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22-Elec-B2 Advanced Control Systems: December 2014

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

  1. Question 1 Proportional-integral design for a double-lag plant
  2. Question 2 State-space model and pole placement for a satellite attitude loop
  3. Question 3 Least-squares identification of a first-order discrete model
  4. Question 4 Transfer functions from step and frequency-response data
  5. Question 5 Sampled-data loop — closed-loop pulse transfer function, root locus and inter-sample response
  6. Question 6 Nyquist analysis and margins for a delayed integrator

Start with Question 1 →

Paper format. National Exams, December 2014, 07-Elec-B2 Advanced Control Systems — three hours, closed book. The paper sets six questions; 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 a Casio or Sharp approved calculator is permitted. All six questions are solved here, because this set is a study resource rather than a timed sitting.

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, PI/PID design); K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, 2nd ed., Princeton (sensitivity functions, loops with transport delay, non-minimum-phase limitations); K. Ogata, Modern Control Engineering, 5th ed., Pearson (state-space realisations, controllability and observability, 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 root loci); 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.

The block diagrams of Questions 1 and 6 both show the disturbance d entering the output summing junction through a minus sign while the plant output enters through a plus, so in both cases $y = P(s)u - d$. The Question 4(a) chart is read from the printed figure: the response holds at zero until $t = 2\text{ s}$, drops instantaneously to $-2$, and rises to a final value of $6$, with a time constant read as $\tau = 2\text{ s}$.