For the general first-order differential equation: \tau \frac{d y^{p}(t)}{d t}+y^{p}(t)=K x^{p}(t) Where t 5 minutes, is the time constant, and K=0.5 is the gain. Obtain the dynamic responses, yP (t),

for the following inputs: A step change of value 1.5, i.e. x (t) = 1.5u(t). An impulse, x" (t) = 1.58(t). A pulse of magnitude 1.5 and duration 1 minutes. A ramp, x(t) = 0.25 t, for a duration of 1 minutes, after which the input stays constant. Develop the Simulink model for the first-order system and simulate the responses indicated in parts (a) to (d). Report the response plots in your assignment report.