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ECE4132 Control System Design - MUM S2 2025
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Given that we are choosing a sampling period of 10 seconds, approximately how many samples are
there in the 10%-90% rise time of the closed loop continuous-time system? (Round your answer to
the nearest whole number.)
A nonlinear state space model has the form\begin{bmatrix} \frac{dx_1}{dt}\\\frac{dx_2}{dt}\end{bmatrix} = \begin{bmatrix} -x_1(t) - x_1(t)x_2(t) + 2\\-x_2(t) + u(t) \end{bmatrix}Which of the following statements is true?
Consider the continuous-time system: \frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1 & -2\\2 & -1\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\\1\end{bmatrix} u(t),\qquad y(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t)Which of the following is true?
A system is described by a state space model of the form
\frac{d\mathbf{x}}{dt} = \begin{bmatrix} 1 & 1\\-1 & 1\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\\0\end{bmatrix}u(t)\qquad y(t) = \begin{bmatrix} 1 & 1\end{bmatrix}\mathbf{x}(t)The transfer function from the input
u to the output
y is: