Classical control design criteria: Typical minimum recommended stability margins in process control are specified as what combination of gain margin and phase margin?

Introduction / Context:
Gain and phase margins are widely used robustness measures for single-loop feedback systems. In process plants, conservative margins are preferred to tolerate modeling errors, actuator nonlinearities, and unmeasured disturbances. Knowing common rule-of-thumb values helps engineers judge whether a design is acceptably robust before commissioning.

Given Data / Assumptions:

• Single-input single-output negative feedback loop.
• Margins extracted from Bode or Nyquist plots.
• Industry-typical targets: generous phase and gain margins to allow safe operation.

Concept / Approach:

Gain margin is how much loop gain can increase before reaching instability; phase margin is how much additional phase lag at the gain-crossover frequency can be tolerated. Larger positive margins indicate more robustness. Common practice adopts gain margin > 1.7 (approximately > 5 dB) and phase margin > 30 degrees as the minimum acceptable; higher values (e.g., 60 degrees) are often targeted for comfort.

Step-by-Step Solution:

Verification / Alternative check:

Many tuning guidelines (IMC/λ tuning, conservative Z-N modifications) result in open-loop shapes that meet or exceed these minimum margins. Plant acceptance tests routinely check margins via frequency response identification.

Why Other Options Are Wrong:

< 1.7 compromises gain robustness; < 30° phase margin risks oscillation and poor damping; mixed cases still fail one of the conventional minimum thresholds.

Common Pitfalls:

Confusing gain margin ratio with decibels; assuming margins guarantee performance (they only indicate stability robustness); ignoring nonlinearity and time delay not captured in simple models.

Final Answer:

> 1.7 and > 30°