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22-Elec-A2 Systems and Control: December 2015

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

  1. Question 1 State space vs. transfer function, controllability/observability, steady-state error (compulsory)
  2. Question 2 Stabilising an unstable plant with PID: Bode, root locus, Routh–Hurwitz (compulsory)
  3. Question 3 Root-locus analysis and gain selection for a RHP-pole plant
  4. Question 4 Second-order dominant model, system type, transient specs, effect of a zero
  5. Question 5 Two-port RLC network: transfer function and step response
  6. Question 6 Nyquist and Routh–Hurwitz stability for a RHP-pole plant
  7. Question 7 Lead-controller design in the frequency domain
  8. Question 8 Canonical forms, signal-flow graph, and transfer function by inspection

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, December 2015, 3 hours, closed book (approved Casio/Sharp calculator plus one signed, double-sided 8.5 × 11" formula/notes sheet; a Laplace-transform table and the standard ζ–overshoot / ζ–resonant-peak design plots are supplied). Questions 1 and 2 are compulsory; a complete paper is five questions, so candidates choose three of 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) — time response and second-order specifications (Ch. 4), block/signal-flow reduction and Mason’s rule (Ch. 5), Routh–Hurwitz stability (Ch. 6), steady-state error and static error constants (Ch. 7), root locus (Ch. 8), PID / lead–lag design (Ch. 9–11), frequency response, Bode, Nyquist, gain and phase margins (Ch. 10–11), state space, controllability/observability and canonical forms (Ch. 3, 12); K. Ogata, Modern Control Engineering (5th ed., Prentice Hall) — dominant-poles modelling and Mason’s gain formula; G. F. Franklin, J. D. Powell & A. Emami-Naeini, Feedback Control of Dynamic Systems. All block diagrams, pole–zero maps, root loci, the Nyquist plot, the network schematic and the signal-flow graph below are redrawn as inline figures.

Reading the exam figures. Every transfer function in this paper is stated exactly, so every boxed result is confirmed analytically and the exact model governs. Q2 supplies a Bode plot ($G_m=32.2$ dB at $3.9$ rad/s, $P_m=-145^\circ$ at $0.324$ rad/s) and a root locus, and Q7 supplies the uncompensated Bode plot; values read from those curves are flagged as reads and cross-checked against the Routh/analytic results.