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Control evaluation steps; PD and PI design

Short answer

Apply step input, record output, compute rise time, overshoot, settling time, steady-state error; check disturbance and stability. PD: u=Kp·e+Kd·de/dt; Kp sets speed, Kd adds damping, reduces overshoot, amplifies noise. PI: u=Kp·e+Ki·∫e dt; Kp for response, Ki eliminates steady-state error, too large Ki causes oscillation; use anti-windup.

What are the evaluation steps used in general control systems input? Explain controller design using PD and PI controller.

Evaluation steps

To evaluate a control system, the response to a standard input (usually a step) is examined:

  1. Apply the reference (step) input and record the output over time.
  2. Compute the metrics: rise time, overshoot, settling time and steady-state error.
  3. Apply a disturbance and check the disturbance rejection.
  4. Check stability (no unbounded output, damping) and robustness to parameter change.
  5. Compare with the specifications and re-tune the controller if not met.

PD controller design

Control law: u = Kp·e + Kd·de/dt.

  • Kp sets the speed of response; Kd adds damping from the error's rate of change, reducing overshoot and improving stability.
  • Procedure: choose Kp for the required rise time, then increase Kd until the overshoot is acceptable.
  • Result: faster and well damped, but the steady-state offset of the plant remains, and noise is amplified.

PI controller design

Control law: u = Kp·e + Ki·∫e dt.

  • Kp gives the main response; the integral accumulates the error and drives the steady-state error to zero.
  • Procedure: choose Kp first, then increase Ki gradually; too large a Ki gives overshoot and oscillation.
  • Result: zero steady-state error (a constant disturbance is rejected), at the cost of slower response; limit the integral for anti-wind-up.
 PD:  e --> [Kp + Kd s] --> u
 PI:  e --> [Kp + Ki/s] --> u

✓ Answer checked by Claude Opus 5.5 (high effort)

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