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22-Mec-A3 System Analysis and Control: December 2017

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

  1. Question 1 Impulse and Step Response; Free Response of a Second-Order ODE
  2. Question 2 Routh Stability — Range of Gain and an Open-Loop Unstable Plant
  3. Question 3 Steady-State Error — Recovering G ( s ) and the Effect of Gain and Damping
  4. Question 4 Root Locus of a Four-Pole Plant and its Imaginary-Axis Crossings
  5. Question 5 Lead-Compensator Design for Specified Damping and Natural Frequency
  6. Question 6 Bode Diagram of a Resonant Plant; Gain Design for a Specified Phase Margin

Start with Question 1 →

Paper format. National Exams, December 2017 — 16-Mec-A3, System Analysis and Control. Three hours, closed book; a Casio or Sharp approved calculator and semi-log graph paper are the only permitted aids. Six questions are printed; any four constitute a complete paper and all questions are of equal value (25 marks each). A table of Laplace transforms is supplied as page 5. All six questions are solved here.

Reference texts. K. Ogata, Modern Control Engineering, 5th ed. (Prentice Hall) — the source of this paper's problem style; N. S. Nise, Control Systems Engineering, 7th ed. (Wiley); R. C. Dorf and R. H. Bishop, Modern Control Systems, 13th ed. (Pearson); G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 8th ed. (Pearson).

Check: conventions used throughout. All transfer functions are written in the Laplace variable s with zero initial conditions unless a question states otherwise. “Unity feedback” means \(H(s)=1\), so the closed-loop transfer function is \(T(s)=G(s)/[1+G(s)]\) and the error signal is \(E(s)=R(s)-C(s)\). Root-locus gains are the gain \(K\) exactly as it appears in the printed \(G(s)\).