Every 5 seconds the robot encounters an ever increasing pulsed forced and must stabilize to keep the pendulum upright. You must do the following. 1. Create the equations of motion for this system. 2. Convert these equations of motion to a transfer function and model this system in Simulink (Remember the goal is 0 not a step!). You will need to include a disturbance force to test you model. 3. Using the model, you designed in Simulink, attempt to tune the PID for this system. 4. Using the Robot Benchmark tool test your simulated PID. As a note, forces that are not known to you are present in this model. You may need to iterate on your gains to obtain satisfactory results. 5. Prepare a short (2 pages without appendix) report detailing both each of these steps as well as the values for your PI and D controller (and the response in both simulation and in the benchmark tool)