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20-Bio-A2 Process Dynamics and Control: Undated paper

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  1. Question 1 Overshoot Condition for a Lead-Zero Second-Order Process
  2. Question 2 Nyquist Stability of a Proportionally-Controlled Open-Loop-Unstable Process
  3. Question 3 Linear vs. Nonlinear-Valve Draining-Tank Dynamics
  4. Question 4 Transfer Function and Step Response from a State-Space Model
  5. Question 5 Routh Stability and Step Response of a PI-Controlled Unstable Process
  6. Question 6 Inverse Laplace Transforms with Time Delay
  7. Question 7 Internal Model Control Design for a Dead-Time-Dominant Process
  8. Question 8 Bode Plot and Gain-Margin Design for a Dead-Time-Plus-Lag Process

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National Exams / EGBC — May 2019 — 04-Bio-A2 Process Dynamics and Control (the paper's own header line alternates between the codes "04-BIO-A2" and "04-BIO-A3" across pages; the subject line and content are unambiguously Process Dynamics and Control, so 04-Bio-A2 is used throughout). 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 the effect of a real zero on step-response overshoot, the Nyquist criterion for an open-loop-unstable process, a two-tank linear-vs-nonlinear-valve comparison, state-space-to-transfer-function conversion, Routh–Hurwitz stability with PI control of an unstable process, inverse Laplace transforms with time delay, Internal Model Control (IMC) design for a dead-time process, and Bode/gain-margin design.

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, and Internal Model Control design; G. Stephanopoulos, Chemical Process Control: An Introduction to Theory and Practice (Prentice Hall) — the Nyquist criterion for open-loop-unstable processes and dead-time systems. Standard control conventions (deviation variables; unity valve/sensor gain unless stated) are used throughout.