01
PID Equation
u(t) = K_p e(t) + K_i ∫e(t)dt + K_d de(t)/dt
The proportional term responds to present error, the integral term accumulates historical error, and the derivative term responds to the rate of change.
02
Practical Problems
- Integral windup can occur when actuators saturate while the integral term continues accumulating.
- Derivative action can amplify measurement noise.
- Sampling and computational delay affect digital implementations.
- Actuator limits constrain achievable control performance.
- Poor tuning can cause sluggishness, oscillation, or excessive control effort.
03
Advanced PID Architectures
- Cascade control uses nested loops.
- Feedforward compensates for measurable disturbances.
- Gain scheduling changes parameters according to operating conditions.
- Anti-windup prevents excessive integral accumulation.
- Derivative filtering reduces sensitivity to high-frequency measurement noise.