Anti-windup for PID control | Understanding PID Control, Part 2

Summary

This video expands on PID controllers, focusing on real-life issues like actuator saturation and integral windup. It explains how the integral component can accumulate errors over time, causing excessive actuator commands when the system saturates. The video uses an example of a drone held near the ground to show how this can result in overshooting when released. To prevent such issues, it introduces anti-windup techniques, like clamping, to limit the integrator's output and improve system performance. Future videos will discuss the derivative path and sensor limitations.

Takeaways

• 🔧 PID controllers combine proportional, integral, and derivative paths to control a system, with each branch serving a different purpose.
• 📈 The integral path in a PID controller helps eliminate steady-state error but can cause issues in practical scenarios, such as actuator saturation.
• ⚙️ Actuators, like motors and heaters, aren't perfect; they have limitations such as backlash, rate constraints, and saturation.
• 🚫 Actuator saturation occurs when the actuator cannot follow the commanded output, which can lead to problems like integral windup.
• ⏳ Integral windup happens when the integrator in the PID controller continues to increase output, even when the actuator has reached its maximum capacity.
• 🚁 In the drone example, if the propeller motors reach their maximum speed, the integral will keep increasing the speed command, even though the motors can’t go faster.
• 🔄 To fix integral windup, an anti-windup method like clamping can be used, which temporarily shuts off the integrator when saturation occurs.
• 📊 Clamping checks if the system is saturating and if the integrator is contributing to the problem, then shuts down the integrator when necessary.
• 🔧 The clamping threshold should be set conservatively below the physical limit of the actuator to avoid future performance issues.
• 🔍 Anti-windup methods, like clamping, improve the performance of PID controllers, especially in real-world systems with nonlinear behaviors like actuator saturation.

Q & A

What is a PID controller and what are its three branches?

A PID controller is a control loop feedback mechanism widely used in industrial control systems. It has three branches: proportional, integral, and derivative. The proportional branch responds to the current error, the integral branch accumulates the error over time to eliminate steady-state errors, and the derivative branch anticipates future error based on the rate of change of the error.

Why can the integral path in a PID controller cause problems?

The integral path in a PID controller can cause problems because it can lead to 'integral windup' when the actuator saturates. This happens when the integrator continues to increase the command even after the actuator has reached its maximum capacity, leading to a large overshoot when the error changes sign.

What is an actuator in the context of a control system?

An actuator in a control system is a device that generates force or energy to change the system's state. Examples include motors, heaters, and other devices that can apply a physical action in response to a control signal.

What is meant by 'saturation' in actuators?

Saturation in actuators refers to the point at which the actuator can no longer respond to an increase in command signal because it has reached its maximum or minimum operating limit. For example, a motor can only spin at a certain maximum RPM, regardless of how high the command signal is.

How does saturation affect the performance of a PID controller?

Saturation affects the performance of a PID controller by limiting the actuator's response to the control signal. This can cause the controller to overestimate the required control action, leading to overshoot or oscillations when the saturation is released.

What is integral windup and why is it problematic?

Integral windup occurs when the integral term in a PID controller continues to increase (or decrease) the control signal even after the actuator has reached its saturation limit. This can cause a large overshoot or undershoot when the error changes sign and the actuator can finally respond to the control signal again.

How can clamping be used as an anti-windup method?

Clamping can be used as an anti-windup method by limiting the output of the integral term to a specified maximum or minimum value. This prevents the integral term from increasing past the actuator's saturation point, ensuring that the control signal can respond quickly when the error changes sign.

Why is it important to set the saturation limit conservatively in an anti-windup algorithm?

It is important to set the saturation limit conservatively in an anti-windup algorithm to account for variations in the actuator's performance over time or due to environmental factors. Setting the limit too close to the physical limit can lead to windup if the actuator's capacity decreases.

What is conditional integration in the context of PID controllers?

Conditional integration refers to the practice of temporarily disabling the integral term in a PID controller when certain conditions are met, such as when the actuator is saturating and the error is of the same sign as the controller output. This helps to prevent integral windup.

How does the clamping method determine whether to clamp the integral term?

The clamping method determines whether to clamp the integral term by checking if the output of the PID controller is saturating and if the error is of the same sign as the controller output. If both conditions are met, the integral term is clamped to prevent further windup.

What are some other anti-windup methods besides clamping?

Other anti-windup methods besides clamping include rate limiting, where the rate of change of the integral term is limited; and state augmentation, where an additional state variable is introduced to represent the effect of the integrator on the system.