Introduction to PID Control
Proportional-Integral-Derivative (PID) controllers are feedback mechanisms widely used in control systems to regulate processes like speed and steering in vehicles. In self-driving cars, PID controllers help maintain desired trajectories by minimizing errors between the actual and target states.
A PID controller computes an error value as the difference between a measured process variable and a desired setpoint. The control output is a sum of three terms:
- Proportional (P): Responds to the current error, $u_p(t) = K_p e(t)$, where $K_p$ is the proportional gain and $e(t)$ is the error.
- Integral (I): Accounts for past errors to eliminate steady-state offset, $u_i(t) = K_i \int_0^t e(\tau) \, d\tau$.
- Derivative (D): Predicts future errors based on the rate of change, $u_d(t) = K_d \frac{de(t)}{dt}$.
The total control signal is $u(t) = u_p(t) + u_i(t) + u_d(t)$.
PID tuning involves adjusting $K_p$, $K_i$, and $K_d$ to achieve stability and performance, often using methods like Ziegler-Nichols.
This builds on trajectory optimization by providing real-time corrective actions to follow optimized paths.