TUNING OF PID

Ankit Ladda [44045]Pushkar Gupta [44026]

Harish Joshi [44030]

Basics

Setpoint (SP): Input from the operator Process Variable (PV): Feedback Control Variable (CV): Output Kp: Proportional Gain Error: Difference between SP and CV

It stands for proportional gain, integral and derivative controller.

PID helps you automatically achieve your desired response

What is PID

 

 

 

SP

PV

Controller outpute(t)

Derivative Function:1] The derivative function reduces the

transient response of the system by reducing overshoot and hunting.

2] And the ability to increase the proportional gain with increased stability, reduced and reduced offset.

Components of PID

Integral Function:1] In closed loop PID system, the integral

system accumulates the system error over time and corrects the error to be zero or nearly zero.

PID tuning is the process of finding the values of proportional, integral, and derivative gains of a PID controller to achieve desired performance and meet design requirements.

Tuning of PID

There are two methods of Tuning PID

1] Adjust and Observe Method2] Ziegler-Nichols Method a] Oscillation Method b] Open loop Method

Methods of Tuning

It Involves making of initial adjustments to the PID constants, observing the response of the machine.

Further more adjustments are made to correct the undesirable properties of the machine response.

Adjust and Observe

1] Initialize the PID controllers , i.e. , Set Td and Ti to zero, and Kp to initial value between 1 to 5.

2] With the machine operating, quickly move the set point to a new value and observe the response.

3] Increase Td until the overshoot is reduced to a desired value. If No overshoot is desired, this can also be achieved by further increase in Td.

Procedure

4] Adjust Ti such that PID will eliminate the offset. Since Ti is the inverse of Ki, this adjustment should begin with high values of Ti and then be reduced to achieve the desired response.

5] Value of Ti that are too small will cause PID system to correct the offset quickly.

The Ziegler – Nicholas Tuning method was developed in 1942 by J. G. Ziegler and N. B. Nichols.

They proposed that the consistent and approximate tuning of any PID controller system could be achieved by mathematical process that involves measuring the response of system to change the set point and then performing a few simple calculations.

Ziegler-Nichols Method

In ZN Method the target amount of overshoot is to have the peak to peak amplitude of each cycle of overshoot be ¼ of the previous amplitude.

It is also called as ¼ Wave Decay method.

The system must be operated in closed loop in an oscillating condition or open loop.

Initialize all the PID constants to zero. Increase the proportional gain constant Kp

to minimum value that will cause the system to oscillate.

Record the value of Kp as Ultimate gain Ku. Measure the period of the oscillation

waveform. This period is Ultimate Period Tu. Shut down the system and readjust the PID

constants to the following values

Oscillation MethodProcedure

Readjust PID constants to the following values

Kp = 0.6 Ku Ti = 0.5 Tu Td = 0.125 Tu

1] To find Kd, Ti and Td, we first need to determine L (deadtime), T (Process time constant) and K (Process gain).

2] Feedback is open circuited, and proportional gain is set to 1 and the integral and derivative gains are set to zero.

3] Input a known change in Setpoint.4] Record the graph, on the graph draw three

intersecting lines;

Open Loop MethodProcedure

- First line is tangential to the steepest part of the rising waveform.

- Second line is horizontal line on the left of the graph at an amplitude equal to the initial value of PV until it intersects the first line.

- Third line is horizontal line on right of the graph at an amplitude equal to the final value of PV

5] Find the parameters L, T and K - L= first and second line intersect - T= time difference between the points

where first line intersects the second and the third line.

- K= percent of PV w.r.t CV6] Shut down the system.

6] Readjusts the PID constants to the following values;

Kp= 1.5T/KL Ti = 2.5L Td= 0.4L