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Short note: Characteristics of PI and PD control

Short answer

PI control adds a pole at the origin, increasing system type; it eliminates steady-state error for step inputs but slows response and may cause overshoot, behaving like a lag compensator. PD control adds a zero providing phase lead; it increases damping, reduces rise time and overshoot, improves bandwidth, and acts like a lead compensator, but does not remove steady-state error and amplifies noise.

Write a short note on characteristics of PI and PD control actions.

PI control action

Gc(s)=Kp+KisG_c(s) = K_p + \dfrac{K_i}{s}; output depends on the present error and the accumulated (integrated) error.

  • Adds a pole at the origin, so the system type increases by one.
  • Removes steady-state error to a step for a type-0 plant (no offset).
  • Makes the response slower, with more overshoot; relative stability falls.
  • Reduces bandwidth, so it filters noise. Behaves like a lag compensator.

PD control action

Gc(s)=Kp+KdsG_c(s) = K_p + K_d s; output depends on the present error and its rate of change.

  • Adds a zero, giving phase lead; acts in anticipation of the error.
  • Increases damping, so overshoot, rise time and settling time decrease.
  • Improves stability and increases bandwidth.
  • Does not change the system type, so steady-state error is not removed.
  • Amplifies high-frequency noise. Behaves like a lead compensator.

✓ Answer checked by Claude Opus 5.5 (high effort)

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