Comprehensive Report on PID Controllers: Functionality & Limitations

This report provides a detailed overview of Proportional-Integral-Derivative (PID) controllers, which are widely used in industrial automatic process control for regulating variables like temperature, pressure, and flow. It explains how PID controllers work by continuously adjusting variables based on the error between the process variable and the set point. The report discusses different PID equations, including the parallel, ideal (ISA), and series equations, highlighting their unique characteristics and applications. It also addresses the limitations of PID controllers, such as large time delays and poor performance with integrating processes, and presents several countermeasures, including the use of two PID controllers, feedforward and feedback loops, model reduction tuning strategies, and dead time compensators. The document concludes with a list of references used to compile the information.

PID In Control System
PID Controller –It stands for proportional–integral–derivative controller (PID controller).
They are used in many industries as automatic process control. They can be used to regulate
temperature, pressure, changing flow and many other processes in industries. The 3
coefficients of PID are different in different PIDs according to the need to get optimal
response [2].
Fig 1: PID controller [2]
Example: Temperature Control using a PID controller
How PID works?
In manual control the controller will read the process variable time to time to change or
control different variables. In case of automatic control adjustments and changes are made
continuously to make continuous changes and maintain control over the variable [1].
Industries use PID. This algorithm is basically for manipulating the error.
ERROR = PV – SP
PV - process variable,
SP - Set point [3].

Fig 2: Working of PID [1]
Different PID Equations
Each action (P, I, and D) occurs in separate equations, with the combined effect being a sum:
In the parallel equation, each action parameter (Kp, τi, τd) is independent. It is a drawback
because adjustment made to the controller should only affect one aspect of the action and
sometimes it is necessary that gain parameter should affect all the control actions (P, I, and
D) [3].
To provide this very functionality another PID equation exist. This PID equation is called
the Ideal or ISA equation:
In this equation, the gain constant (Kp) is distributed to all the terms inside the parentheses,
affecting equally all control actions. Increasing gain constant of PID controller makes the
individual actions P, I and D more aggressive [3].
Another third equation with origins in the unusual pressure and analog electronic circuit is
there, and it is called the Series or Interacting equation:

Here, In this equation the gain constant (Kp) affects all three actions just as with the “ideal”
equation. Here the integral and derivative cost effect proportional action means adjusting
either τi or τd does not adjust those actions, but influences the aggressiveness of proportional
action [3].
Limitations and Countermeasures of PID Controllers
 PID controllers show large time delay process.
 PID controllers show poor control performance for integrating process.
 PID controller cannot incorporate ramp type set point change/slow disturbance [4].
To resolve/remove above limitations several techniques have been proposed:
1. To avoid these poor control performances and incapability of controllers.
2. Control structure with 2 PID controllers is introduced to manipulate set point change
process and the input disturbance rejection process.
3. To resolve ramp type set point and disturbance a feed forward and feedback loop are
proposed. An additional feedback loop is also introduced to incorporate integrating
process.
4. Tuning strategy by using model reduction is proposed to tune up the controller for
high order processes.
5. To manipulate large time delay process a dead time compensator is used [4].
References
1. R. Deshpande, “PID Controller-Working and Tuning Methods,” Electronics Hub, 24-
Dec-2017. [Online]. Available: https://www.electronicshub.org/pid-controller-
working-and-tuning-methods/. [Accessed: 22-May-2018].
2. H. (2018). How does a PID controller work? - jjrobots. [online] jjrobots. Available at:
https://www.jjrobots.com/pid/ [Accessed 23 May 2018].
3. Students.iitk.ac.in. (2018). [online] Available at:
http://students.iitk.ac.in/roboclub/lectures/PID.pdf [Accessed 23 May 2018].
4. “Limitations and Countermeasures of PID Controllers,” C&EN: WHAT'S THAT
STUFF? JELL-O. [Online]. Available:
https://pubs.acs.org/doi/abs/10.1021/ie960090 . [Accessed: 23-May-2018].