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22-Elec-B2 Advanced Control Systems: May 2018

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

  1. Question 1 Nineteen short-answer items on error constants, stability, the root locus and frequency response
  2. Question 2 Angle of departure, break-in point, asymptotes and the imaginary-axis crossing
  3. Question 3 Cascade-compensator design for a double-integrator plant
  4. Question 4 Asymptotic Bode construction and the stability margins of $K/[s(s+1)(s+5)]$
  5. Question 5 Root-locus design on an open-loop unstable, non-minimum-phase plant

Start with Question 1 →

Paper format. 16-Elec-B2 Advanced Control Systems, May 2018 — open book, three hours, five questions, 17 pages. The cover page states that “any four questions constitute a complete paper” and that “all questions are of equal value (25%)”, so each question below carries 25 marks and a candidate answers four. Tables of Laplace and z-transforms are appended to the paper. All five questions are worked here, because this set is a study resource rather than a three-hour sitting. Question 1 is a nineteen-item short-answer block whose per-item mark weights are printed in the margin as [1] or [2] and total 25. Tables of inverse Laplace transforms and of Laplace and z-transforms are printed on pages 16 and 17, and pages 11 to 14 are blank Bode-plot templates supplied for the Question 4 sketches.

Reference texts. N. S. Nise, Control Systems Engineering, 8th ed. (Ch. 7 steady-state error and system type, Ch. 8 root-locus sketching rules, Ch. 9 root-locus design of cascade compensators, Ch. 10 frequency response and stability margins); R. C. Dorf and R. H. Bishop, Modern Control Systems, 13th ed. (Ch. 5, 7, 8); K. Ogata, Modern Control Engineering, 5th ed. (Ch. 5 transient response, Ch. 6 root-locus design, Ch. 7 frequency-response design); G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 8th ed. (Ch. 3, 5, 6). These are the references listed for exam code 07-Elec-B2 / 16-Elec-B2 in the Engineers Canada syllabus; the vocabulary of this particular paper (percent overshoot, settling time, “compensated system gain”, asymptote intercept) follows Nise closely.