Question 5.5.1: Simulink Model of a Rocket-Propelled Sled A rocket-propelled...

a. There are several ways to create the input function θ = (π/100)t². Here we note that $\ddot{θ} = \pi/50  rad/s$ and that
$\dot{θ} = \int^{t}_{0}  {\ddot{θ}   dt} = \frac{\pi}{50}  t$

and
$θ = \int^{t}_{0}  {\dot{θ} d t} = \frac{\pi}{100} t^{2}$
Thus we can create θ(t) by integrating the constant $\ddot{θ} = \pi/50$ twice. The simulation diagram is shown in Figure 5.5.2. This diagram is used to create the corresponding Simulink model shown in Figure 5.5.3.
There are two new blocks in this model. The Constant block is in the Sources library. After placing it, double click on it and type pi/50 in its Constant Value window.
The Trigonometric function block is in the Math Operations library. After  placing it, double click on it and select cos in its Function window.
Set the Stop Time to 10, run the simulation, and examine the results in the Scope.
b. Modify the model in Figure 5.5.3 as follows to obtain the model shown in Figure 5.5.4.
We use the Saturation block in the Discontinuities library to limit the range of θ to 60π/180 rad. After placing the block as shown in Figure 5.5.4, double-click on it and type 60*pi/180 in its Upper Limit window. Then type 0 or any negative value in its Lower Limit window.
Enter and connect the remaining elements as shown, and run the simulation. The upper Constant block and Integrator block are used to generate the solution when the engine angle is θ = 0, as a check on our results. [The equation of motion for θ = 0 is $\dot{v} = 80/9$, which gives v(t) = 80t/9.]
If you prefer, you can substitute a To Workspace block for the Scope. Then you can plot the results in MATLAB. The resulting plot is shown in Figure 5.5.5.