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ECE4132 Control System Design - MUM S2 2025

ECE4132 Control System Design - MUM S2 2025

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A plant with transfer function $P(s) = \frac{1}{s+1}$ P(s) = \frac{1}{s+1} is connected in unity feedback with controller C(s) that is BIBO stable and strictly proper (has strictly more poles than zeros). Which of the following statements is correct:

Bode's integral formula applies to $S(j\omega) = \frac{1}{1+P(j\omega)C(j\omega)}$ S(j\omega) = \frac{1}{1+P(j\omega)C(j\omega)} without any additional assumptions.

❌

Bode's intgeral formula does not apply in this case.

❌

Bode's integral formula applies to $S(j\omega) = \frac{1}{1+P(j\omega)C(j\omega)}$ S(j\omega) = \frac{1}{1+P(j\omega)C(j\omega)} as long as $\frac{1}{1+P(s)C(s)}$ \frac{1}{1+P(s)C(s)} is stable.

✅

View this question

Consider the following four plots (labelled Plots 1–4, for reference).

Which plot corresponds to a plot of the output of the linearised plant (position) vs time when

the input is a step reference that steps from 0 to 1 at time t = 2 seconds and the initial state

is (0 0.2 0 0.2)?

Plot 3

Plot 1

100%

Plot 2

Plot 4

View this question

Consider the following four plots (labelled Plots 1–4, for reference).

Which plot corresponds to a plot of the ouptut of the nonlinear system (position of the crane) vs time when the input is a step reference that steps from 0 to 1 at time t = 2, and the initial state is (0 0.2 0 0.2) ?

Plot 3

Plot 1

Plot 2

Plot 4

100%

View this question

Consider the following six plots (labelled Plots 1–6, for reference)