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20-Bio-A2 Process Dynamics and Control: May 2018

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  1. Question 1 Bode Plot and Exact Phase Margin of a Lightly-Damped Second-Order System
  2. Question 2 Closed-Loop Stability With a Non-Minimum-Phase Level Sensor
  3. Question 3 Phase Margin, Gain Margin and Maximum Stable Gain for a Dead-Time Process
  4. Question 4 Step Response and Overshoot Condition for a Process With an Adjustable Zero
  5. Question 5 Linearization of a Radiative Calrod Heating Element
  6. Question 6 Internal Model Control of a Dead-Time-Dominant Process
  7. Question 7 Stability and Step Response of a PI-Controlled First-Order Process
  8. Question 8 Linearization of a Nonlinear (Second-Order-Reaction) CSTR

Start with Question 1 →

National Exams / EGBC — May 2018 — 04-Bio-A2 Process Dynamics and Control. Three-hour open-book examination; any non-communicating calculator is permitted. The cover page states that only the first five questions in the answer book are marked, yet all eight problems are printed on the paper — all eight are solved below for completeness, since the full set is a study resource. Content spans second-order Bode/phase-margin analysis, feedback stability with a non-minimum-phase sensor, dead-time Nyquist/gain-margin design, zero-location effects on step response, nonlinear radiative-heat-transfer linearization, Internal Model Control (IMC) of a dead-time process, PI-controller stability/response, and nonlinear-CSTR linearization. Note: Problem 2's printed sub-part weights (10%+20%=30%) exceed its stated 20% problem total — both sub-parts are fully answered below.

Reference texts: D. E. Seborg, T. F. Edgar, D. A. Mellichamp & F. J. Doyle III, Process Dynamics and Control (4th ed., Wiley) — Laplace-domain modelling, transfer functions, Routh stability, Nyquist/Bode frequency response, linearization and IMC design; G. Stephanopoulos, Chemical Process Control: An Introduction to Theory and Practice (Prentice Hall) — Nyquist criterion and dead-time systems. Standard control conventions (deviation variables; unity valve gain unless stated) are used throughout.