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22-Mec-A3 System Analysis and Control: May 2014

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Bode plot, gain margin and phase margin
  2. Question 2 Routh–Hurwitz ranges of a parameter
  3. Question 3 Root locus for positive and negative gain
  4. Question 4 Transient-response terms under proportional control
  5. Question 5 Steady-state errors for step and ramp inputs
  6. Question 6 Sinusoidal steady-state response of a first-order system

Start with Question 1 →

Paper format. National Exams, May 2014 — 07-Mec-A3 System Analysis and Control. Closed book, 3 hours; a Casio or Sharp approved calculator and semi-log graph paper are the only aids. Six questions are printed; any four constitute a complete paper and all questions are of equal value (25 marks each). All six questions are solved in full. A Laplace-transform table is appended to the exam (pages 5–6) and two sheets of blank four-cycle semi-log paper are provided for the Bode work.

Reference texts. K. Ogata, Modern Control Engineering, 5th ed. (Pearson) — Chapters 5–7; N. S. Nise, Control Systems Engineering, 8th ed. (Wiley) — Chapters 6–10; R. C. Dorf and R. H. Bishop, Modern Control Systems, 13th ed. (Pearson); G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 8th ed. (Pearson). These are the standard Canadian undergraduate control texts and cover every technique used below (Routh–Hurwitz, root locus, Bode margins, static error constants, frequency response).

Notation. Throughout, K denotes the root-locus (pole–zero form) gain that multiplies the open-loop transfer function as printed, and ω is in rad/s. Magnitudes in decibels are 20 log10 of the magnitude ratio.