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22-Elec-A2 Systems and Control: May 2014

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

  1. Question 1 Nyquist stability of a proportional loop (compulsory)
  2. Question 2 Routh–Hurwitz and root locus of the same plant (compulsory)
  3. Question 3 Second-order RLC two-port: transfer function & step specs
  4. Question 4 PID with rate feedback by pole–zero cancellation
  5. Question 5 Signal-flow graph / Mason and proportional-control error
  6. Question 6 Lag compensator from Bode plots
  7. Question 7 State-space model, controllability/observability, pole placement
  8. Question 8 Analytical step response and derivation of the 2nd-order specs

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, May 2014, 3 hours, closed book (approved calculator plus one signed 8.5 × 11" formula sheet). Questions 1 and 2 are compulsory; answer three of the remaining six (Q3–Q8). Each question is worth 20 marks. All eight are worked below so the set is a complete study resource.

Reference texts: N. S. Nise, Control Systems Engineering (7th ed., Wiley) — Routh–Hurwitz and stability (Ch. 6), steady-state error and error constants (Ch. 7), root locus (Ch. 8), PID and lag/lead design (Ch. 9–11), frequency response, Nyquist and gain/phase margins (Ch. 10–11), state space, controllability/observability and pole placement (Ch. 3, 12); K. Ogata, Modern Control Engineering (5th ed., Prentice Hall) — companion treatment of dominant-poles modelling and Mason’s rule; G. F. Franklin, J. D. Powell & A. Emami-Naeini, Feedback Control of Dynamic Systems. All block diagrams, pole–zero maps, root loci, Bode/Nyquist plots and signal-flow graphs below are redrawn as inline figures.

Reading the exam figures. Q1 supplies an open-loop Bode plot and Q6 supplies open-loop Bode plots of the process. Where a transfer function is given exactly in the text (Q1’s system is the same plant as Q2, stated exactly there), every graphical reading is also confirmed analytically and the exact model governs. Q6 is a pure graph-reading problem (no closed form given); its numeric reads are approximate and are flagged accordingly. Note the printed exam mislabels the header of the last two pages “May 2013” — this is the May 2014 sitting throughout.