NivaarExam PrepOfficial exam papers ↗

22-Elec-A2 Systems and Control: December 2013

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

  1. Question 1 Stability by Bode plot and Routh–Hurwitz (compulsory)
  2. Question 2 Root-locus analysis of an unstable plant (compulsory)
  3. Question 3 PI-controller design from a dominant-poles model
  4. Question 4 PD vs. proportional-plus-rate-feedback control
  5. Question 5 Proportional vs. lead control; margins and dominant model
  6. Question 6 Additional poles/zeros and step-response specifications
  7. Question 7 State space, canonical forms, eigenvalues and stability

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, December 2013, 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 five (Q3–Q7). Each question is worth 20 marks. All seven are worked below so the set is complete.

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

Reading the exam figures. Two questions supply printed plots: Q1 gives an open-loop Bode plot (used for the gain-margin reading) and Q6 Part B gives a measured step-response curve (used to read $K_{dc},\zeta,\omega_n$). The transfer functions are given exactly in the question text, so every reading below is also confirmed analytically (Bode by direct evaluation, stability by Routh–Hurwitz). Where the printed plot annotation and the exact model differ slightly, the exact model governs.