oscillates. Then set P to about half the previously set value. Then increase I until the process fits within the required time (although raising I too much can cause instability). Finally, increase D, if necessary, until the loop is fast enough to reach its reference after a sudden change in load.

A very fast PID loop reaches its setpoint quickly, a not so fast PID loop reaches its setpoint not so quickly. Some systems are not capable of accepting this abrupt trigger; In these cases, another loop is required with a P less than half of the P of the previous control system.

Ziegler-Nichols method

The Ziegler-Nichols method allows a test to be carried out on the system to be controlled and from this test the PID parameters necessary to achieve a good, fast response with little overpulse are calculated.

While PID controllers are applicable to most control problems, they may be poor in other applications.

PID controllers, when used alone, can give poor performance when the PID loop gain must be reduced so that it does not trip or oscillate above the "setpoint" value. The performance of the control system can be improved by combining the closed loop of a PID control with an open loop. Knowing the system (such as the necessary acceleration or inertia) can be actuated and combined with the PID output to increase the final performance of the system. Only the advance value (or Feedforward Control) can provide the largest portion of the controller output. The PID controller can be used primarily to respond to any differences or "errors" that remain between the setpoint and the current value of the process. Since the output of the feedback loop is not affected by the feedback of the process, it can never cause the system to oscillate, increasing system performance, response and stability.

For example, in most motion control systems, to accelerate a mechanical load, more force (or torque) is required for the motor. If a PID loop is used to control the speed of the load and drive the force or torque needed by the motor, it may be useful to take the desired instantaneous acceleration value for the load, and add it to the output of the PID controller. This means that regardless of whether the load is being accelerated or decelerated, a proportional amount of force is being handled by the motor in addition to the PID feedback value. The PID loop in this situation uses the feedback information to increase or decrease the difference between the setpoint and the value of the first. Working together, the feed-forward combination provides a more reliable and stable system.

Another problem that the PID has is that it is linear. Mainly the performance of PID controllers in non-linear systems") is variable.

Another common problem that the PID has is that in the derivative part, noise can affect the system, causing those small variations to cause the change in the output to be very large. Generally a Low Pass Filter helps, as it eliminates the high frequency components of the noise. However, an FPB and a derivative control can cause them to cancel each other out. Alternatively, derivative control can be removed in some systems without much loss of control. This is equivalent to using a PID controller as a PI only.

It is desired to control the flow rate of an inlet flow into a chemical reactor.

First of all, a flow control valve for said flow must be installed, and a flow meter, in order to have a constant measurement of the value of the flow that circulates.

The controller will monitor that the flow rate that circulates is the one established by us; When it detects an error, it will send a signal to the control valve so that it will open or close, correcting the measured error. And in this way we will have the desired and necessary flow.

The PID is a mathematical calculation, what sends the information is the PLC.

It is desired to maintain the internal temperature of a chemical reactor at its reference value.

You must have a temperature control device (it can be a heater, an electrical resistance,...), and a sensor (thermometer). The P, PI or PID will control the variable (in this case the temperature). The moment this is not correct, it will notify the control device so that it can act, correcting the error.

In any case, the most correct thing is to put a PID; If there is a lot of noise, a PI, but a P is not very useful since it would not correct the exact value.

A very common example is the altitude control of a drone, where the signal to be controlled is the altitude using an altitude sensing instrument (it can be an ultrasound sensor on the drone or possibly a camera connected externally in wireless communication, etc.), and where the variable to be controlled is the speed and therefore the upward thrust of the drone's ground. A P control would directly give a response to each variation trying to compensate for the error, immediately, as this is not practical, the Derivative part (D) is added, where this part of the control is dedicated to compensating for the variations by "smoothing" them and allowing a temporal-longitudinal space between the spaces and the responses of the control, in this case not being able to react in the same way, it is not enough to compensate for the error by generating an "offset", finally an Integral part will be added to the control (I), providing it with the facility to adjust the variations between responses to the error, minimizing the "offset" generated between responses.

Contenido

Para el correcto funcionamiento de un controlador PID que regule un proceso o sistema se necesita, al menos:.

