PID Contorl
(photo)
- Combining the Proportional, Integral, and Derivative components, PID control reduces the system's error to make the output reach the set point and maintain that sate effectively.
- u(t) = {Kp x e(t)} + {Ki x Ie®dr} + {Kd x de(t)/dt}
- u(t): control signal
- e(t) = Set point - process variable
- Kp: Proportional gain, Ki: Integral gain, Kd: Derivative gain
(i) Proportional
(photo): Waveform comparison: (Small Kp) vs (Large Kp)
- The error is corrected in proportion to its current magnitude.
- P control output = Kp x Error
- If Kp is too large, overshoot and oscillation may occur.
(ii) Integral
- Waveform comparison: (Kp + Kd) vs (Kp + Kd + Ki)
- The error is corrected by considering the accumulated error over time.
- It helps eliminate small, long-standing errors, known as steady-state error.
- I control output = Ki x I(Error)dt
- If Ki is too large, the system may respond slowly or become unstable.
(iii) Derivative
- Waveform comparison: (Kp only) vs (Kp + Kd)
- The derivative term predicts future error by analyzing the rate of change of the error and suppresses excessive responses.
- D control output = Kd x d(Error)/dt
- It reduces oscillation and helps stabilize the system smoothly.