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22-Elec-B2 Advanced Control Systems: May 2015

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

  1. Question 1 Disturbance rejection and phase margin of a cruise-control loop
  2. Question 2 State-space model, modal response, controllability and observability
  3. Question 3 Least-squares identification of a first-order discrete model
  4. Question 4 Pole placement by state feedback with reference scaling
  5. Question 5 Sampled-data loop — discrete model, Jury stability and ramp error
  6. Question 6 Feedback around a pure transport delay

Start with Question 1 →

Paper format. National Exams, May 2015, 07-Elec-B2 Advanced Control Systems — three hours, closed book. Six questions are set; the rubric states that “any four questions constitute a complete paper” and that “all questions are of equal value”, so each carries 25 marks. Tables of inverse Laplace and inverse z-transforms are appended as pages 4 and 5, and only an approved Casio or Sharp calculator is permitted. All six questions are solved here, because this set is a study resource rather than a timed sitting. The paper deliberately mixes continuous-time frequency-response work (Questions 1 and 6), state-space methods (Questions 2 and 4) and sampled-data design (Questions 3 and 5).

Reference texts. G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 7th ed., Pearson (frequency response, stability margins, steady-state error, lead compensation); K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, 2nd ed., Princeton (sensitivity functions and loops containing transport delay); K. Ogata, Modern Control Engineering, 5th ed., Pearson (state-space realisations, controllability, observability and pole placement); G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, 3rd ed., Addison-Wesley (zero-order-hold equivalents, the Jury test, discrete steady-state error); L. Ljung, System Identification: Theory for the User, 2nd ed., Prentice Hall (least-squares estimation of difference-equation models). These are the works listed by Engineers Canada and EGBC for the Elec-B2 syllabus.

Two readings matter for the marks: in Question 1 the disturbance d enters the plant-input summing junction through a minus sign while u enters through a plus, so the plant sees $u - d$; and the Question 3 table is $y = \{0,\,10,\,4,\,3,\,1.6,\,0.4,\,0.3\}$ against $u = \{1,\,0,\,0,\,0,\,0,\,0,\,0\}$.