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L09: System Identification

Prerequisites: L00-L08 | Effort: 90 min | Seborg: Chapter 7

Learning Objectives

  1. ✅ Generate PRBS (Pseudo-Random Binary Sequence) excitation signals
  2. ✅ Collect input-output data for system identification
  3. ✅ Understand train/test data splits for model validation
  4. ✅ Export data for ARX/FOPTD model fitting in Python
  5. ✅ Validate identified models against test data

Theory Recap: System Identification (Seborg Ch. 7)

Goal: Determine process model (K, τ, θ) from input-output data

Steps: 1. Design experiment: Choose excitation signal (PRBS, steps, ramps) 2. Collect data: Run test, record input (u) and output (y) 3. Fit model: Estimate parameters using least squares, ARX, etc. 4. Validate: Test model on independent data set

PRBS (Pseudo-Random Binary Sequence): - Binary signal that switches between two levels - "Pseudo-random" pattern excites all frequencies - Better than single step (more information content) - Switchtime ≈ 0.5τ to 2τ (need rough τ estimate)

Odibi Hands-On

Example 1: Generate PRBS Input Data

# prbs_excitation.yaml
# Generates PRBS input + FOPTD response for system ID

Working example: /examples/cheme_course/L09_system_id/prbs_excitation.yaml

Example 2: Train/Test Split

Split data 70/30 for model fitting and validation.

Working example: /examples/cheme_course/L09_system_id/train_test_split.yaml

Example 3: Python Analysis Script

# fit_arx_model.py
# Loads Odibi-generated PRBS data
# Fits ARX model using scipy or control library
# Validates on test set

Working example: /examples/cheme_course/L09_system_id/fit_arx_model.py

Summary

  • ✅ PRBS excites process better than single step
  • ✅ Odibi generates identification data
  • ✅ Python fits models (ARX, FOPTD)
  • ✅ Always validate on test data

Next: L10: Interacting Loops