Normally the PID function is used to control process variables such as temperature, pressure, liquid level, or flow rate. The PID controller receives the process variable (PV) and controls the manipulation variable (MV) in order to adjust the PV to match the set value (SV). The figure below shows a typical configuration for a PID control system.
In the above figure:
Process: A reaction which is controlled by physical values such as temperature, pressure, flow rate, etc.
Sensor: A detector that detects the controlled physical values. It can be a thermocouple, RTD, pressure gage, flow meter, etc.
Signal Converter: A device that transmits a weak sensor signal to the PID controller by converting it into the signal suited for the environment such as 4 - 20 mA, 1 - 5 Vdc, pulse train, etc.
Actuator: A device that regulates fluid or electric power to the process according to the signal generated by the PID controller. It can be a control valve, thyristor, variable speed drive, etc.
PV: Process variable ... normally 4 - 20 mA or 1 - 5 Vdc analog signals
MV: Manipulation variable ... normally 4 - 20 mA, 1 - 5 Vdc or a time-proportional pulse.
SV: Set value.
PID Equation: Controls the MV based on the magnitude of e and De and the PID tuning parameters. These parameters may be more or less aggressive based on system time responses and operator preferences.
PID Basics
NOTE: The above equation for the D control is the complete derivative. However, for the actual process, such complete derivative action is harmful. Therefore, in the PID3, an incomplete derivative action is used. Also, in the PID3, derivative is applied only for a change in PV, not for the error. This is called pre-derivative PID. This method is used to prevent the unnecessary large changing of the MV for the SV is being changed.
Operation Mode
Generally a PID controller has two operation modes, Auto mode and Manual mode. Auto mode is the mode in which the MV is controlled by the PID equation. Manual mode is the mode in which the MV is changed by operator.
When the operation mode is changed from Manual to Auto, and vice versa, the MV should not be changed rapidly (bumped). Normally a PID controller has a function that enables it to hold the current MV during mode changes. This function is called bumpless transfer.
Some PID algorithms have a function called SV(Set point) tracking. When the SV tracking function is enabled, the SV is automatically over-written by the current PV during Manual mode. As the result, when the mode is changed from Manual to Auto, the control operation continues smoothly, since the SV and the PV are identical. A frequent operator complaint about SV tracking is that the SV must always be re-entered after each change from manual to auto mode. Therefore when SV tracking is implemented in a PID algorithm a manual switch is normally provided to allow operators the option of disabling it.
NOTE: In the PID3 instruction, a bumpless transfer function is available. The PID3 does not have the SV tracking function. However, this function can be easily programmed into preceding circuits in the PLC. See section 4.4, “Adding SV Tracking”
References :
In the above figure:
Process: A reaction which is controlled by physical values such as temperature, pressure, flow rate, etc.
Sensor: A detector that detects the controlled physical values. It can be a thermocouple, RTD, pressure gage, flow meter, etc.
Signal Converter: A device that transmits a weak sensor signal to the PID controller by converting it into the signal suited for the environment such as 4 - 20 mA, 1 - 5 Vdc, pulse train, etc.
Actuator: A device that regulates fluid or electric power to the process according to the signal generated by the PID controller. It can be a control valve, thyristor, variable speed drive, etc.
PV: Process variable ... normally 4 - 20 mA or 1 - 5 Vdc analog signals
MV: Manipulation variable ... normally 4 - 20 mA, 1 - 5 Vdc or a time-proportional pulse.
SV: Set value.
PID Equation: Controls the MV based on the magnitude of e and De and the PID tuning parameters. These parameters may be more or less aggressive based on system time responses and operator preferences.
PID Basics
- Direct action and reverse action
There are two basic actions of PID with respect to the control direction of MV. These are direct action and reverse action.
· Direct action will lead the MV to increase when the PV is larger than the SV.
(For example, cooling application)
· Reverse action will lead the MV to decrease when the PV is larger than the SV.
(For example, heating application) - PID Parameters
- Proportional (P) control action
Proportional (P) control generates the MV in proportion to the error (E). Here, the error (E) is the difference between the SV and the PV, and defined as follows:
E = SV-PV
In the P control action, the MV is calculated as follows.
MV=KP×E
KP is called proportional gain.
