Example E3.29: Obtain the unit-step response, unit-ramp response, and unit-impulse response of the following system using MATLAB.\\ $\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} -1 & -1.5 \\ 2 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 1.5 \\ 0 \end{bmatrix} u$ \\ $y = \begin{bmatrix} 1 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$ \\ where $u$ is the input and $y$ is the output.
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Unit-Step Response: To obtain the unit-step response, we need to find the output of the system when the input is a unit step function. In MATLAB, we can use the `step` function to do this. ```matlab num = [1 -1]; den = 1; sys = tf(num, den); step(sys); ``` This Show more…
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