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22-Elec-A2 Systems and Control: December 2014

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

  1. Question 1 Frequency-response & Routh stability of a proportional loop (compulsory)
  2. Question 2 Root-locus design of a PD controller (compulsory)
  3. Question 3 Second-order dominant-pole models three ways
  4. Question 4 PID design by pole placement with rate feedback
  5. Question 5 Robot-joint servo: Mason reduction & step response
  6. Question 6 Lead/lag controller design in the frequency domain
  7. Question 7 State-space model, controllability & pole placement
  8. Question 8 Mason’s gain formula & second-order derivations

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, December 2014, 3 hours, closed book (approved Casio/Sharp calculator plus one signed, double-sided 8.5 × 11" formula sheet). 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 specs (Ch. 4), Routh–Hurwitz stability (Ch. 6), steady-state error and error constants (Ch. 7), root locus (Ch. 8), PID and 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 rule; G. F. Franklin, J. D. Powell & A. Emami-Naeini, Feedback Control of Dynamic Systems. All block diagrams, pole–zero maps, root loci, Bode plots and signal-flow graphs below are redrawn as inline figures.

Reading the exam figures. Q1 supplies open- and closed-loop Bode plots and Q6 supplies uncompensated/compensated open-loop Bode plots. Where a transfer function is stated exactly in the text, every graphical reading is also confirmed analytically and the exact model governs; where only a plot is given (Q6), the values are read from the printed curves and flagged as such.