In classical control, what capabilities does a proportional–integral (PI) controller typically add to a feedback loop, particularly for steady-state error and lag compensation?

Introduction / Context:
The proportional–integral (PI) controller is ubiquitous in industrial control because it is simple yet effective. By combining proportional action with integral action, PI controllers reduce steady-state error and help compensate for lag-type dynamics in many plants, improving tracking and disturbance rejection without the derivative noise amplification of full PID.

Given Data / Assumptions:

• We consider typical linear time-invariant plants with lag behaviour.
• We focus on qualitative capabilities rather than exact tuning formulas.
• “System type” refers to the number of pure integrators in the open-loop transfer path.

Concept / Approach:
Integral action adds a pole at the origin, effectively increasing system type and driving steady-state error for steps (and sometimes ramps) toward zero, depending on type. Proportional action supplies immediate corrective effort. Together, PI can compensate lag, though tuning must balance performance and stability. The claim that a PI loop has “no transient response” is false; all real systems exhibit transients.

Step-by-Step Solution:

Verification / Alternative check:
Standard control texts show type increase with integral action and present PI tuning methods (Ziegler–Nichols variants) for lag-dominant plants.

Why Other Options Are Wrong:

Common Pitfalls:
Over-integral action leading to oscillations or windup; failing to include anti-windup safeguards.

Final Answer:
Both (b) and (c).