9.2. PID Control Strategy

PID Control is the most widely used control strategy in engineering applications. It uses three basic actions—proportional, integral, and derivative—to adjust the system output:

PID Control, which stands for Proportional-Integral-Derivative Control, is a fundamental controller in engineering that helps manage the output of systems. Its purpose is to achieve a desired performance by adjusting the system output based on three actions: proportional, integral, and derivative. Each component plays a specific role in guiding the output toward the target.

Think of a PID controller like a thermostat in your home. The thermostat continuously measures the room temperature (the current state) and compares it to the desired temperature (the setpoint). If the room is too cold, the proportional action increases heating. If it has been too cold for a while, the integral action helps ensure warmth does not lag, and the derivative action prepares for any temperature changes ahead by adjusting the heating rate.

● Proportional: Reacts to the current error.

The proportional action is responsible for reacting based on the present error, which is the difference between the desired setpoint and the current output of the system. If the error is large, the controller generates a large output to correct the current state. Conversely, if the error is small, the output is minor.

Imagine driving a car. If you’re steering significantly off course (a big error), you’ll turn the steering wheel a lot to correct your path (large output). If you’re almost on track (small error), a gentle touch on the wheel will suffice.

● Integral: Eliminates steady-state error by considering past errors.

The integral action addresses any accumulated errors over time. If the system consistently remains off the desired setpoint, the integral term increases the controller output to eliminate this persistent error known as steady-state error, ensuring that the system ultimately stabilizes at the desired value.

Consider a student who consistently scores below their target on exams. The integral action is like realizing that their study habits need adjustment based on all past performances. They might decide to study more hours to gradually achieve their score goal, eliminating their steady underperformance.

● Derivative: Predicts future error based on the rate of change.

The derivative action helps to anticipate future errors by measuring the rate at which the current error is changing. If the error is increasing rapidly, the controller can react more aggressively to prevent overshooting the setpoint by adjusting the output promptly.

This action is akin to a driver using a rearview mirror to observe how quickly they are approaching the stop sign. If they see they are approaching too quickly, they will begin to slow down sooner rather than later, preventing a sudden stop that could cause discomfort or danger.

Applications:

1. Temperature Control: PID controllers are used in systems such as furnaces, ovens, and air-conditioning systems to maintain a set temperature.
2. Motor Speed Control: In DC motors, PID controllers regulate the speed by adjusting the voltage applied to the motor based on speed deviations.
3. Robotics: PID control is widely used to maintain position and orientation in robotic arms and drones.

PID control is versatile and utilized in various applications across different fields. In temperature control systems like furnaces and air conditioners, PID helps maintain a consistent temperature. In motor systems, it ensures that the speed of the motor remains steady, and in robotics, it helps control movements, positions, and orientations accurately.

Think of a PID controller in an air-conditioning system like a chef cooking a dish. The chef continuously tastes the food (the process) and adjusts the seasonings (outputs) based on the taste (feedback) until the dish reaches perfection (the setpoint). For a motor, it’s similar to a bicycle rider adjusting their pedaling speed based on how fast they want to go when riding uphill or downhill.

In a furnace heating system, the temperature needs to be maintained at a set value. A PID controller can adjust the heating power to ensure that the temperature follows the desired trajectory, minimizing both steady-state error and overshoot.

In this example, the PID controller regulates a furnace's temperature. If the temperature falls below the set value, the proportional component adjusts the heating power. If this low temperature has been an issue for a while, the integral component boosts the heating further to address the ongoing error. Lastly, the derivative component helps control heating intensity to avoid overshooting the desired temperature.

Picture the furnace like a kettle on the stove. When you want hot water, you turn the burner on (proportional), but if you often run the kettle too cool, you might let it boil longer to ensure it’s always hot enough (integral). You also keep an eye on it to avoid letting it boil over (derivative), adjusting the flame as needed based on how it heats up.

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