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22-Elec-A2 Systems and Control: May 2015

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

  1. Question 1 Proportional + rate-feedback design: transfer function, error and overshoot (compulsory)
  2. Question 2 Root-locus analysis and gain selection (compulsory)
  3. Question 3 Top-down controller design by pole matching
  4. Question 4 Stability range from Bode, root locus and Routh–Hurwitz
  5. Question 5 Second-order dominant model three ways, and step estimates
  6. Question 6 Lag-controller design in the frequency domain
  7. Question 7 State space: controllability, pole placement, closed-loop transfer function
  8. Question 8 Signal-flow state model (Mason) and Nyquist stability

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, May 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 design plots are supplied with the paper). 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 pole placement (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, Bode plots, signal-flow graphs and the Nyquist plot below are redrawn as inline figures.

Reading the exam figures. Where a transfer function is stated exactly (Q1–Q5, Q7, Q8A) every result is confirmed analytically and the exact model governs. Q4 supplies a Bode plot ($G_m=16.1$ dB at $2.05$ rad/s, $P_m=-85.1^\circ$ at $0.589$ rad/s) and a root locus; Q5 Parts A–B and Q6 use printed frequency-response plots, and Q8B a printed Nyquist diagram — values read from those curves are flagged as reads and cross-checked against the analytics wherever a transfer function is available.