Step 1: Understanding the Concept:
A PID controller is the most common control algorithm used in industrial process control. It continuously calculates an "error" value as the difference between a desired setpoint and a measured process variable.
Step 2: Key Formula or Approach:
The controller output $u(t)$ is:
\[ u(t) = K_p e(t) + K_i \int e(t)dt + K_d \frac{de(t)}{dt} \]
Step 3: Detailed Explanation:
Each term serves a specific purpose:
Proportional (P): Corrects the error based on its current size.
Integral (I): Eliminates the "steady-state offset" by looking at the history of the error.
Derivative (D): Predicts future error by looking at the rate of change, which helps dampen oscillations.
Step 4: Final Answer:
A PID controller combines Proportional, Integral, and Derivative actions.