El sensor proporciona una señal analógica o digital al controlador, la cual representa el punto actual en el que se encuentra el proceso o sistema. La señal puede representar ese valor en tensión eléctrica, intensidad de corriente eléctrica o frecuencia. En este último caso la señal es de corriente alterna, a diferencia de los dos anteriores, que también pueden ser con corriente continua.

El controlador recibe una señal externa que representa el valor que se desea alcanzar. Esta señal recibe el nombre de punto de consigna (o punto de referencia, valor deseado o setpoint), la cual es de la misma naturaleza y tiene el mismo rango de valores que la señal que proporciona el sensor. Para hacer posible esta compatibilidad y que, a su vez, la señal pueda ser entendida por un humano, habrá que establecer algún tipo de interfaz (HMI-Human Machine Interface), son pantallas de gran valor visual y fácil manejo que se usan para hacer más intuitivo el control de un proceso.

El controlador resta la señal de punto actual a la señal de punto de consigna, obteniendo así la señal de error, que determina en cada instante la diferencia que hay entre el valor deseado (consigna) y el valor medido. La señal de error es utilizada por cada uno de los 3 componentes del controlador PID. Las 3 señales sumadas, componen la señal de salida que el controlador va a utilizar para gobernar al actuador. La señal resultante de la suma de estas tres se llama variable manipulada y no se aplica directamente sobre el actuador, sino que debe ser transformada para ser compatible con el actuador utilizado.

Las tres componentes de un controlador PID son: parte Proporcional, acción Integral y acción Derivativa. El peso de la influencia que cada una de estas partes tiene en la suma final viene dado por la constante proporcional, el tiempo integral y el tiempo derivativo, respectivamente.

Se pretenderá lograr que el bucle de control corrija eficazmente y en el mínimo tiempo posible los efectos de las perturbaciones.

Proportional

The proportional part consists of the product between the error signal and the proportional constant to make the steady-state error approach zero, but in most cases, these values ​​will only be optimal in a certain portion of the total control range, with the optimal values ​​being different for each portion of the range. However, there is also a limit value "in the proportional constant beyond which, in some cases, the system reaches values ​​higher than desired. This phenomenon is called overoscillation") and, for safety reasons, it should not exceed 30%, although it is advisable that the proportional part does not even produce overoscillation.

There is a continuous linear relationship between the value of the controlled variable and the position of the final control element (the valve moves to the same value per unit of deviation).

The proportional part does not consider time, therefore, the best way to solve the permanent error") and make the system contain some component that takes into account the variation with respect to time, is by including and configuring the integral and derivative actions.

The proportional formula is given by:.

Where:.

is the proportional gain, tuning value.

is the error (SP is the set point, and PV(t) is the process variable).

It is the time or instantaneous time (the current one).

The error, the proportional band and the initial position of the final control element are expressed as one. It will indicate the position that the final control element will occupy.

Example: Change the position of a valve (final control element) proportionally to the deviation of the temperature (variable) with respect to the set point (desired value).

Comprehensive

The purpose of the Integral control mode is to reduce and eliminate the error in steady state, caused by external disturbances and which cannot be corrected by proportional control.

Integral control acts when there is a deviation between the variable and the set point, integrating this deviation over time and adding it to the proportional action.

The error is integrated, which has the function of averaging or adding it for a given period; It is then multiplied by a constant Ki. Subsequently, the integral response is added to the Proportional mode to form the P + I control with the purpose of obtaining a stable response of the system without stationary error.

The integral mode presents a lag in the response of 90° which, added to the 180° of feedback (negative), brings the process closer to having a delay of 270°, then it will only be necessary for the dead time to contribute with 90° of delay to cause the oscillation of the process. <<< the total gain of the control loop must be less than 1, and thus induce an attenuation in the controller output to lead the process to stability. >>>

It is characterized by the integral action time in minutes per repetition. It is the time in which, in front of a step signal, the final control element repeats the same movement corresponding to the proportional action.

Integral control is used to avoid the drawback of the offset (permanent deviation of the variable with respect to the set point) of the proportional band.

The integral formula is given by:.

Where:.

is the integral gain, a tuning parameter.

is the integration variable (takes into account the value from instant 0 to the current instant).

Example: Move the valve (final control element) at a speed proportional to the deviation from the set point (desired variable).

