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(It doesn't necessarily have to be in pdf I just want the information shown)

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Feedback control of an inverted pendulum An inverted pendulum is a simplified model for systems such as a Segway's handle. If there is no controller in place, a small disturbance will make the pendulum fall. Design a controller for this pendulum such that we can set a reference position (p) and the closed-loop system adjusts the pendulum's position to that angle, while performing according to the design criteria mentioned below. Pendulum specs: The bar is 20 cm long and has a square cross section of 1 cm by 1 cm. The bar has a density of 2700 kg/m. The pendulum is initially at vertical position. Rotational damping coefficient at the pin: 0.002 N.m.s. g Desired input: Your closed loop should work well for any angle set as step input, but for the purpose of graphs, 0 use a unit step input. Needed closed loop features: Maximum percent overshoot no more than 20% and settling time no more than 10 seconds. Use the provided block diagram for the closed loop. + Controller Plant (Inverted pendulum) A PDF report containing the following: 1) Open-loop system's a. model (show all the work for finding the equation of motion) b. transfer function c. eigenvalues d. unit step response (graph of position versus time) 2) Your designed controller's transfer function 3) Closed-loop controlled system's a transfer function b. eigenvalues c. unit step response (graph of position versus time) 4) Your Matlab code or Simulink block. You can include these as an appendix in the report but be prepared in case you are asked to upload the code files too