Consider the first order system: y_dot + y = u where y is the output and u is the input,
a) Plot the frequency response curves in Matlab using the analytic functions for the amplitude ratio and phase as a function of w.
b) Plot the frequency response curves in Matlab using bode command and compare the results with part a
c) Derive the total response due to u = sin (10 t)
d) Plot the total response as a function of time.
e) Determine the corner frequency using bode plot. What is the interpretation of this corner frequency?
f) Describe the difference between the total response and the frequency response.
g) Draw the transfer function of the system in a form of block diagrams using a unity feedback configuration.
h) Determine the unit step, unit impulse and unit ramp response of the system analytically and plot the results in Matlab.
i) Plot the unit step, unit ramp and also response due to u = sin (10 t) using SIMULINK.
j) Give an example of a physical system (except an electrical circuit) that has a similar 1st order dynamics as above.