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PID Controller

A PID controller helps a mechanism reach and hold a target. For example, it can turn a robot to a certain angle, move an elevator to a certain height, or spin a shooter at a certain speed.

The controller repeatedly compares the target, called the setpoint, with the current sensor measurement:

error = setpoint - measurement

It uses that error to calculate how much output to send to the motor. PID stands for the three parts of the calculation:

  • P — Proportional: Reacts to the current error. A larger error creates a stronger response.
  • I — Integral: Adds up error over time. It can correct a small error that does not go away.
  • D — Derivative: Reacts to how quickly the error is changing. It can reduce overshoot and bouncing.

Try the Simulator​

Move one slider at a time so you can see what each gain changes:

  1. Set I and D to zero, then slowly increase P. The response becomes faster, but too much P makes it bounce around the target.
  2. Add D until the bouncing settles down. D acts like a brake as the mechanism approaches the target.
  3. Add a small amount of I if the mechanism stops near the target but does not quite reach it.

The simulator represents a generic motor-driven mechanism. Its values are meant to build intuition and should not be copied directly to a real robot.

02550750s3s6s9s12s15sSet pointResponseSet point
Reading the graph

The dashed line is the desired setpoint. The red line shows the simulated mechanism's response. A good response reaches the setpoint quickly without moving far past it or repeatedly bouncing around it.

What a perfect PID curve looks like
02550750s3s6s9s12s15sSet pointResponseSet point

Simple Example​

Suppose an elevator needs to move to 1.0 metre, but its sensor reads 0.7 metres:

error = 1.0 - 0.7
error = 0.3 metres

The PID controller uses this error to move the elevator upward. As the elevator gets closer to the setpoint, the error becomes smaller, so the controller reduces the motor output.

Tuning PID​

The values that control the strength of P, I, and D are called gains. Tuning means adjusting these gains until the mechanism responds well.

A common starting process is:

  1. Set I and D to zero.
  2. Slowly increase P until the mechanism responds quickly but does not shake.
  3. Add a small amount of D if the mechanism overshoots or bounces around the target.
  4. Add I only if a small, steady error remains.
warning

Test PID values carefully. Start with low gains, keep the mechanism away from people, and be ready to disable the robot if it moves unexpectedly.

PID values are different for every mechanism. Values that work for one robot should not be copied directly to another.