Derivative

The derivative action is proportional to the speed of change of the error, that is, it takes into account the inertia of the measured variable. This gives the derivative action a forward-looking nature, allowing the error to oscillate and providing the controller with the ability to adapt to unforeseen changes in the characteristics of the system (for example, changes in ambient temperature or the material worked on in a temperature controller).

Derivative action manifests itself when there is a change in the absolute value of the error; (if the error is constant, only the proportional and integral modes act).

The error is derived with respect to time and multiplied by a constant Kd and then added to the previous signals (P+I).

The derivative formula is given by:.

Where:.

is the derivative gain, a tuning parameter.

It is time or instantaneous time (the present).

Derivative control is characterized by the derivative action time in minutes of advance.

Derivative action is appropriate when there is a delay between the moment of the corrective action and its impact on the controlled variable.

When the derivative action time is large, there is instability in the process.

When the derivative action time is small, the variable oscillates too much in relation to the set point.

It is usually rarely used due to its sensitivity to noise and the complications that this entails.

The optimal time of derivative action is the one that returns the variable to the set point with the minimum oscillations.

Example: Corrects the position of the valve (final control element) proportionally to the speed of change of the controlled variable.

The derived action can help reduce the overshoot of the variable during the start of the process. It can be used in systems with considerable delay times, because it allows a rapid impact of the variable after a disturbance occurs in the process.

Kp proportionality constant: can be set as the controller gain value or proportional band percentage.

Example: Changes the position of the valve proportionally to the deviation of the variable with respect to the set point. The P signal moves the valve faithfully following the temperature changes multiplied by the gain.

Integration constant Ki: indicates the speed with which the proportional action is repeated.

Kd derivation constant: makes the response of the proportional action present by doubling it, without waiting for the error to double. The value indicated by the derivation constant is the period during which the proportional action corresponding to 2 times the error will manifest and then disappear.

Example: Moves the valve at a speed proportional to the deviation from the set point. The I signal adds the different areas between the variable and the set point, repeating the proportional signal according to the derived action time (minutes/repetition).

Both the Integral action and the Derivative action affect the dynamic gain of the process. The integral action serves to reduce the stationary error, which would always exist if the constant Ki were zero.

Example: Corrects the valve position proportionally to the speed of change of the controlled variable. The signal d is the slope (tangent) along the curve described by the variable.

The output of these three terms, the proportional, the integral, and the derivative are added to calculate the output of the PID controller. Defining y (t) as the output of the controller, the final form of the PID algorithm is:.

El objetivo de los ajustes de los parámetros PID es lograr que el bucle de control corrija eficazmente y en el mínimo tiempo los efectos de las perturbaciones; se tiene que lograr la mínima integral de error.

Si los parámetros del controlador PID (la ganancia del proporcional, integral y derivativo) se eligen incorrectamente, el proceso a controlar puede ser inestable, por ejemplo, que la salida de este varíe, con o sin oscilación, y está limitada solo por saturación o rotura mecánica. Ajustar un lazo de control") significa ajustar los parámetros del sistema de control a los valores óptimos para la respuesta del sistema de control deseada.

El comportamiento óptimo ante un cambio del proceso o cambio del "setpoint" varía dependiendo de la aplicación. Generalmente, se requiere estabilidad ante la respuesta dada por el controlador, y este no debe oscilar ante ninguna combinación de las condiciones del proceso y cambio de "setpoints". Algunos procesos tienen un grado de no linealidad y algunos parámetros que funcionan bien en condiciones de carga máxima no funcionan cuando el proceso está en estado de "sin carga".

Hay varios métodos para ajustar un lazo de PID. El método más efectivo generalmente requiere del desarrollo de alguna forma del modelo del proceso, luego elegir P, I y D basándose en los parámetros del modelo dinámico. Los métodos de ajuste manual pueden ser muy ineficientes.

La elección de un método dependerá de si el lazo puede ser "desconectado" para ajustarlo, y del tiempo de respuesta del sistema. Si el sistema puede desconectarse, el mejor método de ajuste a menudo es el de ajustar la entrada, midiendo la salida en función del tiempo, y usando esta respuesta para determinar los parámetros de control.

