AME Unit 11 Q4

Proportional action is the simplest form of control action in a control system. It involves adjusting a control output in direct proportion to the error between a desired setpoint and a measured process variable.

Key points:

• Error: The difference between the desired setpoint and the actual process value.
• Control output: The action taken to correct the error (e.g., valve position, heater power).
• Proportionality: The control output is directly proportional to the error.

Example:

• A thermostat controlling room temperature:
  • The setpoint is the desired temperature.
  • The process variable is the actual room temperature.
  • The error is the difference between the setpoint and the actual temperature.
  • The control output is the heating or cooling system.
  • If the room is too cold (large negative error), the heater is turned on to a high level.
  • If the room is slightly too cold (small negative error), the heater is turned on to a low level.

Mathematical representation:

• Control output = Kp * Error
• Where:
  • Kp is the proportional gain (a constant)
  • Error is the difference between the setpoint and the process variable.

In essence, proportional action provides a basic corrective action based on the current error, but it often results in a steady-state error, meaning the process variable never quite reaches the setpoint.

Integral action is a control mode designed to eliminate the steady-state error in a control system.

What is steady-state error?

Steady-state error is the difference between the desired setpoint and the actual process value after the system has settled. A proportional controller alone often results in a steady-state error.

How integral action works:

• The integral term continuously accumulates the error over time.
• This accumulated error is then used to adjust the control output.
• As long as there is an error, the integral term will continue to grow, driving the control output to correct the error.

Benefits of integral action:

• Eliminates steady-state error
• Improves system performance by reducing the time it takes to reach the setpoint

In summary, integral action acts as a “memory” of the past errors, allowing the controller to take corrective actions to eliminate any persistent offset between the desired and actual values.

One of the primary negative effects of excessive integral action is overshoot and oscillation.

• Overshoot: The system’s output may overshoot the desired setpoint before settling down. This is because the integral term continues to accumulate error even after the process variable has started to approach the setpoint, causing the control output to become excessively large.
• Oscillation: In severe cases, excessive integral action can lead to sustained oscillations around the setpoint. This happens when the integral term overcompensates for the error, causing the system to overcorrect and then undercorrect repeatedly.

It’s important to note that while integral action is essential for eliminating steady-state error, it must be tuned carefully to avoid these negative effects.

Derivative action is a control mode that anticipates future errors by responding to the rate of change of the error between the setpoint and the process variable.  

1. Derivative (Rate) Control | Closed-loop Control Systems | Textbook

How it works:

• The controller calculates the rate of change of the error.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org
• A derivative gain is multiplied by this rate of change to produce a derivative output.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org
• This derivative output is added to the control signal.

Purpose:

• Improve stability: Derivative action helps to dampen oscillations and improve system stability.   1. [Solved] Derivative controller improves the stability by: – Testbook testbook.com
• Reduce overshoot: By predicting the future behavior of the system, derivative action can help to reduce overshoot.

Essentially, derivative action acts as a “predictor,” anticipating how the process variable will change and adjusting the control output accordingly.

Excessive derivative action can lead to instability and oscillation in a control system.  

1. Understanding Derivative in PID Control

Here’s why:

• Amplification of noise: Derivative action is sensitive to noise in the process variable. If the derivative gain is too high, it can amplify the effects of noise, leading to rapid changes in the control output.   1. The PID Controller & Theory Explained – NI – National Instruments www.ni.com2. Proportional Integral Derivative (PID) | Dynamics and Control – APMonitor apmonitor.com
• Overshoot and oscillation: By overreacting to process changes, excessive derivative action can cause the system to overshoot the setpoint and oscillate around it.   1. How Does Derivative Kick Affect PID Controller Performance? – IndMALL Automation www.indmall.in
• Reduced damping: Derivative action helps to damp oscillations, but excessive derivative action can actually reduce damping, making the system more prone to instability.

It’s important to remember that while derivative action can improve system performance, it should be tuned carefully to avoid these negative effects.