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ECE4132 Control System Design - MUM S2 2025

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Which of the following statements is true about the state feedback controller using the design

parameters from Q6 and Q7:

The state feedback controller can stabilise the nonlinear system at the equilibrium point

x = (0, 0, 0, 0)

if the initial angular position is less than 1. The state feedback controller can

stabilise the linearised system at the equilibrium point

x = (0, 0, 0, 0)

for any initial value of

the angular position.

The state feedback controller can stabilise the nonlinear system at the equilibrium point x = (0, 0, 0, 0) if the initial angular position is less than 0.5. The state feedback controller can stabilise the linearised system at the equilibrium point x = (0, 0, 0, 0) for any initial value of the angular position.

✅

The state feedback controller can stabilise the nonlinear system at the equilibrium point x = (0, 0, 0, 0) if the initial angular position is less than 1. The state feedback controller can stabilise the linearised system at the equilibrium point x = (0, 0, 0, 0) only if the initial value of the angular position is less than 0.5.

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The following plot shows how the four states of the system evolve over time, but the states are

labelled A, B, C, D. Match the labels A, B, C, D, to the state variables (position, angular position,

linear velocity, and angular velocity).

Image failed to load

State C

State B

State A

State D

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Which of the following statements is correct about the system response?

The controller can move the cart from position 0 to position 1, keep the pendulum balanced,

and do so with a 2% settling time that is at most half of what was found in Q14.

The controller does not moves the cart from position 0 to position 1 while keeping the pendulum balanced.

✅

The controller moves the cart from position 0 to position 1, keeps the pendulum balanced, but does not do so with a 2% settling time that is at most half of what was found in Q14.

❌

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