Controller tuning criteria – selecting the most effective error-integral In process control (PID/PI tuning), which performance index (error integral) is generally regarded as the best overall criterion for practical controller settings under typical setpoint and load changes?

Introduction / Context:
Controller tuning often relies on minimising an error-integral performance index. Common choices include IAE, ISE, ITSE, and ITAE. Each criterion weights error differently over time and therefore produces distinct compromises among rise time, overshoot, settling time, and robustness. The question asks which of these indices is generally considered the best all-around criterion for tuning practical process loops.

Given Data / Assumptions:

• We compare standard error-integral indices used for tuning.
• Processes are typical first/second-order with or without small dead time.
• Goal is balanced performance: low overshoot, shorter settling, good disturbance rejection.

Concept / Approach:
Definitions (for error e(t)): IAE = ∫|e| dt; ISE = ∫e^2 dt; ITSE = ∫t e^2 dt; ITAE = ∫t |e| dt. ISE penalises large errors heavily but tends to produce higher overshoot. IAE often yields slower responses with less aggressive peaks but may not prioritise late-time tails. Time-weighted criteria (ITSE, ITAE) penalise late error more strongly, encouraging designs that settle faster with reduced lingering deviations. Among these, ITAE is widely adopted for practical tuning because it consistently gives fast settling with modest overshoot across many process classes and dead-time ratios.

Step-by-Step Solution:

Verification / Alternative check:
Classical tuning tables (e.g., ITAE-optimal settings) are published for many canonical processes (FOPDT/second-order), reflecting its popularity and balanced transient quality. Simulated step responses tuned by ITAE typically show shorter settling than IAE and less overshoot than ISE for comparable robustness.

Why Other Options Are Wrong:

• IAE: Simple and robust but can allow long error tails.
• ISE: Reduces large errors but often produces excessive overshoot.
• ITSE: Time-weighted squared error can still bias toward oscillatory behaviour relative to ITAE.
• None of these: Incorrect; ITAE is a well-known preferred choice.

Common Pitfalls:
Assuming a single criterion is universally best for every plant; ITAE is a strong default, but special constraints (actuator limits, noise) may shift preferences.

Final Answer:
Integral of time-weighted absolute error (ITAE)