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L13: Nonlinearity + Saturation

Prerequisites: L12 | Effort: 60 min | Seborg: Chapter 16

Learning Objectives

  1. ✅ Handle nonlinear processes (pH, valve saturation)
  2. ✅ Implement gain scheduling
  3. ✅ Use clamp() and conditional logic
  4. ✅ Simulate valve saturation effects

Theory Recap: Nonlinearity (Seborg Ch. 16)

Common Nonlinearities: - pH control: Titration curve (steep near equivalence) - Valve saturation: 0-100% physical limits - Gain variation: Process gain changes with operating point

Solutions: 1. Gain scheduling: Switch controller gains based on PV 2. Adaptive control: Continuously adjust gains 3. Advanced control: MPC handles constraints natively

Odibi Hands-On

Example 1: Valve Saturation

# valve_saturation.yaml
# Large disturbance → valve hits 100%
# Integral windup demonstration

Working example: /examples/cheme_course/L13_nonlinearity/valve_saturation.yaml

Example 2: pH Nonlinearity

# ph_control.yaml
# Gain scheduling: Different Kp for pH 3-5 vs 5-9

Working example: /examples/cheme_course/L13_nonlinearity/ph_control.yaml

Summary

  • ✅ Saturation and nonlinearity are real-world facts
  • ✅ Gain scheduling helps
  • ✅ Always use output limits and anti-windup

Next: L14: MPC-lite