1. Use MATLAB to solve and plot the step response of the differential equation shown below:
$$3\dot{x} + 2x = f(t)$$
Use a time increment of 0.01 seconds, and a time interval of 10 seconds for the solution. Plot
the response (on the same graph) for a unit step force input and for a force step input of
magnitude of 2. Provide the final steady state value for each of these cases. Are the steady
state values proportional to the magnitude of the step input? Provide the code you used, your
answers to the above questions with justification, and a properly labeled plot (i.e. a plot with
axis labels, title, and legend). Add your name to the plot using the gtext() function. Use help on
step() function. Note that you need to have the control systems toolbox installed in your copy of
MATLAB to do this assignment. Also, to have two step responses shown on the same plot, you
can use the following command:
step (sys1, 'r',sys2, 'b',t);
Where sys1 and sys2 are the names of the transfer function models for system 1 and system 2,
respectively, t is the time vector, and r and b are colors for the plots. To have a step magnitude
of 2 for system2, the numerator of the transfer function for system2 should be 2 instead of 1.
2. Use MATLAB to solve and plot the step response of the differential equation shown below:
$$\ddot{x} + 3\dot{x} + 5x = f(t)$$
Use a time increment of 0.02 seconds, and a time interval of 8 seconds for the solution. Plot the
response (on the same graph) for a unit a step input and for a step input of magnitude of 2.
Provide the peak and steady state values for each of these cases (use the data cursor in MATLAB
to get these value). Are these values proportional to the magnitude of the step input? Provide
the code you used, your answers to the above questions with justification, and a properly
labeled plot (i.e. a plot with axis labels, title and legend). Add your name to the plot using the
gtext() function.
