Control-system design objective: If the closed-loop response must be free from steady-state offset (zero steady-state error) and also free from sustained oscillations, which controller structure is most suitable?

Introduction / Context:
In practical process control, two frequent performance goals are (1) elimination of steady-state offset and (2) avoiding oscillatory or underdamped behavior. Offset commonly appears with proportional control, while oscillations arise from insufficient damping or excessive loop gain. Selecting the appropriate controller architecture helps achieve both goals together.

Given Data / Assumptions:

• Closed-loop control of a typical first- or second-order process with no pure integrator unless noted.
• We seek zero steady-state error to a step in set point or load, as appropriate.
• We also want a non-oscillatory, well-damped transient.
• Controller options considered: P, PD, PI, and PID.

Concept / Approach:
Integral action is required to drive the steady-state error to zero for a step input. Derivative action provides phase lead that counters phase lag from the process and sensor, improving damping and reducing overshoot and oscillations. Combining proportional, integral, and derivative terms (PID) therefore addresses both offset (via I) and oscillations (via D), when properly tuned.

Step-by-Step Solution:

Verification / Alternative check:
Standard tuning correlations (e.g., Ziegler–Nichols modified, Cohen–Coon, IMC tuning) show that adding I eliminates offset and adding D improves phase margin and damping. With conservative tuning, the closed-loop response becomes well-damped without sustained oscillations.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming any PID will be non-oscillatory; poor tuning can still cause ringing. Also, integral windup must be mitigated with anti-windup strategies, especially under saturation.

Final Answer:
Proportional–integral–derivative (PID) controller