# PID regulator

## What is PID regulation?

As the name suggests, this article will give a precise idea of the structure and operation of the PID controller. However, to go into detail, let's see an introduction to PID controllers.

PID controllers are used in a wide range of applications for industrial process control. About 95% of closed-loop operations in the industrial automation industry use PID controllers. PID stands for Proportional-Integral-Derivative. These three controllers are combined to produce a control signal.

As a feedback controller, it delivers control output at desired levels. Before microprocessors were invented, PID control was implemented by analog electronic components. But today all PID controllers are processed by microprocessors. Programmable controllers also have the built-in instructions of PID controllers. Due to the flexibility and reliability of PID controllers, these are traditionally used in process control applications.

## PID controller operation

With the use of a simple and inexpensive ON-OFF controller, two control states are possible, such as completely or completely off. It is used for a limited control application where these two control states are sufficient for the control purpose. However, the oscillating nature of this control limits its use and is therefore replaced by PID controllers.

The PID controller holds the output so that there is no error between the process variable and the desired set point / output during closed loop operations. The PID uses three basic control behaviors which are explained below.

Regulator - P:

The proportional controller or P gives an output proportional to the current error e (t). It compares the desired point or set point to the actual value or to the value of the feedback process. The resulting error is multiplied by the proportional constant to get the output. If the error value is zero, the controller output is zero.

This controller requires manual bias or reset when used alone. This is because it never reaches the steady state condition. It provides stable operation but still maintains steady state error. The speed of the response increases as the proportional constant Kc increases.

#### Regulator - PI:

Due to the limitation of the p controller when there is still an offset between the process variable and the set point, the I controller is required, which provides the necessary action to clear the steady state error. It incorporates the error over a period of time until the error value reaches zero. It contains the value of the final control device at which the error becomes zero.

Full control decreases its output in the event of a negative error. This limits the speed of response and affects the stability of the system. The speed of the response is increased by decreasing the integral gain Ki.

In the figure above, as the gain of controller I decreases, the steady state error also decreases. In most cases, the PI controller is used especially when a high speed response is not required.

When using the PI controller, the output of the I controller is limited to a certain distance in order to overcome the integral winding conditions, the integral output increasing even at the zero error state, due to the non-linearities of the installation.

#### Regulator - PID:

I-controller does not have the ability to predict future error behavior. Therefore, it reacts normally once the set point has been changed. D-controller overcomes this problem by anticipating the future behavior of the error. Its output depends on the rate of change of the error with respect to time multiplied by the derivative constant. It kicks off the exit, thereby increasing the response of the system.

In the figure above, the response of controller D is greater than that of the PI controller, and the output settling time is also reduced. It improves the stability of the system by compensating for the phase shift caused by controller I. Increasing the derivative gain increases the speed of response.

So we finally found that by combining these three controllers, we could achieve the desired response for the system. Different manufacturers design different PID algorithms.

## PID controller tuning methods

Before the PID controller works, it must be adapted to the dynamics of the process to be controlled. Designers give the default values for the terms P, I and D. These values could not give the desired performance and sometimes resulted in instability and slow control performance. Different types of tuning methods are developed to tune PID controllers and require special attention from the operator in order to select the best proportional, integral and derivative gain values. Some of them are given below.

Trial and error method: This is a simple method of tuning the PID controller. When the system or the controller is working, we can adjust the controller. In this method, we must first set the Ki and Kd values to zero and increase the proportional term (Kp) until the system achieves oscillating behavior. Once it oscillates, adjust Ki (integral term) so that the oscillations stop, then adjust D for a quick response.

Process reaction curve technique: This is an open loop tuning technique. It produces a response when a step input is applied to the system. Initially, we need to manually apply some control outputs to the system and record the response curve.

After that, we have to calculate the slope, the dead time, the rise time of the curve and finally substitute these values for the equations P, I and D to obtain the gain values in terms of PID.

Zeigler-Nichols Method: Zeigler-Nichols proposed closed loop methods for tuning the PID controller. These are a continuous cycle method and a damped oscillation method. The procedures for the two methods are identical but the oscillation behavior is different. For this we must first set the controller constant p, Kp, to a particular value, while the values of Ki and Kd are zero. The proportional gain is increased until the system oscillates at a constant amplitude.

The gain for which the system produces constant oscillations is called ultimate gain (Ku) and the period of oscillations is called ultimate period (Pc). Once reached, we can enter the values of P, I and D into the PID controller thanks to the Zeigler-Nichols table which depends on the controller used, such as P, PI or PID as shown below.

PID controller structure

The PID controller has three terms, namely proportional control, integral control and derivative control. The combined operation of these three controllers results in a control strategy for process control. The PID controller manipulates process variables such as pressure, speed, temperature, flow, etc. Some applications use PID controllers in cascade networks where two or more PIDs are used to achieve control.

The figure above shows the structure of the PID controller. It consists of a PID block which gives its output to the process block. Process / Plant consists of final control devices such as actuators, control valves and other control devices to control various industry / plant processes.

The feedback signal from the treatment plant is compared to a set point or to the reference signal u (t) and the corresponding error signal e (t) is transmitted to the PID algorithm. Based on the algorithm's proportional, integral and derivative control calculations, the controller produces a combined response or controlled output that is applied to the plant's control devices.

Not all control applications need all three control elements. Combinations such as PI and PD commands are very often used in practical applications.

We hope we have been able to provide some basic, but precise, knowledge about PID controllers. Here is a simple question for all of you. Among the different tuning methods, which method is preferably used to achieve optimal operation of the PID controller and why?