## Instrumentation

### PID Theory

In this lesson, we will study the PID Theory.

• Proportional Response
The proportional component depends only on the difference between the setpoint and the process variable.
• This difference is referred to as the Error term. The proportional gain (Kp) determines the ratio of output response to the error signal.

• In general, increasing the proportional gain will increase the speed of the control system response.
• However, if the proportional gain is too large, the process variable will begin to oscillate.
• If Kp is increased further, the oscillations will become larger and the system will become unstable and may even oscillate out of control.

Integral Response

• The integral component sums the error term over time. The result is that even a small error term will cause the integral component to increase slowly.
• The integral response will continually increase over time unless the error is zero. so the effect is to drive the Steady-State error to zero. Steady-State error is the final difference between the process variable and setpoint.

With Integral Action, the Controller output is proportional to the amount of time the error is present.

Integral action eliminates offset.

Derivative Response

• The derivative component causes the output to decrease if the process variable is increasing rapidly.
• The derivative response is proportional to the rate of change of the process variable. Increasing the derivative time (Td) parameter will cause the control system to react more strongly to changes in the error term and will increase the speed of the overall control system response.
• Most practical control systems use very small derivative time (Td) because the Derivative Response is highly sensitive to noise in the process variable signal. If the sensor feedback signal is noisy or if the control loop rate is too slow, the derivative response can make the control system unstable. Controller Output:

Y= E(t)(Kp+1/Ti( ∫ E(t)dt)+ Td( d/dt E(t)/dt)).

It is clear from the above equation that Controller Output increases with Kp and Td and decreases with Ti.

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