PID (Proportional-Integral-Derivative) Control

Image Source

I. INTRODUCTION

A control system is used to control, manage, direct or regulate the behavior of devices or even other systems. According to (Suryadi and Widodo, 2007), control System (CS) is used to control position, velocity, and acceleration is very common in industrial and military applications. They have been given the special name of servomechanisms. With all their many advantages, CS in inadvertently act as an oscillator.

The controllers used to control processes can have several structures. The choice of the structure determines how well the plant can be controlled. The plant poses some guidelines and restrictions on the controller. The choice of controller determines the best possible performance achieved of a well-tuned controller. PID controllers are used extensively in the industry as an all-in-all controller, mostly because it is an intuitive control algorithm (Åström and Hägglund, 1995). The controller does not explicitly take the varying time-delay, which this thesis is dealing with, into account. Since the PID controller is widely used, it is investigated to see if it nonetheless could be used by selecting a suitable tuning.

The controller has three parts: the proportional part which is proportional to the error, the integral part which removes the steady-state error and the derivative part reduces the overshoot. The weights of the controller’s actions are adjusted with the P, I and D gains. The PID controller is traditionally suitable for second and lower order systems. It can also be used for higher order plants with dominant second order behaviour. The controller is usually implemented in a computer that does calculations in discrete-time. In networked control systems a discrete-time version of the controller is needed because the measurements are sent over the network as packets.

II. PROPORTIONAL CONTROL

A proportional control system is a type of linear feedback control system. Proportional control is how most drivers control the speed of a car. If the car is at target speed and the speed increases slightly, the power is reduced slightly, or in proportion to the error (the actual versus target speed), so that the car reduces speed gradually and reaches the target point with very little, if any, "overshoot", so the result is much smoother control than on-off control.

III. INTEGRAL CONTROL

In a proportional control of a plant there is a steady-state error, or offset, in the response to a step input. Such an offset can be eliminated if integral controller is included in the system. In the integral control of a plant, the control signal, the output signal from the controller, at any instant is the area under the actuating error signal curve up to that instant.

According to Instrumentation and Control System, 2015, Integral control is the control mode where the controller output is proportional to the integral of the error with respect to time, i.e.controller output∝integral of error with timeand so we can writeI controller output=Ki×integral of error with timewhere Ki is the constant of proportionality and, when the controller output is expressed as a percentage and the error as a percentage, has units of s−1.

But while removing the steady-state error, it may lead to oscillatory response of slowly decreasing amplitude or even increasing amplitude, both of which is usually undesirable.

IV. DERIVATIVE CONTROL

According to Overview of Industrial Process Automation (Second Edition), 2017 Derivative control is the reaction to the rate at which the error has been changing, and it slows the rate of change of the controller output. The derivative mode of the PID controller is an additional and separate term added to the end of the equation that considers the derivative (or rate of change) of the error as it varies over time. The proportional term considers how far PV is from SP at any instant in time.

V. PROPORTIONAL PLUS INTEGRAL CONTROLLER

In control engineering, a PI Controller (proportional-integral controller) is a feedback controller which drives the plant to be controlled by a weighted sum of the error (difference between the output and desired set-point) and the integral of that value. It is a special case of the PID controller in which the derivative (D) part of the error is not used.

VI. PROPORTIONAL PLUS DERIVATIVE CONTROLLER

Proportional-Derivative or PD control combines proportional control and derivative control in parallel. Derivative action acts on the derivative or rate of change of the control error. This provides a fast response, as opposed to the integral action, but cannot accommodate constant errors.

VII. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLER

The PID controller was first placed on the market in 1939 and has remained the most widely used controller in process control until today. An investigation performed in 1989 in Japan indicated that more than 90% of the controllers used in process industries are PID controllers and advanced versions of the PID controller. PI controllers are fairly common, since derivative action is sensitive to measurement noise.
The three element of PID produces outputs with the following nature:

1. P element: proportional to the error at the instant t, this is the “present” error.
2. I element: proportional to the integral of the error up to the instant t, which can be interpreted as the accumulation of the “past” error.
3. D element: proportional to the derivative of the error at the instant t, which can be interpreted as the prediction of the “future” error.

Thus, the PID controller can be understood as a controller that takes the present, the past, and the future of the error into consideration.

VII. APPLICATIONS

In the early history of automatic process control the PID controller was implemented as a mechanical device. These mechanical controllers used a lever, spring and a mass and were often energized by compressed air. These pneumatic controllers were once the industry standard. Electronic analog controllers can be made from a solid-state or tube amplifier, a capacitor and a resistance.

Electronic analog PID control loops were often found within more complex electronic systems, for example, the head positioning of a disk drive, the power conditioning of a power supply, or even the movement-detection circuit of a modern seismometer. Nowadays, electronic controllers have largely been replaced by digital controllers implemented with microcontrollers or FPGAs. Most modern PID controllers in industry are implemented in programmable logic controllers (PLCs) or as a panel-mounted digital controller. Software implementations have the advantages that they are relatively cheap and are flexible with respect to the implementation of the PID algorithm.

VIII. CONCLUSION

In the recent years, control system has assumed an increasingly important role in the development and advancement of modern civilization and technology. Practically every aspect of our day-to-day activities is affected by some type of control systems.

Automatic control system are found in abundance in all sectors of industry, such as quality control of manufactured products, automatic assembly line, machine-tool control, space technology and weapon system, computer control, transportation systems, power systems, robotics and many others. It is essential in such industrial operations as controlling pressure, temperature, humidity, and flow in the process industries.

IX.REFERENCES:

Wood, A.J. and B.F. Wollenberg, Power Generation, Operation, and Control, 2 nd ed., Wiley India (P.) Ltd., 4435/7, Ansari Road, Daryaganj, New Delhi 110 002, India, 2007, Chapter 9, pp. 328-360

Dorf, Richard C. and Robert H. Bishop, Modern Control Systems, 9 th ed., Prentice–Hall Inc., New Jersey-07458, USA, 2001, Chapters 1, 5, pp. 1-23, pp. 173-206.

Bhattacharyya, S.P. and L.H. Keel, “PID controller synthesis free of analytical methods,” Proc. of IFAC 16th Triennial World Congress, Prague, Czech Republic, 2005

https://www.sciencedirect.com/topics/engineering/derivative-control
Date Accessed: July 11,2019

https://www.sciencedirect.com/topics/engineering/integral-control
Date Accessed: July 11,2019

https://pixabay.com/photos/mars-rover-curiosity-space-travel-1241266/

Date Accessed: July 11, 2019