PID Controllers Explained

by Dermot Tynan in Control Theory

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Posted on Saturday, February 11, 2023 at 12:40

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PID controllers are one of the most widely used control algorithms in the control systems industry. They are simple, reliable and have a proven track record of delivering accurate control in a variety of applications. In this post, we'll discuss what PID controllers are, how they work, and why they are so popular.

A PID controller is a type of control algorithm that uses three control terms, Proportional (P), Integral (I), and Derivative (D), to regulate the behaviour of a system. The goal of a PID controller is to bring the system’s behaviour to a desired set-point, or target value, by continuously adjusting the control signal. The setpoint is usually defined by the user or system operator and is the desired value that the system should strive to achieve.

The proportional term of a PID controller is the simplest control term and is responsible for providing the primary control signal. The proportional term calculates the difference between the set-point and the actual process value (also known as the process variable or PV) and generates a control signal that is proportional to this error. This means that the larger the error, the larger the control signal will be, and the smaller the error, the smaller the control signal will be. The proportional term provides the bulk of the control signal, but it does not have the ability to eliminate the error completely.

The integral term of a PID controller is responsible for eliminating the residual error that may be present after the proportional term has acted. The integral term works by summing the error over time, and using this accumulated error to generate a control signal. This control signal is then added to the control signal generated by the proportional term to provide a more complete control signal. The integral term provides a steady control signal that compensates for any residual error and helps to bring the system behaviour to the set-point.

The derivative term of a PID controller is responsible for anticipating the future behaviour of the system. The derivative term calculates the rate of change of the error and generates a control signal that is proportional to this rate of change. This control signal is then added to the control signals generated by the proportional and integral terms to provide a more complete control signal. The derivative term provides a quick response to changes in the system behaviour, allowing the PID controller to respond quickly to any deviations from the set-point.

PID controllers are widely used in control systems because they are simple to understand, implement, and tune. They are also very flexible and can be used in a variety of applications, from simple control loops to complex systems. Additionally, PID controllers are very reliable and have a proven track record of delivering accurate control in a variety of applications.

One of the most important aspects of using a PID controller is tuning the control parameters, which determines the behaviour of the controller. The three control parameters, P, I, and D, can be adjusted to optimise the performance of the controller. The goal of tuning is to find the optimal values for these parameters that will provide the best control performance for a given system.

Tuning a PID controller can be done manually, by making adjustments to the control parameters and observing the effect on the system behaviour, or it can be done automatically using an optimisation algorithm. There are several different optimisation algorithms available, each with its own strengths and weaknesses. Some of the most commonly used optimisation algorithms include the Ziegler-Nichols method, the Cohen-Coon method, and the Tyreus-Luyben method.

In conclusion, PID controllers are a simple, reliable and widely used control algorithm that are well suited for a variety of applications. They are relatively easy to understand, implement, and tune, making them an ideal choice for many control systems.

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