Generally, P control action works as follows:
With just P control, an offset (residual error) will remain. Therefore, P control is used with I control (PI control) to eliminate the offset. - Integral (I) control action
Integral (I) control will generate the MV in proportion to the time-integral of the error (E). While the error (E) exists, the I control will modulate the MV to eliminate the error (E). Generally the MV with I control is calculated as follows:
TI is called integral time, the unit of measure is ‘seconds per repeat’
When TI is large, the MV will change slowly. When TI is small, the MV will change rapidly. That is, the smaller the TI, the larger the integral gain. When TI is too small, oscillation of PV will appear as figure below.
The I control is not used by itself. It is used with P (PI control) or P and D (PID control).
NOTE: When the SV is changed, E may remain for a relatively long time, and the MV may reach either its minimum or maximum value. If I continues to integrate beyond this point there will be a significant lag time in response to an overshoot (a change in the direction of E). This problem is called ‘reset windup’, the name originating with pneumatic controls and their ‘gain, reset and rate’ tuning parameters. To prevent this, the PID3 instruction has a feature called anti-reset windup, which stops the I control action when the MV reaches its limit. - Derivative (D) control action
Derivative (D) control will generate the MV in proportion to the rate of change in the error (E). By adding the D control, quick corrective action can be obtained at the beginning of an upset condition. Generally the MV by the D control is written as follows.
TD is called derivative time, the unit of measure is ‘repeats per second’.
When TD is large, MV is relatively large for any E. That is, the larger the TD, the larger the derivative gain. If TD is 0 (zero), the D control does not function. When TD is too large, short periodic oscillations of PV will appear:
The D control is not used by itself. It is used with P and I (PID control). D control is poorly suited for processes which oscillate rapidly and is seldom used in processes which have a fast response time (most pressure or flow loops). For processes with long lag times (many temperature and some level loops), D control can reduce both the magnitude of e and the potential for large overshoots caused by a given upset condition. Note that these same processes often act as mechanical integrators and the I tuning parameter can actually stimulate a worsening of the overshoot or oscillationproblem.
NOTE: The above equation for the D control is the complete derivative. However, for the actual process, such complete derivative action is harmful. Therefore, in the PID3, an incomplete derivative action is used. Also, in the PID3, derivative is applied only for a change in PV, not for the error. This is called pre-derivative PID. This method is used to prevent the unnecessary large changing of the MV for the SV is being changed.
Operation Mode
Generally a PID controller has two operation modes, Auto mode and Manual mode. Auto mode is the mode in which the MV is controlled by the PID equation. Manual mode is the mode in which the MV is changed by operator.
When the operation mode is changed from Manual to Auto, and vice versa, the MV should not be changed rapidly (bumped). Normally a PID controller has a function that enables it to hold the current MV during mode changes. This function is called bumpless transfer.
Some PID algorithms have a function called SV(Set point) tracking. When the SV tracking function is enabled, the SV is automatically over-written by the current PV during Manual mode. As the result, when the mode is changed from Manual to Auto, the control operation continues smoothly, since the SV and the PV are identical. A frequent operator complaint about SV tracking is that the SV must always be re-entered after each change from manual to auto mode. Therefore when SV tracking is implemented in a PID algorithm a manual switch is normally provided to allow operators the option of disabling it.
NOTE: In the PID3 instruction, a bumpless transfer function is available. The PID3 does not have the SV tracking function. However, this function can be easily programmed into preceding circuits in the PLC. See section 4.4, “Adding SV Tracking”
References :
- PROGRAMMABLE CONTROLLER PROSEC T-series. APPLICATION GUIDE - PID Function - . TOSHIBA CORPORATION
- Balchen, Jens G. and Kenneth I. Mumme. Process Control, Structures and Applications. New York: Van Nostrand Reinhold Company, 1988.
- Anderson, Norman A. Instrumentation for Process Measurement and Control. 3rd ed.
Rednor, PA: Chilton Company, 1980. Intech December 1994, Controller Tuning and Control Loop Performance by David W. St. Clair of Straight-Line Control Company at 302-731-4699. - Corripio, Armando B. Tuning of Industrial Control Systems. Instrumentation Society of America, 1990.
- Shinskey, F.G. Process Control Systems. 3rd ed. New York, NY. McGraw-Hill Book Company, 1988.
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