Ahora describimos como realizar un ajuste manual.

manual adjustment

If the system must be kept online, one tuning method is to first set the I and D values ​​to zero. Next, increase P until the loop output oscillates. Then set P to about half the previously set value. Then increase I until the process fits within the required time (although raising I too much can cause instability). Finally, increase D, if necessary, until the loop is fast enough to reach its reference after a sudden change in load.

A very fast PID loop reaches its setpoint quickly, a not so fast PID loop reaches its setpoint not so quickly. Some systems are not capable of accepting this abrupt trigger; In these cases, another loop is required with a P less than half of the P of the previous control system.

Ziegler-Nichols method

The Ziegler-Nichols method allows a test to be carried out on the system to be controlled and from this test the PID parameters necessary to achieve a good, fast response with little overpulse are calculated.

While PID controllers are applicable to most control problems, they may be poor in other applications.

PID controllers, when used alone, can give poor performance when the PID loop gain must be reduced so that it does not trip or oscillate above the "setpoint" value. The performance of the control system can be improved by combining the closed loop of a PID control with an open loop. Knowing the system (such as the necessary acceleration or inertia) can be actuated and combined with the PID output to increase the final performance of the system. Only the advance value (or Feedforward Control) can provide the largest portion of the controller output. The PID controller can be used primarily to respond to any differences or "errors" that remain between the setpoint and the current value of the process. Since the output of the feedback loop is not affected by the feedback of the process, it can never cause the system to oscillate, increasing system performance, response and stability.

For example, in most motion control systems, to accelerate a mechanical load, more force (or torque) is required for the motor. If a PID loop is used to control the speed of the load and drive the force or torque needed by the motor, it may be useful to take the desired instantaneous acceleration value for the load, and add it to the output of the PID controller. This means that regardless of whether the load is being accelerated or decelerated, a proportional amount of force is being handled by the motor in addition to the PID feedback value. The PID loop in this situation uses the feedback information to increase or decrease the difference between the setpoint and the value of the first. Working together, the feed-forward combination provides a more reliable and stable system.

Another problem that the PID has is that it is linear. Mainly the performance of PID controllers in non-linear systems") is variable.

Another common problem that the PID has is that in the derivative part, noise can affect the system, causing those small variations to cause the change in the output to be very large. Generally a Low Pass Filter helps, as it eliminates the high frequency components of the noise. However, an FPB and a derivative control can cause them to cancel each other out. Alternatively, derivative control can be removed in some systems without much loss of control. This is equivalent to using a PID controller as a PI only.

It is desired to control the flow rate of an inlet flow into a chemical reactor.

First of all, a flow control valve for said flow must be installed, and a flow meter, in order to have a constant measurement of the value of the flow that circulates.

The controller will monitor that the flow rate that circulates is the one established by us; When it detects an error, it will send a signal to the control valve so that it will open or close, correcting the measured error. And in this way we will have the desired and necessary flow.

The PID is a mathematical calculation, what sends the information is the PLC.

It is desired to maintain the internal temperature of a chemical reactor at its reference value.

You must have a temperature control device (it can be a heater, an electrical resistance,...), and a sensor (thermometer). The P, PI or PID will control the variable (in this case the temperature). The moment this is not correct, it will notify the control device so that it can act, correcting the error.

In any case, the most correct thing is to put a PID; If there is a lot of noise, a PI, but a P is not very useful since it would not correct the exact value.

A very common example is the altitude control of a drone, where the signal to be controlled is the altitude using an altitude sensing instrument (it can be an ultrasound sensor on the drone or possibly a camera connected externally in wireless communication, etc.), and where the variable to be controlled is the speed and therefore the upward thrust of the drone's ground. A P control would directly give a response to each variation trying to compensate for the error, immediately, as this is not practical, the Derivative part (D) is added, where this part of the control is dedicated to compensating for the variations by "smoothing" them and allowing a temporal-longitudinal space between the spaces and the responses of the control, in this case not being able to react in the same way, it is not enough to compensate for the error by generating an "offset", finally an Integral part will be added to the control (I), providing it with the facility to adjust the variations between responses to the error, minimizing the "offset" generated between responses.