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22-Elec-B2 Advanced Control Systems: December 2013

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

  1. Question 1 Gain limit, phase margin and steady-state tracking of a non-minimum-phase plant
  2. Question 2 State-space realisation, controllability, observability and the sampled-data poles
  3. Question 3 Pole placement by state feedback with unity DC gain
  4. Question 4 Deadbeat design of a digital PI controller for an integrating plant
  5. Question 5 Identification of a first-order plant with transport delay from step data
  6. Question 6 Proportional design to a specified gain margin for a plant with transport delay

Start with Question 1 →

Paper format. National Examinations, 07-Elec-B2 Advanced Control Systems, December 2013 — 3 hours, closed book. Six questions; the rubric states that “any four questions constitute a complete paper” and that “all questions are of equal value”, so each is worth 25 marks. Tables of Laplace and z-transforms are appended to the paper. Only a Casio FX-991 or Sharp EL-540 calculator is permitted.

Reference texts. G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 7th ed., Pearson (Routh–Hurwitz, stability margins, steady-state error, frequency response); K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, 2nd ed., Princeton (sensitivity function, 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., Ellis-Kagle (zero-order-hold equivalents, deadbeat design, discrete identification). These are the works listed by Engineers Canada / EGBC for the Elec-B2 syllabus.

Scope of this solution. Although the paper is marked on four questions, all six are worked here so that the set serves as a complete study resource. Every boxed number is recomputed from the question’s own data for this paper.

Check: two printing defects in the source paper. In Question 3 the leading entry of the second row of the system matrix is missing from the print — the row reads “ 0  −1” with the first column blank — and the equation is typeset as “$\dots x + B = [0\ 1\ 1]^{\mathsf T}u$” rather than $\dot x = Ax + Bu$. Reading the column alignment against rows 1 and 3, the missing entry is $a_{21}=0$; that reading is adopted throughout and makes the system controllable, so the design asked for is well posed. In Question 4(b) the paper asks for “$T(z)$ that relates $X(z)$ to $R(z)$”, but no signal $X$ is defined anywhere in the question or its figure; $X(z)$ is read as $Y(z)$.