ENG4042/ENG5022 CONTROL 4/M DIGITAL 2020

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Degrees of MEng, BEng, MSc and BSc in Engineering

CONTROL 4/M DIGITAL (ENG4042/ENG5022)

[OPEN BOOK EXAM] [RESULTS]

XX December 2020

Answer ALL questions in Section A and ONE question from Section B and ONE question from Section C.

SECTION A

Q1       (a)        …                                                                                                                       []

(b)       …                                                                                                                       []

Q2       (a)       The formula:

can be used for reconstructing a continuous signal r (t ) from its samples r (kT )

(i)         State  under  which  condition(s)  exact  reconstruction  is theoretically possible.          [3]

(ii)       Explain why this formula cannot be implemented in a realistic scenario, and state arealizable, approximated version of the formula.               [4]

(iii)      Explain what can be done to improve the reconstruction of the signal in quasi-real-time, and what is the potential impact on system control and signal broadcasting. Use sketches of time-signal plots as required.    [8]

(b)       Given the following system of two transfer functions in series:

Discuss  the   system’s   asymptotic   and   BIBO   stabilities,   after   zero-pole cancellations, and justify your answers      [5]

SECTION B

Q3       (a)        …                                                                                                                       []

Q4       (a)       ...                                                                                                                        []

SECTION C

Q5       Consider the following digital plant with sample time T = 0.1 s:

(a)       Design a digital PD controller that cancels the unstable pole of the plant, and find the open-loop transfer function L(z). [ K ]                  [4]

(b)       Select  the  open-loop  gain K such that the time constant of the closed-loop system is approximately [6]

(c)       Find the values of the damping and natural frequency of the closed-loop system. [0.243; 20.5733 rad/s]               [5]

(d)       Estimate the steady-state error (of the closed-loop system) in response to a unit step input. [0.803]         [5]

Q6       Consider the following low-pass filter:

(a)       Find the sampling time that corresponds to 10 times the bandwidth of the filter (frequency at 0 dB). [0. 15 s]      [4]

(b)       Now set a sample time T = 0.1 s . Calculate the Nyquist frequency.  [31.4159 rad/s]        [2]

(c)       Find the discrete  equivalent of the  filter, using the pole-zero matching rule; calculate the gain at 负c = 4.19 rad / s , and compare it to that of the continuous filter at the same frequency. [8]

(d)       Now design another discrete equivalent, using the Tustin rule with pre-warping at  frequency c = 4.19 rad / s .  Show  that  the  gain  is  now  preserved. [6]


2023-08-11